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SCmomentumAperture.m
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SCmomentumAperture.m
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function dbounds = SCmomentumAperture(RING,REFPTS,inibounds,varargin)
% SCmomentumAperture
% ==================
%
% NAME
% ----
% SCmomentumAperture - Calculates the momentum aperture
%
% SYNOPSIS
% --------
% `dbounds = SCmomentumAperture(RING, REFPTS, inibound [, options])`
%
%
% DESCRIPTION
% -----------
% Calculates the momentum aperture of `RING` at the given `REFPTS`. `dbounds`
% is a `[2,length(REFPTS)]`-array containing the upper and lower bounds of the
% local momentum aperture either the positive (default) or negative direction,
% depending on the sign of `'inibounds'`, which is an initial guess for the
% bounds of the momentum apeture. This is automatically refined in this
% routine, so a rough guess is good enough.
%
%
% INPUT
% -----
% `RING`::
% Lattice cell structure.
% `REFPTS`::
% `[1xN]` array of lattice ordinates at which the MA should be calculated.
% `inibounds`::
% `[inner,outer]` array of inner and outer bounds intial guess for the MA.
%
%
% OPTIONS
% -------
% The following options can be given as name/value-pairs:
%
% `'nturns'` (1000)::
% is the number of turns used to determine whether a particle is stable.
% `'accuracy'`(1e-4)::
% is the accuracy to which the momentum aperture is determined.
% `'stepsize'`(1e-3)::
% stepsize, with which the boundaries are expanded, when the critial
% point is not within them.
% `'debug'` (0)::
% if true, debug information is printed.
% `'plot'` (0)::
% if true, results are plotted.
%
% GLOBALS
% -------
% `runParallel`:: If true, a parfor loop is executed instead of a regular for loop.
%
% RETURN VALUE
% ------------
% `dbounds`:: `2xlength(REFPTS)` array containing the local momentum apertures
% bounds.
%
%
% EXAMPLES
% --------
% Calculates the positive MA bounds for the first 10 lattice elements of `SC.RING` with
% intial guess of [0,4E-2] over 1000 turns. Debug information is printed and the results
% are plotted.
% ------------------------------------------------------------------
% dbounds = SCmomentumAperture(SC.RING,1:10,[0,4E-2],'debug',1,'plot',1);
% ------------------------------------------------------------------
%
% Calculates the negative MA bounds at all `SD` magnets of `SC.RING` with the initial
% guess of [-5E-3,-2E-2] over 10000 turns in parallel mode.
% ------------------------------------------------------------------
% ords = SCgetOrds(SC.RING,'SD');
% global runParallel
% runParallel = 1;
% dbounds = SCmomentumAperture(SC.RING,ords,[-5E-3,-2E-2],'nturns',10000);
% ------------------------------------------------------------------
% Parse input
p = inputParser;
addOptional(p,'nturns',1000);
addOptional(p,'accuracy',1e-4);
addOptional(p,'stepsize',1e-3);
addOptional(p,'plot',0);
addOptional(p,'debug',0);
parse(p,varargin{:});
par = p.Results;
% Check if parallel computation should be used
global runParallel
if runParallel
parforArg = Inf;
else
parforArg = 0;
end
% Initialize output arrays
dboundHI = zeros(length(REFPTS),1);
dboundLO = zeros(length(REFPTS),1);
% Closed orbits at reference points
ZCOs = findorbit6(RING,REFPTS);
if any(~isfinite(ZCOs(:)))
dbounds = [dboundHI,dboundLO];
warning('Closed Orbit could not be determined during MA evaluation. MA set to zero.');
return;
end
% Loop over reference points
parfor (i=1:length(REFPTS),parforArg)
ord = REFPTS(i);
% Reset bounds to initial values
local_bounds=inibounds;
% Shift so that ord-th element is the first
SHIFTRING = circshift(RING,-ord+1);
% Closed orbit at current element
ZCO = ZCOs(:,i);
% Scale boundaries up until dp is included
while ~check_bounds(local_bounds,SHIFTRING,ZCO,par.nturns)
local_bounds = increment_bounds(local_bounds,par.stepsize);
if par.debug; fprintf('ord: %d; Incremented: %+0.5e %+0.5e\n',ord,local_bounds(1),local_bounds(2)); end
end
% Refine boundaries until requested accuracy is reached
while abs((local_bounds(2)-local_bounds(1))/max(local_bounds)) > par.accuracy
local_bounds = refine_bounds(local_bounds,SHIFTRING,ZCO,par.nturns);
if par.debug; fprintf('ord: %d; Refined: %e %e\n',ord,local_bounds(1),local_bounds(2)); end
end
% Store final boundaries
dboundHI(i) = local_bounds(1);
dboundLO(i) = local_bounds(2);
if par.debug; fprintf('ord: %d; Found: %+0.5e %+0.5e\n',ord,local_bounds(1),local_bounds(2)); end
end
% Store function output
dbounds = [dboundHI,dboundLO];
% Plot results
if par.plot
spos=findspos(RING,REFPTS);
figure(81222);clf;hold on;
plot(spos,dboundHI,'kx-');
plot(spos,dboundLO,'rx-');
xlabel('s [m]');ylabel('MA');drawnow;
end
end
function local_bounds = refine_bounds(local_bounds,RING,ZCO,nturns)
% bounds shall be absolute-ordered i.e.
% [0.1,0.2] or [-0.1,-0.3]
dmean = mean(local_bounds);
% Add momentum deviations to closed orbit
Z0 = ZCO;
Z0(5) = Z0(5) + dmean;
% Track
ROUT = atpass(RING,Z0,1,nturns,[]);
if isnan(ROUT(1)) % Particle dead :(
local_bounds(2) = dmean; % Set abs-upper bound to midpoint
else % Particle alive :)
local_bounds(1) = dmean; % Set abs-lower bound to midpoint
end
end
function check = check_bounds(local_bounds,RING,ZCO,nturns)
% Returns true when the lower (upper) bound is (un)stable
% Add momentum deviations to closed orbit
Z=[ZCO,ZCO];
Z(5,:)=Z(5,:)+local_bounds(:)';
% Track
ROUT = atpass(RING,Z,1,nturns,[]);
% Throw error if the less-deviating particle is unstable and the other is not
if isnan(ROUT(1,1)) && ~isnan(ROUT(1,2))
warning('Closer-to-momentum particle is unstable. This shouldnt be!');
end
% Closer-to-momentum should be stable,
% farther-from-momentum particle should be unstable
check = ~isnan(ROUT(1,1)) && isnan(ROUT(1,2));
end
function local_bounds = increment_bounds(local_bounds,stepsize)
local_bounds = local_bounds + [-1,1] .* mysign(local_bounds)*stepsize;
end
function s = mysign(v)
s = 1 - 2 * (v<0);
end
function out = scale_bounds(local_bounds,alpha)
lower = mean(local_bounds)-(mean(local_bounds)-local_bounds(1)) * alpha;
upper = mean(local_bounds)-(mean(local_bounds)-local_bounds(2)) * alpha;
% Prohibit zero-crossing during scaling
if sign(lower) ~= sign(local_bounds(1))
lower = 0.0;
end
if sign(upper) ~= sign(local_bounds(2))
upper = 0.0;
end
out = [lower,upper];
end