From 03015db0239ce88e17d256b3bd691a7598e48b5e Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 4 Dec 2024 02:01:33 +0000 Subject: [PATCH] build based on 733e14f --- previews/PR27/.documenter-siteinfo.json | 1 + previews/PR27/assets/documenter.js | 1082 +++++++++++++++++ previews/PR27/assets/style.css | 5 + .../PR27/assets/themes/catppuccin-frappe.css | 1 + .../PR27/assets/themes/catppuccin-latte.css | 1 + .../assets/themes/catppuccin-macchiato.css | 1 + .../PR27/assets/themes/catppuccin-mocha.css | 1 + .../PR27/assets/themes/documenter-dark.css | 7 + .../PR27/assets/themes/documenter-light.css | 9 + previews/PR27/assets/themeswap.js | 84 ++ previews/PR27/assets/warner.js | 52 + previews/PR27/charged_particle_3d/index.html | 24 + previews/PR27/guiding_center_4d/index.html | 43 + previews/PR27/index.html | 2 + previews/PR27/initial_conditions.png | Bin 0 -> 212238 bytes previews/PR27/initialization/index.html | 17 + previews/PR27/normalization/index.html | 25 + previews/PR27/objects.inv | Bin 0 -> 981 bytes previews/PR27/pauli_particle_3d/index.html | 2 + previews/PR27/search_index.js | 3 + previews/PR27/siteinfo.js | 1 + 21 files changed, 1361 insertions(+) create mode 100644 previews/PR27/.documenter-siteinfo.json create mode 100644 previews/PR27/assets/documenter.js create mode 100644 previews/PR27/assets/style.css create mode 100644 previews/PR27/assets/themes/catppuccin-frappe.css create mode 100644 previews/PR27/assets/themes/catppuccin-latte.css create mode 100644 previews/PR27/assets/themes/catppuccin-macchiato.css create mode 100644 previews/PR27/assets/themes/catppuccin-mocha.css create mode 100644 previews/PR27/assets/themes/documenter-dark.css create mode 100644 previews/PR27/assets/themes/documenter-light.css create mode 100644 previews/PR27/assets/themeswap.js create mode 100644 previews/PR27/assets/warner.js create mode 100644 previews/PR27/charged_particle_3d/index.html create mode 100644 previews/PR27/guiding_center_4d/index.html create mode 100644 previews/PR27/index.html create mode 100644 previews/PR27/initial_conditions.png create mode 100644 previews/PR27/initialization/index.html create mode 100644 previews/PR27/normalization/index.html create mode 100644 previews/PR27/objects.inv create mode 100644 previews/PR27/pauli_particle_3d/index.html create mode 100644 previews/PR27/search_index.js create mode 100644 previews/PR27/siteinfo.js diff --git a/previews/PR27/.documenter-siteinfo.json b/previews/PR27/.documenter-siteinfo.json new file mode 100644 index 0000000..8462b0d --- /dev/null +++ b/previews/PR27/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-04T02:01:28","documenter_version":"1.8.0"}} \ No newline at end of file diff --git a/previews/PR27/assets/documenter.js b/previews/PR27/assets/documenter.js new file mode 100644 index 0000000..7d68cd8 --- /dev/null +++ b/previews/PR27/assets/documenter.js @@ -0,0 +1,1082 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on( + "click", + ".docstring .docstring-article-toggle-button", + function () { + let articleToggleTitle = "Expand docstring"; + const parent = $(this).parent(); + + debounce(() => { + if (parent.siblings("section").is(":visible")) { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +/////// SEARCH MAIN /////// + +function runSearchMainCode() { + // `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! + const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), + ]; + const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; + const worker_blob = new Blob([worker_str], { type: "text/javascript" }); + const worker = new Worker(URL.createObjectURL(worker_blob)); + + // Whether the worker is currently handling a search. This is a boolean + // as the worker only ever handles 1 or 0 searches at a time. + var worker_is_running = false; + + // The last search text that was sent to the worker. This is used to determine + // if the worker should be launched again when it reports back results. + var last_search_text = ""; + + // The results of the last search. This, in combination with the state of the filters + // in the DOM, is used compute the results to display on calls to update_search. + var unfiltered_results = []; + + // Which filter is currently selected + var selected_filter = ""; + + $(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } + }); + + function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); + } + + worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); + }; + + $(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); + }); + + /** + * Make/Update the search component + */ + function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } + } + + /** + * Make the modal filter html + * + * @returns string + */ + function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; + } +} + +function waitUntilSearchIndexAvailable() { + // It is possible that the documenter.js script runs before the page + // has finished loading and documenterSearchIndex gets defined. + // So we need to wait until the search index actually loads before setting + // up all the search-related stuff. + if (typeof documenterSearchIndex !== "undefined") { + runSearchMainCode(); + } else { + console.warn("Search Index not available, waiting"); + setTimeout(waitUntilSearchIndexAvailable, 1000); + } +} + +// The actual entry point to the search code +waitUntilSearchIndexAvailable(); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` + + `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/previews/PR27/assets/style.css b/previews/PR27/assets/style.css new file mode 100644 index 0000000..f9bc4d6 --- /dev/null +++ b/previews/PR27/assets/style.css @@ -0,0 +1,5 @@ +img { + display: block; + 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.button.is-primary.is-light.is-hovered,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-primary.is-light:active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-frappe .button.is-primary.is-light.is-active,html.theme--catppuccin-frappe .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link{background-color:#8caaee;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:hover,html.theme--catppuccin-frappe .button.is-link.is-hovered{background-color:#81a2ec;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-link:focus,html.theme--catppuccin-frappe 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.button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-outlined:focus,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-focused{background-color:#8caaee;border-color:#8caaee;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #8caaee #8caaee !important}html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe 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.button.is-link.is-light.is-hovered{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:active,html.theme--catppuccin-frappe .button.is-link.is-light.is-active{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:hover,html.theme--catppuccin-frappe .button.is-info.is-hovered{background-color:#78c4b9;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus,html.theme--catppuccin-frappe .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus:not(:active),html.theme--catppuccin-frappe .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe .button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe 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.button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe 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.button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-focused{background-color:#e5c890;border-color:#e5c890;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:hover,html.theme--catppuccin-frappe .button.is-danger.is-hovered{background-color:#e57779;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus,html.theme--catppuccin-frappe .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger:focus:not(:active),html.theme--catppuccin-frappe .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(231,130,132,0.25)}html.theme--catppuccin-frappe .button.is-danger:active,html.theme--catppuccin-frappe .button.is-danger.is-active{background-color:#e36d6f;border-color:transparent;color:#fff}html.theme--catppuccin-frappe .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger{background-color:#e78284;border-color:#e78284;box-shadow:none}html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-frappe .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text 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a.navbar-item:focus,html.theme--catppuccin-frappe a.navbar-item:focus-within,html.theme--catppuccin-frappe a.navbar-item:hover,html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link:focus,html.theme--catppuccin-frappe .navbar-link:focus-within,html.theme--catppuccin-frappe .navbar-link:hover,html.theme--catppuccin-frappe .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#8caaee}html.theme--catppuccin-frappe .navbar-item{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .navbar-item img{max-height:1.75rem}html.theme--catppuccin-frappe .navbar-item.has-dropdown{padding:0}html.theme--catppuccin-frappe .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--catppuccin-frappe .navbar-item.is-tab:focus,html.theme--catppuccin-frappe .navbar-item.is-tab:hover{background-color:rgba(0,0,0,0);border-bottom-color:#8caaee}html.theme--catppuccin-frappe .navbar-item.is-tab.is-active{background-color:rgba(0,0,0,0);border-bottom-color:#8caaee;border-bottom-style:solid;border-bottom-width:3px;color:#8caaee;padding-bottom:calc(0.5rem - 3px)}html.theme--catppuccin-frappe .navbar-content{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .navbar-link:not(.is-arrowless){padding-right:2.5em}html.theme--catppuccin-frappe .navbar-link:not(.is-arrowless)::after{border-color:#fff;margin-top:-0.375em;right:1.125em}html.theme--catppuccin-frappe .navbar-dropdown{font-size:0.875rem;padding-bottom:0.5rem;padding-top:0.5rem}html.theme--catppuccin-frappe .navbar-dropdown .navbar-item{padding-left:1.5rem;padding-right:1.5rem}html.theme--catppuccin-frappe .navbar-divider{background-color:rgba(0,0,0,0.2);border:none;display:none;height:2px;margin:0.5rem 0}@media screen and (max-width: 1055px){html.theme--catppuccin-frappe 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a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#838ba7}html.theme--catppuccin-frappe .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#8caaee}.navbar.is-spaced html.theme--catppuccin-frappe .navbar-dropdown,html.theme--catppuccin-frappe .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--catppuccin-frappe .navbar-dropdown.is-right{left:auto;right:0}html.theme--catppuccin-frappe .navbar-divider{display:block}html.theme--catppuccin-frappe .navbar>.container .navbar-brand,html.theme--catppuccin-frappe .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--catppuccin-frappe .navbar>.container .navbar-menu,html.theme--catppuccin-frappe .container>.navbar 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body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--catppuccin-frappe a.navbar-item.is-active,html.theme--catppuccin-frappe .navbar-link.is-active{color:#8caaee}html.theme--catppuccin-frappe a.navbar-item.is-active:not(:focus):not(:hover),html.theme--catppuccin-frappe .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--catppuccin-frappe .navbar-item.has-dropdown:focus .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown:hover .navbar-link,html.theme--catppuccin-frappe .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--catppuccin-frappe .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--catppuccin-frappe .pagination{font-size:1rem;margin:-.25rem}html.theme--catppuccin-frappe .pagination.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--catppuccin-frappe .pagination.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .pagination.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .pagination.is-rounded .pagination-previous,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--catppuccin-frappe .pagination.is-rounded .pagination-next,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:9999px}html.theme--catppuccin-frappe .pagination.is-rounded .pagination-link,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:9999px}html.theme--catppuccin-frappe .pagination,html.theme--catppuccin-frappe .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link{border-color:#626880;color:#8caaee;min-width:2.5em}html.theme--catppuccin-frappe .pagination-previous:hover,html.theme--catppuccin-frappe .pagination-next:hover,html.theme--catppuccin-frappe .pagination-link:hover{border-color:#737994;color:#99d1db}html.theme--catppuccin-frappe .pagination-previous:focus,html.theme--catppuccin-frappe .pagination-next:focus,html.theme--catppuccin-frappe .pagination-link:focus{border-color:#737994}html.theme--catppuccin-frappe .pagination-previous:active,html.theme--catppuccin-frappe .pagination-next:active,html.theme--catppuccin-frappe .pagination-link:active{box-shadow:inset 0 1px 2px 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768px){html.theme--catppuccin-frappe .pagination{flex-wrap:wrap}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .pagination-list li{flex-grow:1;flex-shrink:1}}@media screen and (min-width: 769px),print{html.theme--catppuccin-frappe .pagination-list{flex-grow:1;flex-shrink:1;justify-content:flex-start;order:1}html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis{margin-bottom:0;margin-top:0}html.theme--catppuccin-frappe .pagination-previous{order:2}html.theme--catppuccin-frappe .pagination-next{order:3}html.theme--catppuccin-frappe .pagination{justify-content:space-between;margin-bottom:0;margin-top:0}html.theme--catppuccin-frappe .pagination.is-centered .pagination-previous{order:1}html.theme--catppuccin-frappe .pagination.is-centered 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a.is-active{border-bottom-color:#0a0a0a}html.theme--catppuccin-frappe .panel.is-black .panel-block.is-active .panel-icon{color:#0a0a0a}html.theme--catppuccin-frappe .panel.is-light .panel-heading{background-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .panel.is-light .panel-tabs a.is-active{border-bottom-color:#f5f5f5}html.theme--catppuccin-frappe .panel.is-light .panel-block.is-active .panel-icon{color:#f5f5f5}html.theme--catppuccin-frappe .panel.is-dark .panel-heading,html.theme--catppuccin-frappe .content kbd.panel .panel-heading{background-color:#414559;color:#fff}html.theme--catppuccin-frappe .panel.is-dark .panel-tabs a.is-active,html.theme--catppuccin-frappe .content kbd.panel .panel-tabs a.is-active{border-bottom-color:#414559}html.theme--catppuccin-frappe .panel.is-dark .panel-block.is-active .panel-icon,html.theme--catppuccin-frappe .content kbd.panel .panel-block.is-active .panel-icon{color:#414559}html.theme--catppuccin-frappe .panel.is-primary 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.button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus,html.theme--catppuccin-latte .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black:focus:not(:active),html.theme--catppuccin-latte .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-latte .button.is-black:active,html.theme--catppuccin-latte .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:hover,html.theme--catppuccin-latte .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus,html.theme--catppuccin-latte .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light:focus:not(:active),html.theme--catppuccin-latte .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-latte .button.is-light:active,html.theme--catppuccin-latte .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-latte 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.button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark,html.theme--catppuccin-latte .content kbd.button{background-color:#ccd0da;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:hover,html.theme--catppuccin-latte .content kbd.button:hover,html.theme--catppuccin-latte .button.is-dark.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-hovered{background-color:#c5c9d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark:focus,html.theme--catppuccin-latte .content kbd.button:focus,html.theme--catppuccin-latte .button.is-dark.is-focused,html.theme--catppuccin-latte .content kbd.button.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte 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kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-focused{background-color:#ccd0da;border-color:#ccd0da;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.docstring>section>a.button.is-active.docs-sourcelink{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary[disabled],html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:#1e66f5;box-shadow:none}html.theme--catppuccin-latte .button.is-primary.is-inverted,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-primary.is-inverted:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-hovered,html.theme--catppuccin-latte 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.button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table td,html.theme--catppuccin-latte .content table th{border:1px solid #acb0be;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-latte .content table th{color:#41445a}html.theme--catppuccin-latte .content table th:not([align]){text-align:inherit}html.theme--catppuccin-latte .content table thead td,html.theme--catppuccin-latte .content table thead th{border-width:0 0 2px;color:#41445a}html.theme--catppuccin-latte .content table tfoot td,html.theme--catppuccin-latte .content table tfoot th{border-width:2px 0 0;color:#41445a}html.theme--catppuccin-latte .content table tbody tr:last-child td,html.theme--catppuccin-latte .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-latte .content .tabs li+li{margin-top:0}html.theme--catppuccin-latte .content.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-latte 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.file.is-boxed .file-name{border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-boxed .file-icon{height:1.5em;width:1.5em}html.theme--catppuccin-latte .file.is-boxed .file-icon .fa{font-size:21px}html.theme--catppuccin-latte .file.is-boxed.is-small .file-icon .fa,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-boxed .