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OneDimensionalTracking.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge,IE=9,chrome=1"><meta name="generator" content="MATLAB 2021a"><title>One-dimensional tracking (Section 11.1)</title><style type="text/css">.rtcContent { padding: 30px; } .S0 { margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(0, 0, 0); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: normal; text-align: left; }
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.S9 { margin: 10px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(0, 0, 0); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: normal; text-align: left; }
.S10 { border-left: 1px solid rgb(233, 233, 233); border-right: 1px solid rgb(233, 233, 233); border-top: 1px solid rgb(233, 233, 233); border-bottom: 1px solid rgb(233, 233, 233); border-radius: 0px 0px 4px 4px; padding: 6px 45px 4px 13px; line-height: 17.234px; min-height: 18px; white-space: nowrap; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 14px; }</style></head><body><div class = rtcContent><div class = 'S0'><span>Companion software for "Volker Ziemann, </span><span style=' font-style: italic;'>Hands-on Accelerator physics using MATLAB, CRCPress, 2019</span><span>" (https://www.crcpress.com/9781138589940)</span></div><h1 class = 'S1'><span>One-dimensional tracking (Section 11.1)</span></h1><div class = 'S0'><span>Volker Ziemann, 211120</span></div><div class = 'S0'><span>In this example we show the phase-space plot of a ring where a single sextupole provides the non-linearity that is defined by Equation 11.3. We follow particles with increasing initial values for 1024 iterations and plot a dot at their phase-space coordinate after every iteration.</span></div><div class = 'S0'><span>We first define teh number of turns to follow and provide a selection of tunes </span><span style=' font-family: monospace;'>Q</span><span> to choose from and a slider to set the offset </span><span style=' font-family: monospace;'>dx</span><span>. Then we define the transfer matrix, which is just a rotation matrix with phase advance given by </span><span texencoding="2\pi Q" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="29" height="18" /></span><span>. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >clear </span><span style="color: rgb(170, 4, 249);">all</span><span >;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Nturn=1024;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Qstr=</span></span><span style="color: rgb(170, 4, 249);">"0.2526"</span><span style="white-space: pre"><span >; </span><span style="color: rgb(2, 128, 9);">% select tune</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S4'><span style="white-space: pre"><span >Q=str2double(Qstr)</span></span></div><div class = 'S5'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>Q = 0.2526</div></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >dx=</span></span><span>0</span><span style="white-space: pre"><span > </span><span style="color: rgb(2, 128, 9);">% misalignment</span></span></div><div class = 'S5'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>dx = 0</div></div></div><div class="inlineWrapper"><div class = 'S7'><span style="white-space: pre"><span >R=@(mu)[cos(mu),sin(mu);-sin(mu),cos(mu)];</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >RR=R(2*pi*Q);</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >clf</span></span></div></div></div><div class = 'S9'><span>With the preliminaries defined, we set the sacle of the axes and loop over initial starting values</span><span style=' font-family: monospace;'> x0</span><span>.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >hold </span><span style="color: rgb(170, 4, 249);">on</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >axis([-1.2,1.2,-1.2,1.2]); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >title([</span><span style="color: rgb(170, 4, 249);">'Q = '</span><span >,num2str(Q,4),</span><span style="color: rgb(170, 4, 249);">', dx = '</span><span >,num2str(dx,2)]);</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >x0=0.05:0.05:2</span></span></div></div></div><div class = 'S9'><span>For each starting value we allocate an array data to hold the phase-space coordinates after each iteration and set the start coordinate, before iterating </span><span style=' font-family: monospace;'>Nturn</span><span> times. In each iteration we apply Equation 11.3 and store the coordinate in data. If the coorsinate is larger than 3, we break the iteration.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > data=zeros(2,Nturn);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x=[x0;0]; </span><span style="color: rgb(2, 128, 9);">% start coordinates</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">for </span><span >n=1:Nturn</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x=RR*[x(1);x(2)-(x(1)-dx)^2];</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >(abs(x(1))>3) </span><span style="color: rgb(14, 0, 255);">break</span><span >; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(:,n)=x;</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S9'><span>And finally we display the phase-space points as a black dot and give MATLAB a little time to update the display and annotate the axes.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > plot(data(1,1:n),data(2,1:n),</span><span style="color: rgb(170, 4, 249);">'k.'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > pause(0.001)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S4'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'x'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'x'''</span><span >)</span></span></div><div class = 'S5'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="007C1DD8" data-scroll-top="null" data-scroll-left="null" data-testid="output_2" style="width: 1327px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" 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<!--
##### SOURCE BEGIN #####
%%
% Companion software for "Volker Ziemann, _Hands-on Accelerator physics using
% MATLAB, CRCPress, 2019_" (https://www.crcpress.com/9781138589940)
%% One-dimensional tracking (Section 11.1)
% Volker Ziemann, 211120
%
% In this example we show the phase-space plot of a ring where a single sextupole
% provides the non-linearity that is defined by Equation 11.3. We follow particles
% with increasing initial values for 1024 iterations and plot a dot at their phase-space
% coordinate after every iteration.
%
% We first define teh number of turns to follow and provide a selection of tunes
% |Q| to choose from and a slider to set the offset |dx|. Then we define the transfer
% matrix, which is just a rotation matrix with phase advance given by $2\pi Q$.
clear all;
Nturn=1024;
Qstr="0.2526"; % select tune
Q=str2double(Qstr)
dx=0 % misalignment
R=@(mu)[cos(mu),sin(mu);-sin(mu),cos(mu)];
RR=R(2*pi*Q);
clf
%%
% With the preliminaries defined, we set the sacle of the axes and loop over
% initial starting values |x0|.
hold on
axis([-1.2,1.2,-1.2,1.2]);
title(['Q = ',num2str(Q,4),', dx = ',num2str(dx,2)]);
for x0=0.05:0.05:2
%%
% For each starting value we allocate an array data to hold the phase-space
% coordinates after each iteration and set the start coordinate, before iterating
% |Nturn| times. In each iteration we apply Equation 11.3 and store the coordinate
% in data. If the coorsinate is larger than 3, we break the iteration.
data=zeros(2,Nturn);
x=[x0;0]; % start coordinates
for n=1:Nturn
x=RR*[x(1);x(2)-(x(1)-dx)^2];
if (abs(x(1))>3) break; end
data(:,n)=x;
end
%%
% And finally we display the phase-space points as a black dot and give MATLAB
% a little time to update the display and annotate the axes.
plot(data(1,1:n),data(2,1:n),'k.')
pause(0.001)
end
xlabel('x'); ylabel('x''')
%%
%
##### SOURCE END #####
-->
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