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DispersionSuppressor.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>Dispersion suppressor (Section 3.7.7)</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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.S6 { border-left: 1px solid rgb(233, 233, 233); border-right: 1px solid rgb(233, 233, 233); border-top: 0px none rgb(0, 0, 0); border-bottom: 1px solid rgb(233, 233, 233); border-radius: 0px; padding: 0px 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; }
.S7 { color: rgb(64, 64, 64); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% / auto padding-box border-box; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; }</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>Dispersion suppressor (Section 3.7.7)</span></h1><div class = 'S0'><span>Volker Ziemann, 211119</span></div><div class = 'S0'><span>In this example we illustrate the code that generated Figure 3.30 with the dispersion suppressor in a 90-degree FODO lattice. The suppressor consists of two FODO cells where the full-length dipole magnets are replaced by half-length dipoles.</span></div><div class = 'S0'><span>First we need to add support for the 3D calculations...</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></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >addpath </span><span style="color: rgb(170, 4, 249);">./3D</span><span > </span><span style="color: rgb(2, 128, 9);">% contains the support functions, such as calcmat() </span></span></div></div></div><div class = 'S4'><span>...and define the regular FODO cells that are used in the arcs. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >fodo=[ </span><span style="color: rgb(2, 128, 9);">% regular FODO cell in arc</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0, 8.5511; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 5, 0.2, 0;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 4, 8, 0.5, 1; </span><span style="color: rgb(2, 128, 9);">% 8x0.5m = 4 m long dipole</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 5, 0.2, 0;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0, -4.2483;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 5, 0.2, 0;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 4, 8, 0.5, 1; </span><span style="color: rgb(2, 128, 9);">% 4 m long dipole</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 5, 0.2, 0;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > 2, 1, 0, 8.5511];</span></span></div></div></div><div class = 'S4'><span>The FODO cell in the disp[ersion suppressor is very similar, only the dipoles are shorter and the adjacent drift spaces are a bit longer in order to maintina the length of the cell. Note also that the quadrupoles excitations are the same in both types of cells. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >fodods=[ </span><span style="color: rgb(2, 128, 9);">% FODO cell in dispersion suppressor</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0, 8.5511; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 10, 0.2, 0 ;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 4, 4, 0.5, 1; </span><span style="color: rgb(2, 128, 9);">% 4x0.5m = 2 m long dipole</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 10, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0, -4.2483; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 10, 0.2, 0 ;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 4, 4, 0.5, 1 ; </span><span style="color: rgb(2, 128, 9);">% 2 m long dipole</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 10, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > 2, 1, 0, 8.5511];</span></span></div></div></div><div class = 'S4'><span>Now we calculate the periodic dispersion in an arc cell, which give us the initial value </span><span style=' font-family: monospace;'>D0</span><span> for the dispersion that causes a periodic dispersion in the arcs.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >beamline=fodo; </span><span style="color: rgb(2, 128, 9);">% one arc-fodo cell</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos]=calcmat(beamline); </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Rend=Racc(:,:,end);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >D0=periodic_dispersion(Rend);</span></span></div></div></div><div class = 'S4'><span>In order to verify that the disperison is periodic we plot it</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >D=calculate_dispersion(beamline,D0);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >plot(spos,D,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">' s[m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'D_x [m]'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >drawmag(beamline,0.2,0.2)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'Dispersion in one arc cell'</span><span >)</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="636D4625" data-scroll-top="null" data-scroll-left="null" data-testid="output_0" style="width: 1173px;"><div class="figureElement"><div class="figureContainingNode" style="width: 560px; max-width: 100%; display: inline-block;"><div class="GraphicsView" data-dojo-attach-point="graphicsViewNode,backgroundColorNode" id="uniqName_333_24" widgetid="uniqName_333_24" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_27" widgetid="uniqName_333_27" style="width: 100%; height: auto;">