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .file.is-boxed.is-medium .file-icon .fa{font-size:28px}html.theme--catppuccin-latte .file.is-boxed.is-large .file-icon .fa{font-size:35px}html.theme--catppuccin-latte .file.is-boxed.has-name .file-cta{border-radius:.4em .4em 0 0}html.theme--catppuccin-latte .file.is-boxed.has-name .file-name{border-radius:0 0 .4em .4em;border-width:0 1px 1px}html.theme--catppuccin-latte .file.is-centered{justify-content:center}html.theme--catppuccin-latte .file.is-fullwidth .file-label{width:100%}html.theme--catppuccin-latte .file.is-fullwidth .file-name{flex-grow:1;max-width:none}html.theme--catppuccin-latte .file.is-right{justify-content:flex-end}html.theme--catppuccin-latte .file.is-right .file-cta{border-radius:0 .4em .4em 0}html.theme--catppuccin-latte .file.is-right .file-name{border-radius:.4em 0 0 .4em;border-width:1px 0 1px 1px;order:-1}html.theme--catppuccin-latte .file-label{align-items:stretch;display:flex;cursor:pointer;justify-content:flex-start;overflow:hidden;position:relative}html.theme--catppuccin-latte .file-label:hover .file-cta{background-color:#c5c9d5;color:#41445a}html.theme--catppuccin-latte .file-label:hover .file-name{border-color:#a5a9b8}html.theme--catppuccin-latte .file-label:active .file-cta{background-color:#bdc2cf;color:#41445a}html.theme--catppuccin-latte .file-label:active .file-name{border-color:#9ea2b3}html.theme--catppuccin-latte .file-input{height:100%;left:0;opacity:0;outline:none;position:absolute;top:0;width:100%}html.theme--catppuccin-latte .file-cta,html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-radius:.4em;font-size:1em;padding-left:1em;padding-right:1em;white-space:nowrap}html.theme--catppuccin-latte .file-cta{background-color:#ccd0da;color:#4c4f69}html.theme--catppuccin-latte .file-name{border-color:#acb0be;border-style:solid;border-width:1px 1px 1px 0;display:block;max-width:16em;overflow:hidden;text-align:inherit;text-overflow:ellipsis}html.theme--catppuccin-latte .file-icon{align-items:center;display:flex;height:1em;justify-content:center;margin-right:.5em;width:1em}html.theme--catppuccin-latte .file-icon .fa{font-size:14px}html.theme--catppuccin-latte .label{color:#41445a;display:block;font-size:1rem;font-weight:700}html.theme--catppuccin-latte .label:not(:last-child){margin-bottom:0.5em}html.theme--catppuccin-latte .label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.label{font-size:.75rem}html.theme--catppuccin-latte .label.is-medium{font-size:1.25rem}html.theme--catppuccin-latte 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.field.has-addons{display:flex;justify-content:flex-start}html.theme--catppuccin-latte .field.has-addons .control:not(:last-child){margin-right:-1px}html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .button,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:not(:first-child):not(:last-child) .select select{border-radius:0}html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:first-child:not(:only-child) .select select{border-bottom-right-radius:0;border-top-right-radius:0}html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .button,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search>input,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search>input,html.theme--catppuccin-latte .field.has-addons .control:last-child:not(:only-child) .select select{border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-hovered:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-hovered:not([disabled]){z-index:2}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]),html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]){z-index:3}html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .button:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .button.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control #documenter .docs-sidebar form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte #documenter .docs-sidebar .field.has-addons .control form.docs-search>input.is-active:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):focus:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-focused:not([disabled]):hover,html.theme--catppuccin-latte .field.has-addons .control .select select:not([disabled]):active:hover,html.theme--catppuccin-latte .field.has-addons .control .select select.is-active:not([disabled]):hover{z-index:4}html.theme--catppuccin-latte .field.has-addons .control.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .field.has-addons.has-addons-centered{justify-content:center}html.theme--catppuccin-latte .field.has-addons.has-addons-right{justify-content:flex-end}html.theme--catppuccin-latte .field.has-addons.has-addons-fullwidth 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.field.is-grouped.is-grouped-multiline:not(:last-child){margin-bottom:0}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field.is-horizontal{display:flex}}html.theme--catppuccin-latte .field-label .label{font-size:inherit}@media screen and (max-width: 768px){html.theme--catppuccin-latte .field-label{margin-bottom:0.5rem}}@media screen and (min-width: 769px),print{html.theme--catppuccin-latte .field-label{flex-basis:0;flex-grow:1;flex-shrink:0;margin-right:1.5rem;text-align:right}html.theme--catppuccin-latte .field-label.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.field-label{font-size:.75rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-normal{padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-medium{font-size:1.25rem;padding-top:0.375em}html.theme--catppuccin-latte .field-label.is-large{font-size:1.5rem;padding-top:0.375em}}html.theme--catppuccin-latte .field-body .field 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form.docs-search>input~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-small~.icon{font-size:.75rem}html.theme--catppuccin-latte .control.has-icons-left .input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-left .select.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right .input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input.is-medium~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-medium~.icon{font-size:1.25rem}html.theme--catppuccin-latte .control.has-icons-left .input.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-left #documenter .docs-sidebar form.docs-search>input.is-large~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-left form.docs-search>input.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-left .select.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-right .input.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-right #documenter .docs-sidebar form.docs-search>input.is-large~.icon,html.theme--catppuccin-latte #documenter .docs-sidebar .control.has-icons-right form.docs-search>input.is-large~.icon,html.theme--catppuccin-latte .control.has-icons-right .select.is-large~.icon{font-size:1.5rem}html.theme--catppuccin-latte .control.has-icons-left .icon,html.theme--catppuccin-latte .control.has-icons-right .icon{color:#acb0be;height:2.5em;pointer-events:none;position:absolute;top:0;width:2.5em;z-index:4}html.theme--catppuccin-latte 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.pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link,html.theme--catppuccin-latte .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--catppuccin-latte .pagination-previous,html.theme--catppuccin-latte .pagination-next,html.theme--catppuccin-latte .pagination-link{border-color:#acb0be;color:#1e66f5;min-width:2.5em}html.theme--catppuccin-latte .pagination-previous:hover,html.theme--catppuccin-latte .pagination-next:hover,html.theme--catppuccin-latte .pagination-link:hover{border-color:#9ca0b0;color:#04a5e5}html.theme--catppuccin-latte .pagination-previous:focus,html.theme--catppuccin-latte .pagination-next:focus,html.theme--catppuccin-latte .pagination-link:focus{border-color:#9ca0b0}html.theme--catppuccin-latte 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kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content 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.button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small 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.container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-macchiato .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-macchiato .content li+li{margin-top:0.25em}html.theme--catppuccin-macchiato .content p:not(:last-child),html.theme--catppuccin-macchiato .content dl:not(:last-child),html.theme--catppuccin-macchiato .content ol:not(:last-child),html.theme--catppuccin-macchiato .content ul:not(:last-child),html.theme--catppuccin-macchiato .content blockquote:not(:last-child),html.theme--catppuccin-macchiato .content pre:not(:last-child),html.theme--catppuccin-macchiato .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-macchiato .content h1,html.theme--catppuccin-macchiato .content h2,html.theme--catppuccin-macchiato .content h3,html.theme--catppuccin-macchiato .content h4,html.theme--catppuccin-macchiato .content h5,html.theme--catppuccin-macchiato .content 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ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-macchiato .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-macchiato .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-macchiato .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-macchiato .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-macchiato .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-macchiato .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-macchiato .content ul ul ul{list-style-type:square}html.theme--catppuccin-macchiato .content dd{margin-left:2em}html.theme--catppuccin-macchiato .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-macchiato 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form.docs-search>input.is-active{box-shadow:0 0 0 0.125em rgba(255,255,255,0.25)}html.theme--catppuccin-macchiato .is-black.textarea,html.theme--catppuccin-macchiato .is-black.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black{border-color:#0a0a0a}html.theme--catppuccin-macchiato .is-black.textarea:focus,html.theme--catppuccin-macchiato .is-black.input:focus,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:focus,html.theme--catppuccin-macchiato .is-black.is-focused.textarea,html.theme--catppuccin-macchiato .is-black.is-focused.input,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-focused,html.theme--catppuccin-macchiato .is-black.textarea:active,html.theme--catppuccin-macchiato .is-black.input:active,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.is-black:active,html.theme--catppuccin-macchiato 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus:not(:active),html.theme--catppuccin-mocha .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(148,226,213,0.25)}html.theme--catppuccin-mocha .button.is-info:active,html.theme--catppuccin-mocha .button.is-info.is-active{background-color:#80ddcd;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:#94e2d5;box-shadow:none}html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons .button:focus:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-mocha .buttons.has-addons .button:active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-mocha .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-mocha .buttons.is-centered{justify-content:center}html.theme--catppuccin-mocha .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-mocha .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-mocha .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-mocha .button.is-responsive.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-mocha .button.is-responsive,html.theme--catppuccin-mocha .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-mocha .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-mocha .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-mocha .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-mocha .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-mocha .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-mocha .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-mocha .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-mocha .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-mocha .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-mocha .content li+li{margin-top:0.25em}html.theme--catppuccin-mocha .content p:not(:last-child),html.theme--catppuccin-mocha .content dl:not(:last-child),html.theme--catppuccin-mocha .content ol:not(:last-child),html.theme--catppuccin-mocha .content ul:not(:last-child),html.theme--catppuccin-mocha .content blockquote:not(:last-child),html.theme--catppuccin-mocha .content pre:not(:last-child),html.theme--catppuccin-mocha .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-mocha .content h1,html.theme--catppuccin-mocha .content h2,html.theme--catppuccin-mocha .content h3,html.theme--catppuccin-mocha .content h4,html.theme--catppuccin-mocha .content h5,html.theme--catppuccin-mocha .content h6{color:#cdd6f4;font-weight:600;line-height:1.125}html.theme--catppuccin-mocha .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-mocha .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-mocha .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-mocha .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-mocha .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-mocha .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-mocha .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-mocha .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-mocha .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-mocha .content blockquote{background-color:#181825;border-left:5px solid #585b70;padding:1.25em 1.5em}html.theme--catppuccin-mocha .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-mocha .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-mocha .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-mocha .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-mocha .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-mocha .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-mocha .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-mocha .content ul ul ul{list-style-type:square}html.theme--catppuccin-mocha .content dd{margin-left:2em}html.theme--catppuccin-mocha .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-mocha .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-mocha .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-mocha .content figure img{display:inline-block}html.theme--catppuccin-mocha .content figure figcaption{font-style:italic}html.theme--catppuccin-mocha .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-mocha .content sup,html.theme--catppuccin-mocha .content sub{font-size:75%}html.theme--catppuccin-mocha .content table{width:100%}html.theme--catppuccin-mocha .content table td,html.theme--catppuccin-mocha .content table th{border:1px solid #585b70;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-mocha .content table th{color:#b8c5ef}html.theme--catppuccin-mocha .content table th:not([align]){text-align:inherit}html.theme--catppuccin-mocha .content table thead td,html.theme--catppuccin-mocha .content table thead th{border-width:0 0 2px;color:#b8c5ef}html.theme--catppuccin-mocha .content table tfoot td,html.theme--catppuccin-mocha .content table tfoot th{border-width:2px 0 0;color:#b8c5ef}html.theme--catppuccin-mocha .content table tbody tr:last-child td,html.theme--catppuccin-mocha .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-mocha .content .tabs li+li{margin-top:0}html.theme--catppuccin-mocha .content.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-mocha .content.is-normal{font-size:1rem}html.theme--catppuccin-mocha .content.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .content.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-mocha .icon.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-mocha .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-mocha .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-mocha .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-mocha .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-mocha .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-mocha .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-mocha div.icon-text{display:flex}html.theme--catppuccin-mocha .image,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-mocha .image img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-mocha .image img.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-mocha .image.is-fullwidth,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-mocha .image.is-square img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-mocha .image.is-square .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-mocha .image.is-1by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar 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.has-ratio,html.theme--catppuccin-mocha .image.is-5by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-mocha .image.is-5by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-mocha .image.is-16by9 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-mocha .image.is-16by9 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-mocha .image.is-2by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-mocha .image.is-2by1 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-mocha .image.is-3by1 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-mocha 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img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-mocha .image.is-3by5 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-mocha .image.is-9by16 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-mocha .image.is-9by16 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-mocha .image.is-1by2 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-mocha .image.is-1by2 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-mocha .image.is-1by3 img,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-mocha .image.is-1by3 .has-ratio,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-mocha .image.is-square,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-mocha .image.is-1by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-mocha .image.is-5by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-mocha .image.is-4by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-mocha .image.is-3by2,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-mocha .image.is-5by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-mocha .image.is-16by9,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-mocha .image.is-2by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-mocha .image.is-3by1,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-mocha .image.is-4by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-mocha .image.is-3by4,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--catppuccin-mocha .image.is-2by3,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--catppuccin-mocha .image.is-3by5,html.theme--catppuccin-mocha #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--catppuccin-mocha .image.is-9by16,html.theme--catppuccin-mocha #documenter 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark 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.button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark 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h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/previews/PR27/charged_particle_3d/index.html b/previews/PR27/charged_particle_3d/index.html new file mode 100644 index 0000000..a112c28 --- /dev/null +++ b/previews/PR27/charged_particle_3d/index.html @@ -0,0 +1,24 @@ + +Charged Particles in 3D · ChargedParticleDynamics.jl
GitHub

