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Rename toroidal tokamak equilibrium to circular tokamak equilibrium. …
…Add toroidally regularised equilibrium.
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src/analytic/axisymmetric_tokamak_toroidal_regularization.jl
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| @doc raw""" | ||
| Axisymmetric tokamak equilibrium in (r,θ,ϕ) coordinates with covariant | ||
| components of the vector potential given by | ||
| ```math | ||
| A (r, \theta, \phi) = B_0 \, \bigg( 0 , \, \frac{r R_0}{\cos (\theta)} - \bigg( \frac{R_0}{\cos (\theta)} \bigg)^2 \, \ln \bigg( \frac{R}{R_0} \bigg) , \, - \frac{r^2}{2 q_0} \bigg)^T , | ||
| ``` | ||
| resulting in the magnetic field with covariant components | ||
| ```math | ||
| B (r, \theta, \phi) = \frac{B_0}{q_0} \, \bigg( 0 , \, \frac{r^2}{R}, \, q_0 R_0 \bigg)^T , | ||
| ``` | ||
| where $R = R_0 + r \cos \theta$. | ||
| Parameters: | ||
| * `R₀`: position of magnetic axis | ||
| * `B₀`: B-field at magnetic axis | ||
| * `q₀`: safety factor at magnetic axis | ||
| """ | ||
| module AxisymmetricTokamakToroidalRegularization | ||
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| import ..ElectromagneticFields | ||
| import ..ElectromagneticFields: AnalyticEquilibrium, ZeroPerturbation | ||
| import ..ElectromagneticFields: load_equilibrium, generate_equilibrium_code | ||
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| export AxisymmetricTokamakToroidalRegularizationEquilibrium | ||
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| const DEFAULT_R₀ = 1.0 | ||
| const DEFAULT_B₀ = 1.0 | ||
| const DEFAULT_q₀ = 2.0 | ||
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| struct AxisymmetricTokamakToroidalRegularizationEquilibrium{T <: Number} <: AnalyticEquilibrium | ||
| name::String | ||
| R₀::T | ||
| B₀::T | ||
| q₀::T | ||
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| function AxisymmetricTokamakToroidalRegularizationEquilibrium{T}(R₀::T, B₀::T, q₀::T) where T <: Number | ||
| new("AxisymmetricTokamakEquilibriumToroidalRegularization", R₀, B₀, q₀) | ||
| end | ||
| end | ||
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| AxisymmetricTokamakToroidalRegularizationEquilibrium(R₀::T=DEFAULT_R₀, B₀::T=DEFAULT_B₀, q₀::T=DEFAULT_q₀) where T <: Number = AxisymmetricTokamakToroidalRegularizationEquilibrium{T}(R₀, B₀, q₀) | ||
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| function Base.show(io::IO, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) | ||
| print(io, "Axisymmetric Tokamak Equilibrium with Toroidal Regularization in Circular Coordinates with\n") | ||
| print(io, " R₀ = ", equ.R₀, "\n") | ||
| print(io, " B₀ = ", equ.B₀, "\n") | ||
| print(io, " q₀ = ", equ.q₀) | ||
| end | ||
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| r(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = x[1] | ||
| θ(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = x[2] | ||
| ϕ(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = x[3] | ||
| R(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = equ.R₀ + r(x,equ) * cos(θ(x,equ)) | ||
| X(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = R(x,equ) * cos(ϕ(x,equ)) | ||
| Y(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = R(x,equ) * sin(ϕ(x,equ)) | ||
| Z(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = r(x,equ) * sin(θ(x,equ)) | ||
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| ElectromagneticFields.J(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = r(x,equ) * R(x,equ) | ||
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| ElectromagneticFields.A₁(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = zero(eltype(x)) | ||
| ElectromagneticFields.A₂(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = + equ.B₀ * equ.R₀ / cos(θ(x,equ))^2 * ( r(x,equ) * cos(θ(x,equ)) - equ.R₀ * log(R(x,equ) / equ.R₀) ) | ||
| ElectromagneticFields.A₃(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = + equ.B₀ * r(x,equ)^2 / equ.q₀ / 2 | ||
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| ElectromagneticFields.x¹(ξ::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = X(ξ,equ) | ||
| ElectromagneticFields.x²(ξ::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = Y(ξ,equ) | ||
| ElectromagneticFields.x³(ξ::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = Z(ξ,equ) | ||
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| ElectromagneticFields.ξ¹(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = sqrt((sqrt(x[1]^2 + x[2]^2)-equ.R₀)^2 + x[3]^2) | ||
| ElectromagneticFields.ξ²(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = atan(x[3], sqrt(x[1]^2 + x[2]^2)-equ.R₀) | ||
| ElectromagneticFields.ξ³(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = atan(x[2], x[1]) | ||
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| ElectromagneticFields.g₁₁(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = one(eltype(x)) | ||
| ElectromagneticFields.g₂₂(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = r(x, equ)^2 | ||
| ElectromagneticFields.g₃₃(x::AbstractVector, equ::AxisymmetricTokamakToroidalRegularizationEquilibrium) = R(x, equ)^2 | ||
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| ElectromagneticFields.get_functions(::AxisymmetricTokamakToroidalRegularizationEquilibrium) = (X=X, Y=Y, Z=Z, R=R, r=r, θ=θ, ϕ=ϕ) | ||
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| function ElectromagneticFields.periodicity(x::AbstractVector, ::AxisymmetricTokamakToroidalRegularizationEquilibrium) | ||
| p = zero(x) | ||
| p[2] = 2π | ||
| p[3] = 2π | ||
| return p | ||
| end | ||
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| macro axisymmetric_tokamak_equilibrium_toroidal_regularisation(R₀, B₀, q₀) | ||
| generate_equilibrium_code(AxisymmetricTokamakToroidalRegularizationEquilibrium(R₀, B₀, q₀); output=false) | ||
| end | ||
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| function init(R₀=DEFAULT_R₀, B₀=DEFAULT_B₀, q₀=DEFAULT_q₀; perturbation=ZeroPerturbation()) | ||
| equilibrium = AxisymmetricTokamakToroidalRegularizationEquilibrium(R₀, B₀, q₀) | ||
| load_equilibrium(equilibrium, perturbation; target_module=AxisymmetricTokamakToroidalRegularization) | ||
| return equilibrium | ||
| end | ||
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| end |
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