Charged Particles in 3D

The motion of charged particles in an electromagnetic field $(E,B)$ is governed by the Lorentz force,

\[\ddot{x} (t) = \frac{e}{m} \big[ E(x(t)) + \dot{x} (t) \times B(x(t)) \big] ,\]

where $m$ and $e$ denote the particle's mass and charge, respectively.

Canonical Formulation

The canonical form of the equations can be obtained from the Hamiltonian

\[H (x,p) = \frac{1}{2m} (p-A(x))^2 + e \phi(x),\]

as

\[\begin{aligned} +\dot{x} (t) &= \frac{\partial H}{\partial p} (x(t),p(t)) = \frac{1}{m} (p(t) - A(x(t))), \\ +\dot{p} (t) &= - \frac{\partial H}{\partial x} (x(t),p(t)) = \frac{1}{m} \nabla A(x(t)) \cdot (p(t)-A(x(t))) - \nabla \phi(x(t)) , +\end{aligned}\]

where the fields $(E,B)$ are related to the potentials $(\phi, A)$ by

\[\begin{aligned} +E (x) &= - \nabla \phi (x) , & +B (x) &= \nabla \times A (x) . +\end{aligned}\]

Noncanonical Formulation

The noncanonical form of the equations can be obtained from the phasespace Lagrangian

\[\begin{aligned} +L (x,\dot{x},v,\dot{v}) &= (e A(x) + mv) \cdot \dot{x} - H(x,v) , & +H(x,v) &= \frac{m}{2} v^2 + e \phi(x), +\end{aligned}\]

as

\[\begin{aligned} +\dot{x} (t) &= v (t) , & +\dot{v} (t) &= \frac{e}{m} \big[ \nabla A (x(t)) \cdot \dot{x}(t) - \dot{A} (x(t)) - \nabla \phi(x(t)) \big] . +\end{aligned}\]

Computing the time derivative of $A$ and using the relation between the potentials $(\phi, A)$ and the fields $(E,B)$, this can be rewritten as

\[\begin{aligned} +\dot{x} (t) &= v (t) , & +\dot{v} (t) &= \frac{e}{m} \big[ E(x(t)) + v (t) \times B(x(t)) \big] . +\end{aligned}\]

This constitutes a noncanonical Hamiltonian system of the form

\[\dot{z} (t) = \Omega^{-T} (z(t)) \nabla H(z(t)) ,\]

with $z = (x,v)$ and the symplectic matrix $\Omega$ given by

\[\Omega = \frac{1}{m} \begin{pmatrix} + \mathbb{0} & \mathbb{1} \\ +- \mathbb{1} & e \hat{B} \\ +\end{pmatrix} ,\]

and

\[\hat{B} = \begin{pmatrix} +0 & -B_3 & B_2 \\ +B_3 & 0 & - B_1 \\ +- B_2 & B_1 & 0 \\ +\end{pmatrix} .\]

Modules

diff --git a/previews/PR27/guiding_center_4d/index.html b/previews/PR27/guiding_center_4d/index.html new file mode 100644 index 0000000..a3c6abb --- /dev/null +++ b/previews/PR27/guiding_center_4d/index.html @@ -0,0 +1,43 @@ + +Guiding Center Dynamics in 4D · ChargedParticleDynamics.jl
GitHub

Guiding Center Dynamics in 4D

Guiding centre dynamics is a reduced version of charged particle dynamics, where the motion of the particle in a strong magnetic field $B$ is reduced to the motion of the guiding centre, that is the centre of the gyro motion of the particle about a magnetic field line. The dynamics of the guiding centre can be described in terms of only four coordinates (as compared to six for the full motion of the charged particle), the position of the guiding centre $r = (x,y,z)$ and the parallel velocity $u$, where parallel refers to the direction of the magnetic field.

Lagrangian Formulation

The simplest form of the guiding centre equations can be obtained from the Lagrangian

\[\begin{aligned} +L &= (A (r) + u b (r)) \cdot \dot{r} - H(r,u) , & +H &= \tfrac{1}{2} u^{2} + \mu \vert B (r) \vert , +\end{aligned}\]

where $b = B / \vert B \vert$ is the unit vector of the magnetic field $B = \nabla \times A$ with $A$ the magnetic vector potential and $\mu$ is the magnetic moment. The Euler-Lagrange equations are computed as

\[\begin{aligned} +\nabla \vartheta^{T} ( r(t), u(t) ) \cdot \dot{r} (t) - \dot{\vartheta} ( r(t), u(t) ) &= \nabla H ( r(t), u(t) ) , \\ +b ( r(t) ) \cdot \dot{r} (t) &= u (t) , +\end{aligned}\]

with $\vartheta(r,u) = A (r) + u \, b (r)$ and the gradient $\nabla$ denoting the derivative with respect to $r$.

Hamiltonian Formulation

Computing the time derivative of $\vartheta$, the Euler-Lagrange equations can be rewritten in an explicit form as

\[\begin{aligned} +\dot{r} (t) &= \dfrac{u (t) \, \beta (r (t))}{b (r (t)) \cdot \beta (r (t))} + \dfrac{B (r (t))}{B (r (t)) \cdot \beta (r (t))} \times \nabla H (r (t),u (t)) , \\ +\dot{u} (t) &= - \dfrac{\beta (r (t))}{b (r (t)) \cdot \beta (r (t))} \cdot \nabla H (r (t), u (t)) , +\end{aligned}\]

where $\beta = \nabla \times \vartheta$. This constitutes a noncanonical Hamiltonian system of the form

\[\dot{q} = \Omega^{-T} (q) \nabla H(q) ,\]

with $q = (x,y,z,u)$ and the symplectic matrix $\Omega$ given by

\[\Omega_{ij} = \dfrac{\partial \vartheta_{j}}{\partial q^{i}} - \dfrac{\partial \vartheta_{i}}{\partial q^{j}} .\]

Modules

ChargedParticleDynamics.GuidingCenter4d.SymmetricField — Module

First and second Poincaré invariant for a guiding center particle in an axisymmetric magnetic field of the form $B(x,y,z) = B_0 (1 + x^2 + y^2) e_z$.

The loop for the first invariant is initialized by

\[q (\tau) = \begin{pmatrix} +r_x \cos (2\pi \tau) \\ +r_y \sin (2\pi \tau) \\ +z_0 + z_1 \sin (2\pi \tau) \\ +u_0 + u_1 \cos (2\pi \tau) \\ +\end{pmatrix}\]

with parameters

\[B_0 = 1, \quad +r_x = 0.5, \quad +r_y = 0.3, \quad +z_0 = 0.0, \quad +z_1 = 0.1, \quad +u_0 = 0.5, \quad +u_1 = 0.05, \quad +\mu = 0.01 .\]

The surface for the second invariant is initialized by

\[q (\tau) = \begin{pmatrix} +r_0 (\sigma - 0.5) \\ +r_0 (\tau - 0.5) \\ +z_0 + z_1 \cos (2\pi \sigma) \cos (2\pi \tau) \\ +u_0 + u_1 \sin (2\pi \sigma) \sin (2\pi \tau) \\ +\end{pmatrix}\]

with parameters

\[B_0 = 1, \quad +r_0 = 0.5, \quad +z_0 = 0.0, \quad +z_1 = 0.1, \quad +u_0 = 0.5, \quad +u_1 = 0.01, \quad +\mu = 0.01 .\]

source
ChargedParticleDynamics.GuidingCenter4d.ThetaPinchField — Module

First Poincaré invariant for a guiding center particle in an θ-pinch magnetic field of the form $B(x,y,z) = B_0 \, e_z$.

The loop for the first Poincaré invariant is initialized by

\[q (\tau) = \begin{pmatrix} +r_x \cos (2\pi \tau) \\ +y_0 \\ +r_z \sin (2\pi \tau) \\ +\end{pmatrix}\]

with parameters

\[B_0 = 1, \quad +r_x = 0.5, \quad +r_z = 0.3, \quad +y_0 = 0.0, \quad +u_0 = 0.5, \quad +\mu = 2.5 \times 10^{-6} .\]

source
diff --git a/previews/PR27/index.html b/previews/PR27/index.html new file mode 100644 index 0000000..b3752ea --- /dev/null +++ b/previews/PR27/index.html @@ -0,0 +1,2 @@ + +Overview · ChargedParticleDynamics.jl
GitHub

ChargedParticleDynamics.jl

CI Build Status Coverage Status codecov

General

Models

Acknowledgements

Stefan Possaner contributed vitally to sorting out the appalling details of normalization and initialization.

License

Copyright (c) Michael Kraus <michael.kraus@ipp.mpg.de>

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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b/previews/PR27/normalization/index.html @@ -0,0 +1,25 @@ + +Normalization · ChargedParticleDynamics.jl
GitHub

Normalization

In order to normalize the equations of the various models implemented in this package, we start at the level of the Lagrangian. In the following, this is explained exemplary for the charged particle Lagrangian, however, it generalizes straightforwardly to other systems like the Pauli particle or the guiding center system.

Charged Particle Lagrangian

Consider the phasespace Lagrangian

\[L (q, \dot{q}, v) = ( mv + A (x) ) \cdot \dot{x} - \frac{m}{2} \vert v \vert^2 - e \phi (x) ,\]

and, in full generality, introduce the following normalizations:

\[t = \hat{t} t' , \quad +x = \hat{x} x' , \quad +v = \hat{v} v' , \quad +A = \hat{A} A' , \quad +\phi = \hat{\phi} \phi' , \quad +L = \hat{L} L ' .\]

This leads us to

\[L' += \frac{L}{\hat{L}} += \frac{1}{\hat{L}} \, \big( m \hat{v} v' + e \hat{A} A' \big) \cdot \frac{\hat{x}}{\hat{t}} \dot{x}' - \frac{m \hat{v}^2}{\hat{L}} \frac{\vert v' \vert^2}{2} - \frac{e \hat{\phi}}{\hat{L}} \phi' .\]

Let us choose the following normalizations (and note that others are possible and may be more appropriate, depending on the problem at hand):

\[\begin{aligned} +\hat{A} &= \hat{l} \hat{B} , & +\hat{\phi} &= \hat{l} \hat{E} , & +\hat{L} &= m \hat{v}^2 = e \hat{\phi} , +\end{aligned}\]

with the characteristic length $l$. The normalized Lagrangian becomes

\[L' = \bigg( \frac{\hat{x}}{\hat{t} \hat{v}} \, v' + \underbrace{\frac{e \hat{B}}{m}}_{\hat{\omega}_c} \frac{\hat{x} \hat{l}}{ \hat{t} \hat{v}^2} \, A' \bigg) \cdot \dot{x}' - \frac{\vert v' \vert^2}{2} - \phi' ,\]

where $\hat{\omega}_c = e \hat{B} / m$ is the characteristic gyration frequency. This suggests to set

\[\begin{aligned} +\hat{t} &= \hat{\omega}_c^{-1} , & +\hat{x} &= \hat{l} , & +\hat{v} &= \frac{\hat{x}}{\hat{t}} = \hat{l} \hat{\omega}_c , +\end{aligned}\]

so that

\[L' = ( v' + A' ) \cdot \dot{x}' - \frac{\vert v' \vert^2}{2} - \phi' .\]

We thus have obtained the normalized Lagrangian.

Strongly Magnetized Plasmas

Often, especially when simulating an ensemble of particles, it is more appropriate to normalize the velocity to the thermal velocity and to choose different length scales for $\hat{x}$ and $\hat{l}$, specifically

\[\begin{aligned} +\hat{v} &= v_{\mathrm{th}} , & +\hat{t} &= \hat{\omega}_c^{-1} , & +\hat{A} &= \hat{l} \hat{B} , & +\hat{\phi} &= \hat{l} \hat{E} , & +\hat{L} &= m v_{\mathrm{th}}^2 , +\end{aligned}\]

where $v_{\mathrm{th}} = \sqrt{ W / m}$ denotes the thermal velocity and $W = k_B T$ the thermal energy. Consequently,

\[L' = \bigg( \frac{\hat{x}}{\hat{t}} \frac{m \hat{v}}{m v_{\mathrm{th}}^2} \, v' + \frac{\hat{\omega}_c^2}{v_{\mathrm{th}}^2} \, \hat{x} \hat{l} \, A' \bigg) \cdot \dot{x}' - \frac{m \hat{v}}{m v_{\mathrm{th}}^2} \frac{\vert v' \vert^2}{2} - \frac{e \hat{\phi}}{m v_{\mathrm{th}}^2} \phi' .\]

Further, set

\[\begin{aligned} +\hat{x} &= \hat{v} \hat{t} = \frac{v_{\mathrm{th}}}{\hat{\omega}_c} = \hat{\rho}_{\mathrm{th}} , +\end{aligned}\]

where $\hat{\rho}_{\mathrm{th}}$ is the characteristic gyro radius, and the normalized Lagrangian becomes

\[L' = \bigg( v' + \frac{\hat{l}}{\hat{\rho}_{\mathrm{th}}} \, A' \bigg) \cdot \dot{x}' - \frac{\vert v' \vert^2}{2} - \frac{e \hat{\phi}}{m v_{\mathrm{th}}^2} \phi' .\]

This leaves room for different orderings and consequently different normalizations. For example, in drift kinetics, we have $\hat{\rho}_{\mathrm{th}} / \hat{l} \sim \epsilon$ and $e \hat{\phi} / m v_{\mathrm{th}}^2 \sim 1$, while in gyro kinetics, we have $\hat{\rho}_{\mathrm{th}} / \hat{l} \sim 1$ and $e \hat{\phi} / m v_{\mathrm{th}}^2 \sim \epsilon$.

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GitHub
diff --git a/previews/PR27/search_index.js b/previews/PR27/search_index.js new file mode 100644 index 0000000..e85f215 --- /dev/null +++ b/previews/PR27/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"charged_particle_3d/#Charged-Particles-in-3D","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"","category":"section"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"The motion of charged particles in an electromagnetic field (EB) is governed by the Lorentz force,","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"ddotx (t) = fracem big E(x(t)) + dotx (t) times B(x(t)) big ","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"where m and e denote the particle's mass and charge, respectively.","category":"page"},{"location":"charged_particle_3d/#Canonical-Formulation","page":"Charged Particles in 3D","title":"Canonical Formulation","text":"","category":"section"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"The canonical form of the equations can be obtained from the Hamiltonian","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"H (xp) = frac12m (p-A(x))^2 + e phi(x)","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"as","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"beginaligned\ndotx (t) = fracpartial Hpartial p (x(t)p(t)) = frac1m (p(t) - A(x(t))) \ndotp (t) = - fracpartial Hpartial x (x(t)p(t)) = frac1m nabla A(x(t)) cdot (p(t)-A(x(t))) - nabla phi(x(t)) \nendaligned","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"where the fields (EB) are related to the potentials (phi A) by","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"beginaligned\nE (x) = - nabla phi (x) \nB (x) = nabla times A (x) \nendaligned","category":"page"},{"location":"charged_particle_3d/#Noncanonical-Formulation","page":"Charged Particles in 3D","title":"Noncanonical Formulation","text":"","category":"section"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"The noncanonical form of the equations can be obtained from the phasespace Lagrangian","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"beginaligned\nL (xdotxvdotv) = (e A(x) + mv) cdot dotx - H(xv) \nH(xv) = fracm2 v^2 + e phi(x)\nendaligned","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"as","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"beginaligned\ndotx (t) = v (t) \ndotv (t) = fracem big nabla A (x(t)) cdot dotx(t) - dotA (x(t)) - nabla phi(x(t)) big \nendaligned","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"Computing the time derivative of A and using the relation between the potentials (phi A) and the fields (EB), this can be rewritten as","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"beginaligned\ndotx (t) = v (t) \ndotv (t) = fracem big E(x(t)) + v (t) times B(x(t)) big \nendaligned","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"This constitutes a noncanonical Hamiltonian system of the form","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"dotz (t) = Omega^-T (z(t)) nabla H(z(t)) ","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"with z = (xv) and the symplectic matrix Omega given by","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"Omega = frac1m beginpmatrix\n mathbb0 mathbb1 \n- mathbb1 e hatB \nendpmatrix ","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"and","category":"page"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"hatB = beginpmatrix\n0 -B_3 B_2 \nB_3 0 - B_1 \n- B_2 B_1 0 \nendpmatrix ","category":"page"},{"location":"charged_particle_3d/#Modules","page":"Charged Particles in 3D","title":"Modules","text":"","category":"section"},{"location":"charged_particle_3d/","page":"Charged Particles in 3D","title":"Charged Particles in 3D","text":"Modules = [ChargedParticleDynamics.ChargedParticle3d.SingularField,\n ChargedParticleDynamics.ChargedParticle3d.SymmetricField,\n ChargedParticleDynamics.ChargedParticle3d.ThetaPinchCanonical,\n ChargedParticleDynamics.ChargedParticle3d.ThetaPinchNoncanonical,\n ChargedParticleDynamics.ChargedParticle3d.TokamakSmallCartesian,\n ChargedParticleDynamics.ChargedParticle3d.TokamakSmallCylindrical,\n ChargedParticleDynamics.ChargedParticle3d.TokamakSmallToroidal,\n ChargedParticleDynamics.ChargedParticle3d.TokamakSmallNoncanonical,\n ChargedParticleDynamics.ChargedParticle3d.TokamakIterCylindrical,\n ChargedParticleDynamics.ChargedParticle3d.SolovevIter,\n ChargedParticleDynamics.ChargedParticle3d.SolovevIterXpoint]","category":"page"},{"location":"charged_particle_3d/#ChargedParticleDynamics.ChargedParticle3d.SingularField","page":"Charged Particles in 3D","title":"ChargedParticleDynamics.ChargedParticle3d.SingularField","text":"Charged Particle in a singular magnetic field of the form B(xyz) = (x^2 + y^2)^-32 e_z.\n\n\n\n\n\n","category":"module"},{"location":"charged_particle_3d/#ChargedParticleDynamics.ChargedParticle3d.SymmetricField","page":"Charged Particles in 3D","title":"ChargedParticleDynamics.ChargedParticle3d.SymmetricField","text":"Charged Particle in an axisymmetric magnetic field of the form B(xyz) = (1 + x^2 + y^2) e_z.\n\n\n\n\n\n","category":"module"},{"location":"charged_particle_3d/#ChargedParticleDynamics.ChargedParticle3d.ThetaPinchCanonical","page":"Charged Particles in 3D","title":"ChargedParticleDynamics.ChargedParticle3d.ThetaPinchCanonical","text":"Charged Particle in an uniform magnetic field of the form B(xyz) = B_0 e_z.\n\n\n\n\n\n","category":"module"},{"location":"normalization/#Normalization","page":"Normalization","title":"Normalization","text":"","category":"section"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"In order to normalize the equations of the various models implemented in this package, we start at the level of the Lagrangian. In the following, this is explained exemplary for the charged particle Lagrangian, however, it generalizes straightforwardly to other systems like the Pauli particle or the guiding center system.","category":"page"},{"location":"normalization/#Charged-Particle-Lagrangian","page":"Normalization","title":"Charged Particle Lagrangian","text":"","category":"section"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"Consider the phasespace Lagrangian","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"L (q dotq v) = ( mv + A (x) ) cdot dotx - fracm2 vert v vert^2 - e phi (x) ","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"and, in full generality, introduce the following normalizations:","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"t = hatt t quad\nx = hatx x quad\nv = hatv v quad\nA = hatA A quad\nphi = hatphi phi quad\nL = hatL L ","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"This leads us to","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"L\n= fracLhatL\n= frac1hatL big( m hatv v + e hatA A big) cdot frachatxhatt dotx - fracm hatv^2hatL fracvert v vert^22 - frace hatphihatL phi ","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"Let us choose the following normalizations (and note that others are possible and may be more appropriate, depending on the problem at hand):","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"beginaligned\nhatA = hatl hatB \nhatphi = hatl hatE \nhatL = m hatv^2 = e hatphi \nendaligned","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"with the characteristic length l. The normalized Lagrangian becomes","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"L = bigg( frachatxhatt hatv v + underbracefrace hatBm_hatomega_c frachatx hatl hatt hatv^2 A bigg) cdot dotx - fracvert v vert^22 - phi ","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"where hatomega_c = e hatB m is the characteristic gyration frequency. This suggests to set","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"beginaligned\nhatt = hatomega_c^-1 \nhatx = hatl \nhatv = frachatxhatt = hatl hatomega_c \nendaligned","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"so that","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"L = ( v + A ) cdot dotx - fracvert v vert^22 - phi ","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"We thus have obtained the normalized Lagrangian.","category":"page"},{"location":"normalization/#Strongly-Magnetized-Plasmas","page":"Normalization","title":"Strongly Magnetized Plasmas","text":"","category":"section"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"Often, especially when simulating an ensemble of particles, it is more appropriate to normalize the velocity to the thermal velocity and to choose different length scales for hatx and hatl, specifically","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"beginaligned\nhatv = v_mathrmth \nhatt = hatomega_c^-1 \nhatA = hatl hatB \nhatphi = hatl hatE \nhatL = m v_mathrmth^2 \nendaligned","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"where v_mathrmth = sqrt W m denotes the thermal velocity and W = k_B T the thermal energy. Consequently,","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"L = bigg( frachatxhatt fracm hatvm v_mathrmth^2 v + frachatomega_c^2v_mathrmth^2 hatx hatl A bigg) cdot dotx - fracm hatvm v_mathrmth^2 fracvert v vert^22 - frace hatphim v_mathrmth^2 phi ","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"Further, set","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"beginaligned\nhatx = hatv hatt = fracv_mathrmthhatomega_c = hatrho_mathrmth \nendaligned","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"where hatrho_mathrmth is the characteristic gyro radius, and the normalized Lagrangian becomes","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"L = bigg( v + frachatlhatrho_mathrmth A bigg) cdot dotx - fracvert v vert^22 - frace hatphim v_mathrmth^2 phi ","category":"page"},{"location":"normalization/","page":"Normalization","title":"Normalization","text":"This leaves room for different orderings and consequently different normalizations. For example, in drift kinetics, we have hatrho_mathrmth hatl sim epsilon and e hatphi m v_mathrmth^2 sim 1, while in gyro kinetics, we have hatrho_mathrmth hatl sim 1 and e hatphi m v_mathrmth^2 sim epsilon. ","category":"page"},{"location":"initialization/#Initialization","page":"Initialization","title":"Initialization","text":"","category":"section"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"In the following, we will discuss how to initialise the various models from a common set of initial data, namely","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"the guiding center position X in physical coordinates,\nthe particle energy W in eV,\nthe particle mass m in kg,\nthe particle charge number,\nthe gyro angle theta in 0 2pi,\nthe pitch angle alpha in 0 pi 2.","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"For charged particles we need to convert the energy into a velocity vector. For the Pauli particle we need to compute the coordinates of the guiding centre X of the particle and construct a velocity vector that only holds the component of the velocity that is parallel to the magnetic field, while the perpendicular component goes into the magnetic moment mu. For the guiding center, we need the same coordinate transformation as for the Pauli particle, but we only need the absolute value of the velocity in direction of the magnetic field u and the magnetic moment mu.","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Make sure to read about the Normalization before proceeding.","category":"page"},{"location":"initialization/#Velocities","page":"Initialization","title":"Velocities","text":"","category":"section"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Set e = e hate with e = 1602 176 634 cdot 10^-19 and hate = mathrmC and similarly m = m hatm with hatm = mathrmkg. Some common values for the mass are","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Particle Normalised Mass m\nelectron 91093837015 cdot 10^-31\nproton 16726219237 cdot 10^-27\ndeuteron 33435837724 cdot 10^-27\nalpha 66446573357 cdot 10^-27","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"The absolute value of the velocity is obtained from the particle energy by vert v vert^2 = 2 W m. In normalised units, we have W = W hatW and v = v hatv where hatW = e mathrmV and hatv = hatl hatomega_c = hatl hatB e m.","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Let us compute the normalise kinetic energy,","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"fracvert v vert^22\n= fracW hatWm hatv^2\n= fracW e mathrmV m^2m hatl^2 hatB^2 e^2 ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Usually, we have hatB = T = mathrmkg mathrmC mathrms. Recall that mathrmV = mathrmkg mathrmm^2 mathrmC mathrms^2 and let us set hatl = l_0 mathrmm, then","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"fracvert v vert^22 = fracm We l_0^2 ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Thus for the absolute value of the velocity we have","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"vert v vert = frac1l_0 sqrt 2 W fracme ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"The pitch angle alpha determines the distribution of the kinetic energy into the perpendicular and parallel components by","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"beginaligned\nW_perp = W sin alpha qquad\nW_parallel = W (1 - sin alpha) \nendaligned","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"and accordingly","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"beginaligned\nvert v_perp vert = frac1l_0 sqrt 2 W_perp fracme qquad\nvert v_parallel vert = frac1l_0 sqrt 2 W_parallel fracme \nendaligned","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"The ElectromagneticFields.jl package provides three functions a⃗(t,x), b⃗(t,x), c⃗(t,x) that can be used to construct the velocity vector v. The function b⃗ returns the unit vector of the magnetic field, thus","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"v_parallel = vert v vert (1 - sin alpha) b ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"The functions a⃗ and c⃗ return two unit vectors that span the plane perpendicular to the magnetic field, thus","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"v_perp = vert v vert sin alpha ( - a sin theta - c cos theta ) ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"where theta is the gyro angle. The magnetic moment is computed as","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"mu = frac vert v_perp vert^2 2 vert B vert = frac vert v vert^2 sin alpha 2 vert B vert ","category":"page"},{"location":"initialization/#Gyro-radius-Vector-and-Position","page":"Initialization","title":"Gyro-radius Vector and Position","text":"","category":"section"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"In order to compute the particle position, we need to construct the gyro radius vector rho, which is given by","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"rho = fracb times vomega_c = fracb times hatv vhatomega_c omega_c = l_0 fracb times vvert B vert ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Note that ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"omega_c\n= frace vert B vertm\n= frace vert hatB B vertm\n= frace vert hatB vertm vert B vert\n= hatomega_c omega_c ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"as","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"hatomega_c = frace vert hatB vertm ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"so that","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"omega_c = vert B vert ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"The normalized gyro radius vector reads","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"rho = fracrhol_0 = fracb times vvert B vert ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"so that the normalised particle position is","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"x = X + rho ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"The gyro phase theta is defined as the angle, measured in the clockwise sense, between a and rho, so that","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"fracb times vvert v vert sin alpha = a cos theta - c sin theta ","category":"page"},{"location":"initialization/#Guiding-Center-Coordinates","page":"Initialization","title":"Guiding Center Coordinates","text":"","category":"section"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Instead of the particle energy W and pitch angle alpha, we can also compute all initial conditions from the guiding center initial data, i.e., parallel velocity u = vert v_parallel vert, magnetic moment mu and gyro angle theta.","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Start by computing the absolute value of the perpendicular velocity by","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"vert v_perp vert = sqrt 2 mu vert B vert ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"and the total velocity by","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"vert v vert = sqrt vert v_parallel vert^2 + vert v_perp vert^2 ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"With that, we can compute the perpendicular and total energy,","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"beginaligned\nW_perp = frace l₀^2 vert v_perp vert^22m qquad\nW = frace l₀^2 vert v vert^22m \nendaligned","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"The pitch angle is obtained as","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"alpha = arcsin fracW_perpW ","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"With that, the rest of the quantities can be computed in the same way as above.","category":"page"},{"location":"initialization/#Initial-Conditions","page":"Initialization","title":"Initial Conditions","text":"","category":"section"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"ChargedParticleDynamics.jl provides the InitialConditions module for the computation of the above quantities. Three functions are provided that return the initial conditions for the different models. For charged particles the initial conditions are (x v), for the Pauli particle we have (X v_parallel mu) and for the guiding center we use (X u mu) with u = vert v_parallel vert.","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Modules = [ChargedParticleDynamics]\nOrder = [:type, :function]","category":"page"},{"location":"initialization/#ChargedParticleDynamics.InitialConditions","page":"Initialization","title":"ChargedParticleDynamics.InitialConditions","text":"Store initial conditions for charged particle, Pauli particle and guiding center models.\n\nFields:\n\nx: particle position\nX: gyro center position\nρ: gyro radius vector\nvvec: velocity vector\nvpar: parallel velocity vector\nvper: perpendicular velocity vector\nv: absolute value of velocity\nu: absolute value of parallel velocity\nμ: magnetic moment\nθ: gyro angle ∈ [0,2π]\nα: pitch angle ∈ [0,π/2]\nω: gyro frequency\nmass: mass in kg\nenergy: energy in eV\ncharge: charge number\n\n\n\n\n\n","category":"type"},{"location":"initialization/#ChargedParticleDynamics.InitialConditions-Union{Tuple{T}, Tuple{AbstractVector{T}, T, T, T, T, Any, Vararg{Function, 8}}} where T","page":"Initialization","title":"ChargedParticleDynamics.InitialConditions","text":"Compute initial conditions from the following arguments:\n\nX: gyro center position\nθ: gyro angle\nα: pitch angle\nE: energy\nM: mass\nC: charge number\na, b, c: magnetic field unit vectors in physical coordinates\nb: magnetic field unit vector in contravariant coordinates\nB: amplitude of magnetic field\ng̅: inverse metric coefficients\nDF̄: inverse Jacobian matrix\nJ: Jacobian determinant\nl=1: length normalization\n\n\n\n\n\n","category":"method"},{"location":"initialization/#ChargedParticleDynamics.InitialConditionsGC-Union{Tuple{T}, Tuple{AbstractVector{T}, T, T, T, T, Any, Vararg{Function, 8}}} where T","page":"Initialization","title":"ChargedParticleDynamics.InitialConditionsGC","text":"Compute initial conditions from the following arguments:\n\nX: gyro center position\nθ: gyro angle\nu: absolute value of parallel velocity\nμ: magnetic moment\nM: mass\nC: charge number\na, b, c: magnetic field unit vectors in physical coordinates\nb: magnetic field unit vector in contravariant coordinates\nB: amplitude of magnetic field\ng̅: inverse metric coefficients\nDF̄: inverse Jacobian matrix\nJ: Jacobian determinant\nl=1: length normalization\n\n\n\n\n\n","category":"method"},{"location":"initialization/#ChargedParticleDynamics.charged_particle-Union{Tuple{InitialConditions{T}}, Tuple{T}} where T","page":"Initialization","title":"ChargedParticleDynamics.charged_particle","text":"Extracts the charged particle initial conditions and returns the tuple (x,v). If the keyword argument noncanonical is set to true, the functions returns the vector vcat(x,v).\n\n\n\n\n\n","category":"method"},{"location":"initialization/#ChargedParticleDynamics.guiding_center-Union{Tuple{InitialConditions{T}}, Tuple{T}} where T","page":"Initialization","title":"ChargedParticleDynamics.guiding_center","text":"Extracts the guiding center initial conditions and returns the tuple (vcat(X,u),μ).\n\n\n\n\n\n","category":"method"},{"location":"initialization/#ChargedParticleDynamics.pauli_particle-Union{Tuple{InitialConditions{T}}, Tuple{T}} where T","page":"Initialization","title":"ChargedParticleDynamics.pauli_particle","text":"Extracts the Pauli particle initial conditions and returns the tuple (X,vpar,μ). If the keyword argument noncanonical is set to true, the functions returns the tuple (vcat(X,vpar),μ).\n\n\n\n\n\n","category":"method"},{"location":"initialization/#Example","page":"Initialization","title":"Example","text":"","category":"section"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"As an example, let us consider a deuteron in an ITER-like analytical equilibrium (obtained from ElectromagneticFields.SolovevITER). The guiding center position is 7 0 0, the energy is 1 mathrmMeV, and the pitch angle is pi 2.","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"using LaTeXStrings\nusing Markdown\nusing Plots\n\np = palette(:tab10)\nrectangle(x, y, w, h) = Shape(x .+ [-w/2,-w/2,+w/2,+w/2], y .+ [-h/2,+h/2,+h/2,-h/2])\n\nusing ChargedParticleDynamics\nusing ChargedParticleDynamics: md\n\nimport ElectromagneticFields: code\nimport ElectromagneticFields.Solovev: SolovevEquilibrium\nimport ElectromagneticFields.SolovevITER: init\nequ = init()\n@eval $(code(equ))\n\nX₀ = from_cartesian(0, [7.0, 0, 0])\nE₀ = 1E6\nθ₀ = 0.\nα₀ = π/4\nm₀ = md\n\nic0 = InitialConditions(X₀, θ₀, α₀, E₀, m₀, 1, aₚ, bₚ, cₚ, b⃗, B, ḡ, DF̄, J; l₀=R₀)\n\nnp = 12\nnr = 100\nnz = 120\n\nxgrid = LinRange( 0.5, 1.5, nr)\nygrid = LinRange(-0.75, +0.75, nz)\nfieldlines = zeros((nr,nz))\n\nfor i in 1:nr\n for j in 1:nz\n fieldlines[i,j] = A₃(0, xgrid[i], ygrid[j], 0.0) / xgrid[i]\n end\nend\n\npx = zeros(np)\npy = zeros(np)\n\nfor i in 1:np\n ics = charged_particle(InitialConditions(X₀, 2π*i/np, α₀, E₀, m₀, 1, aₚ, bₚ, cₚ, b⃗, B, ḡ, DF̄, J; l₀=R₀))\n px[i] = ics[1][1]\n py[i] = ics[1][2]\nend\n\nboxw=0.008\nboxh=0.008\n\nplot(aspectratio=1, layout=(1,2), legend=:none, size=(800,600), xguide=L\"R/R_0\", yguide=L\"Z/R_0\")\nplot!(subplot=1, rectangle(X₀[1], X₀[2], 0.1, 0.1), opacity=.5, color=:white)\n\nplot!(subplot=1, xlims=(0.5,1.5), ylims=(-0.75,+0.75))\nplot!(subplot=2, xlims=(X₀[1] .+ [-boxw,+boxw]), ylims=(X₀[2] .+ [-boxh,+boxh]))\n\ncontour!(subplot=1, xgrid, ygrid, fieldlines', levels=50)\nscatter!(subplot=1, px, py, color=p[1])\nscatter!(subplot=1, [X₀[1]], [X₀[2]], color=p[4])\n\nscatter!(subplot=2, px, py, color=p[1])\nscatter!(subplot=2, [X₀[1]], [X₀[2]], color=p[4])\n\nsavefig(\"initial_conditions.png\")\n\nMarkdown.parse(\"\"\"\n| Fields | Value |\n|:-----------|:------|\n| `x` | $(ic0.x) |\n| `X` | $(ic0.X) |\n| `ρ` | $(ic0.ρ) |\n| `v⃗` | $(ic0.vvec) |\n| `v∥` | $(ic0.vpar) |\n| `v⟂` | $(ic0.vper) |\n| `v` | $(ic0.v) |\n| `u` | $(ic0.u) |\n| `μ` | $(ic0.μ) |\n| `θ` | $(ic0.θ) |\n| `α` | $(ic0.α) |\n| `ω` | $(ic0.ω) |\n| `M` | $(ic0.mass) |\n| `E` | $(ic0.energy) |\n| `C` | $(ic0.charge) |\n\"\"\")","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"Below we plot the guiding center position (in red) and the particle position (in blue) in the poloidal plane for various gyro angles in 0 2pi.","category":"page"},{"location":"initialization/","page":"Initialization","title":"Initialization","text":"(Image: )","category":"page"},{"location":"pauli_particle_3d/#Pauli-Particles-in-3D","page":"Pauli Particles in 3D","title":"Pauli Particles in 3D","text":"","category":"section"},{"location":"pauli_particle_3d/#Modules","page":"Pauli Particles in 3D","title":"Modules","text":"","category":"section"},{"location":"pauli_particle_3d/","page":"Pauli Particles in 3D","title":"Pauli Particles in 3D","text":"Modules = [ChargedParticleDynamics.PauliParticle3d.SymmetricField,\n ChargedParticleDynamics.PauliParticle3d.ThetaPinchField,\n ChargedParticleDynamics.PauliParticle3d.TokamakSmallCartesian,\n ChargedParticleDynamics.PauliParticle3d.TokamakSmallCylindrical,\n ChargedParticleDynamics.PauliParticle3d.TokamakSmallToroidal,\n ChargedParticleDynamics.PauliParticle3d.TokamakIterCylindrical,\n ChargedParticleDynamics.PauliParticle3d.SolovevIter,\n ChargedParticleDynamics.PauliParticle3d.SolovevIterXpoint]","category":"page"},{"location":"pauli_particle_3d/#ChargedParticleDynamics.PauliParticle3d.SymmetricField","page":"Pauli Particles in 3D","title":"ChargedParticleDynamics.PauliParticle3d.SymmetricField","text":"Charged Particle in an axisymmetric magnetic field of the form B(xyz) = (1 + x^2 + y^2) e_z.\n\n\n\n\n\n","category":"module"},{"location":"pauli_particle_3d/#ChargedParticleDynamics.PauliParticle3d.ThetaPinchField","page":"Pauli Particles in 3D","title":"ChargedParticleDynamics.PauliParticle3d.ThetaPinchField","text":"Charged Particle in an uniform magnetic field of the form B(xyz) = B_0 e_z.\n\n\n\n\n\n","category":"module"},{"location":"#ChargedParticleDynamics.jl","page":"Overview","title":"ChargedParticleDynamics.jl","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"(Image: CI) (Image: Build Status) (Image: Coverage Status) (Image: codecov)","category":"page"},{"location":"#General","page":"Overview","title":"General","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Pages = [\"normalization.md\",\n \"initialization.md\",\n]","category":"page"},{"location":"#Models","page":"Overview","title":"Models","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Pages = [\"charged_particle_3d.md\",\n \"guiding_center_4d.md\",\n \"pauli_particle_3d.md\",\n]","category":"page"},{"location":"#Acknowledgements","page":"Overview","title":"Acknowledgements","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Stefan Possaner contributed vitally to sorting out the appalling details of normalization and initialization.","category":"page"},{"location":"#License","page":"Overview","title":"License","text":"","category":"section"},{"location":"","page":"Overview","title":"Overview","text":"Copyright (c) Michael Kraus Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.","category":"page"},{"location":"guiding_center_4d/#Guiding-Center-Dynamics-in-4D","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"","category":"section"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"Guiding centre dynamics is a reduced version of charged particle dynamics, where the motion of the particle in a strong magnetic field B is reduced to the motion of the guiding centre, that is the centre of the gyro motion of the particle about a magnetic field line. The dynamics of the guiding centre can be described in terms of only four coordinates (as compared to six for the full motion of the charged particle), the position of the guiding centre r = (xyz) and the parallel velocity u, where parallel refers to the direction of the magnetic field.","category":"page"},{"location":"guiding_center_4d/#Lagrangian-Formulation","page":"Guiding Center Dynamics in 4D","title":"Lagrangian Formulation","text":"","category":"section"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"The simplest form of the guiding centre equations can be obtained from the Lagrangian","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"beginaligned\nL = (A (r) + u b (r)) cdot dotr - H(ru) \nH = tfrac12 u^2 + mu vert B (r) vert \nendaligned","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"where b = B vert B vert is the unit vector of the magnetic field B = nabla times A with A the magnetic vector potential and mu is the magnetic moment. The Euler-Lagrange equations are computed as","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"beginaligned\nnabla vartheta^T ( r(t) u(t) ) cdot dotr (t) - dotvartheta ( r(t) u(t) ) = nabla H ( r(t) u(t) ) \nb ( r(t) ) cdot dotr (t) = u (t) \nendaligned","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"with vartheta(ru) = A (r) + u b (r) and the gradient nabla denoting the derivative with respect to r.","category":"page"},{"location":"guiding_center_4d/#Hamiltonian-Formulation","page":"Guiding Center Dynamics in 4D","title":"Hamiltonian Formulation","text":"","category":"section"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"Computing the time derivative of vartheta, the Euler-Lagrange equations can be rewritten in an explicit form as","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"beginaligned\ndotr (t) = dfracu (t) beta (r (t))b (r (t)) cdot beta (r (t)) + dfracB (r (t))B (r (t)) cdot beta (r (t)) times nabla H (r (t)u (t)) \ndotu (t) = - dfracbeta (r (t))b (r (t)) cdot beta (r (t)) cdot nabla H (r (t) u (t)) \nendaligned","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"where beta = nabla times vartheta. This constitutes a noncanonical Hamiltonian system of the form","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"dotq = Omega^-T (q) nabla H(q) ","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"with q = (xyzu) and the symplectic matrix Omega given by","category":"page"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"Omega_ij = dfracpartial vartheta_jpartial q^i - dfracpartial vartheta_ipartial q^j ","category":"page"},{"location":"guiding_center_4d/#Modules","page":"Guiding Center Dynamics in 4D","title":"Modules","text":"","category":"section"},{"location":"guiding_center_4d/","page":"Guiding Center Dynamics in 4D","title":"Guiding Center Dynamics in 4D","text":"Modules = [ChargedParticleDynamics.GuidingCenter4d.SymmetricField,\n ChargedParticleDynamics.GuidingCenter4d.ThetaPinchField,\n ChargedParticleDynamics.GuidingCenter4d.TokamakSmallCartesian,\n ChargedParticleDynamics.GuidingCenter4d.TokamakSmallCylindrical,\n ChargedParticleDynamics.GuidingCenter4d.TokamakSmallToroidal,\n ChargedParticleDynamics.GuidingCenter4d.TokamakMediumCartesian,\n ChargedParticleDynamics.GuidingCenter4d.TokamakMediumCylindrical,\n ChargedParticleDynamics.GuidingCenter4d.TokamakIterCylindrical,\n ChargedParticleDynamics.GuidingCenter4d.SolovevIter,\n ChargedParticleDynamics.GuidingCenter4d.SolovevIterXpoint]","category":"page"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.SymmetricField","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.SymmetricField","text":"First and second Poincaré invariant for a guiding center particle in an axisymmetric magnetic field of the form B(xyz) = B_0 (1 + x^2 + y^2) e_z.\n\nThe loop for the first invariant is initialized by\n\nq (tau) = beginpmatrix\nr_x cos (2pi tau) \nr_y sin (2pi tau) \nz_0 + z_1 sin (2pi tau) \nu_0 + u_1 cos (2pi tau) \nendpmatrix\n\nwith parameters\n\nB_0 = 1 quad\nr_x = 05 quad\nr_y = 03 quad\nz_0 = 00 quad\nz_1 = 01 quad\nu_0 = 05 quad\nu_1 = 005 quad\nmu = 001 \n\nThe surface for the second invariant is initialized by\n\nq (tau) = beginpmatrix\nr_0 (sigma - 05) \nr_0 (tau - 05) \nz_0 + z_1 cos (2pi sigma) cos (2pi tau) \nu_0 + u_1 sin (2pi sigma) sin (2pi tau) \nendpmatrix\n\nwith parameters\n\nB_0 = 1 quad\nr_0 = 05 quad\nz_0 = 00 quad\nz_1 = 01 quad\nu_0 = 05 quad\nu_1 = 001 quad\nmu = 001 \n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.ThetaPinchField","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.ThetaPinchField","text":"First Poincaré invariant for a guiding center particle in an θ-pinch magnetic field of the form B(xyz) = B_0 e_z.\n\nThe loop for the first Poincaré invariant is initialized by\n\nq (tau) = beginpmatrix\nr_x cos (2pi tau) \ny_0 \nr_z sin (2pi tau) \nendpmatrix\n\nwith parameters\n\nB_0 = 1 quad\nr_x = 05 quad\nr_z = 03 quad\ny_0 = 00 quad\nu_0 = 05 quad\nmu = 25 times 10^-6 \n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.TokamakSmallCartesian","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.TokamakSmallCartesian","text":"Analytic axisymmetric small tokamak equilibrium in cartesian coordinates.\n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.TokamakSmallCylindrical","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.TokamakSmallCylindrical","text":"Analytic axisymmetric small tokamak equilibrium in cylindrical coordinates.\n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.TokamakSmallToroidal","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.TokamakSmallToroidal","text":"Analytic axisymmetric small tokamak equilibrium in circular coordinates.\n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.TokamakMediumCartesian","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.TokamakMediumCartesian","text":"Analytic axisymmetric medium-size tokamak equilibrium in cartesian coordinates.\n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.TokamakMediumCylindrical","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.TokamakMediumCylindrical","text":"Analytic axisymmetric medium-size tokamak equilibrium in cartesian coordinates.\n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.TokamakIterCylindrical","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.TokamakIterCylindrical","text":"Analytic ITER-like Solov'ev equilibrium with X-point.\n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.SolovevIter","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.SolovevIter","text":"Analytic ITER-like Solov'ev equilibrium.\n\n\n\n\n\n","category":"module"},{"location":"guiding_center_4d/#ChargedParticleDynamics.GuidingCenter4d.SolovevIterXpoint","page":"Guiding Center Dynamics in 4D","title":"ChargedParticleDynamics.GuidingCenter4d.SolovevIterXpoint","text":"Analytic ITER-like Solov'ev equilibrium with X-point.\n\n\n\n\n\n","category":"module"}] +} diff --git a/previews/PR27/siteinfo.js b/previews/PR27/siteinfo.js new file mode 100644 index 0000000..63a847b --- /dev/null +++ b/previews/PR27/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR27";
GitHub

Initialization

In the following, we will discuss how to initialise the various models from a common set of initial data, namely

  • the guiding center position $X$ in physical coordinates,
  • the particle energy $W$ in eV,
  • the particle mass $m$ in kg,
  • the particle charge number,
  • the gyro angle $\theta \in [0, 2\pi]$,
  • the pitch angle $\alpha \in [0, \pi / 2]$.

For charged particles we need to convert the energy into a velocity vector. For the Pauli particle we need to compute the coordinates of the guiding centre $X$ of the particle and construct a velocity vector that only holds the component of the velocity that is parallel to the magnetic field, while the perpendicular component goes into the magnetic moment $\mu$. For the guiding center, we need the same coordinate transformation as for the Pauli particle, but we only need the absolute value of the velocity in direction of the magnetic field $u$ and the magnetic moment $\mu$.

Make sure to read about the Normalization before proceeding.

Velocities

Set $e = e' \hat{e}$ with $e' = 1.602 176 634 \cdot 10^{-19}$ and $\hat{e} = \mathrm{C}$ and similarly $m = m' \hat{m}$ with $\hat{m} = \mathrm{kg}$. Some common values for the mass are

ParticleNormalised Mass $m'$
electron$9.1093837015 \cdot 10^{-31}$
proton$1.6726219237 \cdot 10^{-27}$
deuteron$3.3435837724 \cdot 10^{-27}$
alpha$6.6446573357 \cdot 10^{-27}$

The absolute value of the velocity is obtained from the particle energy by $\vert v \vert^2 = 2 W / m$. In normalised units, we have $W = W' \hat{W}$ and $v = v' \hat{v}$ where $\hat{W} = e \mathrm{V}$ and $\hat{v} = \hat{l} \hat{\omega}_c = \hat{l} \hat{B} e / m$.

Let us compute the normalise kinetic energy,

\[\frac{\vert v' \vert^2}{2} += \frac{W' \hat{W}}{m \hat{v}^2} += \frac{W' e \mathrm{V} m^2}{m \hat{l}^2 \hat{B}^2 e^2} .\]

Usually, we have $\hat{B} = T = \mathrm{kg} / \mathrm{C} \mathrm{s}$. Recall that $\mathrm{V} = \mathrm{kg} \mathrm{m}^2 / \mathrm{C} \mathrm{s}^2$ and let us set $\hat{l} = l_0 \mathrm{m}$, then

\[\frac{\vert v' \vert^2}{2} = \frac{m' W'}{e' l_0^2} .\]

Thus for the absolute value of the velocity we have

\[\vert v' \vert = \frac{1}{l_0} \sqrt{ 2 W' \, \frac{m'}{e'} } .\]

The pitch angle $\alpha$ determines the distribution of the kinetic energy into the perpendicular and parallel components by

\[\begin{aligned} +W_{\perp}' &= W' \sin \alpha , \qquad +W_{\parallel}' &= W' \, (1 - \sin \alpha) , +\end{aligned}\]

and accordingly

\[\begin{aligned} +\vert v_{\perp}' \vert &= \frac{1}{l_0} \sqrt{ 2 W_{\perp}' \, \frac{m'}{e'} } , \qquad +\vert v_{\parallel}' \vert &= \frac{1}{l_0} \sqrt{ 2 W_{\parallel}' \, \frac{m'}{e'} } . +\end{aligned}\]

The ElectromagneticFields.jl package provides three functions a⃗(t,x), b⃗(t,x), c⃗(t,x) that can be used to construct the velocity vector $v$. The function b⃗ returns the unit vector of the magnetic field, thus

\[v_{\parallel}' = \vert v' \vert \, (1 - \sin \alpha) \, b .\]

The functions a⃗ and c⃗ return two unit vectors that span the plane perpendicular to the magnetic field, thus

\[v_{\perp}' = \vert v' \vert \, \sin \alpha ( - a \, \sin \theta - c \, \cos \theta ) ,\]

where $\theta$ is the gyro angle. The magnetic moment is computed as

\[\mu = \frac{ \vert v_{\perp}' \vert^2 }{2 \vert B' \vert} = \frac{ \vert v' \vert^2 \sin \alpha }{2 \vert B' \vert} .\]

Gyro-radius Vector and Position

In order to compute the particle position, we need to construct the gyro radius vector $\rho$, which is given by

\[\rho = \frac{b \times v}{\omega_c} = \frac{b \times \hat{v} v'}{\hat{\omega_c} \omega_c'} = l_{0} \, \frac{b \times v'}{\vert B' \vert} .\]

Note that

\[\omega_c += \frac{e \vert B \vert}{m} += \frac{e \vert \hat{B} B' \vert}{m} += \frac{e \vert \hat{B} \vert}{m} \vert B' \vert += \hat{\omega}_c \omega_c' ,\]

as

\[\hat{\omega}_c = \frac{e \vert \hat{B} \vert}{m} ,\]

so that

\[\omega_c' = \vert B' \vert .\]

The normalized gyro radius vector reads

\[\rho' = \frac{\rho}{l_0} = \frac{b \times v'}{\vert B' \vert} ,\]

so that the normalised particle position is

\[x' = X' + \rho' .\]

The gyro phase $\theta$ is defined as the angle, measured in the clockwise sense, between $a$ and $\rho$, so that

\[\frac{b \times v'}{\vert v' \vert \, \sin \alpha} = a \, \cos \theta - c \, \sin \theta .\]

Guiding Center Coordinates

Instead of the particle energy $W$ and pitch angle $\alpha$, we can also compute all initial conditions from the guiding center initial data, i.e., parallel velocity $u = \vert v_{\parallel} \vert$, magnetic moment $\mu$ and gyro angle $\theta$.

Start by computing the absolute value of the perpendicular velocity by

\[\vert v_\perp \vert = \sqrt{ 2 \mu \vert B \vert } ,\]

and the total velocity by

\[\vert v \vert = \sqrt{ \vert v_{\parallel} \vert^2 + \vert v_\perp \vert^2 } .\]

With that, we can compute the perpendicular and total energy,

\[\begin{aligned} +W_{\perp}' &= \frac{e l₀^2 \vert v_\perp \vert^2}{2m} , \qquad +W' &= \frac{e l₀^2 \vert v \vert^2}{2m} . +\end{aligned}\]

The pitch angle is obtained as

\[\alpha = \arcsin \frac{W_{\perp}'}{W'} .\]

With that, the rest of the quantities can be computed in the same way as above.

Initial Conditions

ChargedParticleDynamics.jl provides the InitialConditions module for the computation of the above quantities. Three functions are provided that return the initial conditions for the different models. For charged particles the initial conditions are $(x', v')$, for the Pauli particle we have $(X', v_{\parallel}', \mu)$ and for the guiding center we use $(X', u', \mu)$ with $u' = \vert v_{\parallel}' \vert$.

ChargedParticleDynamics.InitialConditions — Type

Store initial conditions for charged particle, Pauli particle and guiding center models.

Fields:

  • x: particle position
  • X: gyro center position
  • ρ: gyro radius vector
  • vvec: velocity vector
  • vpar: parallel velocity vector
  • vper: perpendicular velocity vector
  • v: absolute value of velocity
  • u: absolute value of parallel velocity
  • μ: magnetic moment
  • θ: gyro angle ∈ [0,2π]
  • α: pitch angle ∈ [0,π/2]
  • ω: gyro frequency
  • mass: mass in kg
  • energy: energy in eV
  • charge: charge number
source
ChargedParticleDynamics.InitialConditions — Method

Compute initial conditions from the following arguments:

  • X: gyro center position
  • θ: gyro angle
  • α: pitch angle
  • E: energy
  • M: mass
  • C: charge number
  • a, b, c: magnetic field unit vectors in physical coordinates
  • b: magnetic field unit vector in contravariant coordinates
  • B: amplitude of magnetic field
  • g̅: inverse metric coefficients
  • DF̄: inverse Jacobian matrix
  • J: Jacobian determinant
  • l=1: length normalization
source
ChargedParticleDynamics.InitialConditionsGC — Method

Compute initial conditions from the following arguments:

  • X: gyro center position
  • θ: gyro angle
  • u: absolute value of parallel velocity
  • μ: magnetic moment
  • M: mass
  • C: charge number
  • a, b, c: magnetic field unit vectors in physical coordinates
  • b: magnetic field unit vector in contravariant coordinates
  • B: amplitude of magnetic field
  • g̅: inverse metric coefficients
  • DF̄: inverse Jacobian matrix
  • J: Jacobian determinant
  • l=1: length normalization
source
ChargedParticleDynamics.charged_particle — Method

Extracts the charged particle initial conditions and returns the tuple (x,v). If the keyword argument noncanonical is set to true, the functions returns the vector vcat(x,v).

source
ChargedParticleDynamics.pauli_particle — Method

Extracts the Pauli particle initial conditions and returns the tuple (X,vpar,μ). If the keyword argument noncanonical is set to true, the functions returns the tuple (vcat(X,vpar),μ).

source

Example

As an example, let us consider a deuteron in an ITER-like analytical equilibrium (obtained from ElectromagneticFields.SolovevITER). The guiding center position is $[7, 0, 0]$, the energy is $1 \, \mathrm{MeV}$, and the pitch angle is $\pi / 2$.

FieldsValue
x[1.129032258064516, 0.005902625716371612, -1.1084431084484249e-5]
X[1.129032258064516, 0.0, 0.0]
ρ[-3.527639575996389e-21, 0.005902625716371612, -1.1084431084484249e-5]
v⃗[-0.004469150989175999, -6.098327183380105e-6, -0.002547591892668252]
v∥[0.0, -6.098327183380105e-6, -0.002547591892668252]
v⟂[-0.004469150989175999, 0.0, 0.0]
v0.032951426156967195
u0.017833183330406035
μ0.0005070194648182154
θ0.0
α0.7853981633974483
ω3.6280811350854e7
M3.3435837724e-27
E1.0e6
C1

Below we plot the guiding center position (in red) and the particle position (in blue) in the poloidal plane for various gyro angles $\in [0, 2\pi]$.