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">
</div></div></div></div></div></div></div></div><div class = 'S4'><span>Now we add two dispersion suppressor cells to one arc cell and calculate all transfer matrices and the positions </span><span style=' font-family: monospace;'>spos</span><span> with </span><span style=' font-family: monospace;'>calcmat()</span><span>.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >beamline=[fodo;repmat(fodods,2,1)]; </span><span style="color: rgb(2, 128, 9);">% one arc and two suppressor cells</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >[Racc,spos]=calcmat(beamline); </span></span></div></div></div><div class = 'S4'><span>Finally, we calculate the dispersion D along the beam line and plot it. For convenience, we also add the magnet lattice to show the positions of the dipoles and their respective lengths.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >D=calculate_dispersion(beamline,D0);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >figure; plot(spos,D,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); </span><span style="color: rgb(2, 128, 9);">% Fig. 3.30</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">' s[m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'D_x [m]'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'Dispersion suppressor'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >drawmag(beamline,0.2,0.2)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >xlim([0,36.1]); </span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="0270BC01" data-scroll-top="null" data-scroll-left="null" data-testid="output_1" style="width: 1173px;"><div class="figureElement"><div class="figureContainingNode" style="width: 560px; max-width: 100%; display: inline-block;"><div class="GraphicsView" data-dojo-attach-point="graphicsViewNode,backgroundColorNode" id="uniqName_333_25" widgetid="uniqName_333_25" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_29" widgetid="uniqName_333_29" style="width: 100%; height: auto;">
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">
</div></div></div></div></div></div></div></div><div class = 'S4'><span>Note that the dispersion is not perfectly zero at the end, because weak focussing of the dipoles which is slightly different for the full-length and half-length dipoles. This can be fixed by slightly changing the quadrupole excitations. </span></div>
<br>
<!--
##### SOURCE BEGIN #####
%%
% Companion software for "Volker Ziemann, _Hands-on Accelerator physics using
% MATLAB, CRCPress, 2019_" (https://www.crcpress.com/9781138589940)
%% Dispersion suppressor (Section 3.7.7)
% Volker Ziemann, 211119
%
% In this example we illustrate the code that generated Figure 3.30 with the
% dispersion suppressor in a 90-degree FODO lattice. The suppressor consists of
% two FODO cells where the full-length dipole magnets are replaced by half-length
% dipoles.
%
% First we need to add support for the 3D calculations...
clear all
addpath ./3D % contains the support functions, such as calcmat()
%%
% ...and define the regular FODO cells that are used in the arcs.
fodo=[ % regular FODO cell in arc
2, 1, 0, 8.5511;
1, 5, 0.2, 0;
4, 8, 0.5, 1; % 8x0.5m = 4 m long dipole
1, 5, 0.2, 0;
2, 1, 0, -4.2483;
1, 5, 0.2, 0;
4, 8, 0.5, 1; % 4 m long dipole
1, 5, 0.2, 0;
2, 1, 0, 8.5511];
%%
% The FODO cell in the disp[ersion suppressor is very similar, only the dipoles
% are shorter and the adjacent drift spaces are a bit longer in order to maintina
% the length of the cell. Note also that the quadrupoles excitations are the same
% in both types of cells.
fodods=[ % FODO cell in dispersion suppressor
2, 1, 0, 8.5511;
1, 10, 0.2, 0 ;
4, 4, 0.5, 1; % 4x0.5m = 2 m long dipole
1, 10, 0.2, 0;
2, 1, 0, -4.2483;
1, 10, 0.2, 0 ;
4, 4, 0.5, 1 ; % 2 m long dipole
1, 10, 0.2, 0;
2, 1, 0, 8.5511];
%%
% Now we calculate the periodic dispersion in an arc cell, which give us the
% initial value |D0| for the dispersion that causes a periodic dispersion in the
% arcs.
beamline=fodo; % one arc-fodo cell
[Racc,spos]=calcmat(beamline);
Rend=Racc(:,:,end);
D0=periodic_dispersion(Rend);
%%
% In order to verify that the disperison is periodic we plot it
D=calculate_dispersion(beamline,D0);
plot(spos,D,'k');
xlabel(' s[m]'); ylabel('D_x [m]');
drawmag(beamline,0.2,0.2)
title('Dispersion in one arc cell')
%%
% Now we add two dispersion suppressor cells to one arc cell and calculate all
% transfer matrices and the positions |spos| with |calcmat()|.
beamline=[fodo;repmat(fodods,2,1)]; % one arc and two suppressor cells
[Racc,spos]=calcmat(beamline);
%%
% Finally, we calculate the dispersion D along the beam line and plot it. For
% convenience, we also add the magnet lattice to show the positions of the dipoles
% and their respective lengths.
D=calculate_dispersion(beamline,D0);
figure; plot(spos,D,'k'); % Fig. 3.30
xlabel(' s[m]'); ylabel('D_x [m]');
title('Dispersion suppressor')
drawmag(beamline,0.2,0.2)
xlim([0,36.1]);
%%
% Note that the dispersion is not perfectly zero at the end, because weak focussing
% of the dipoles which is slightly different for the full-length and half-length
% dipoles. This can be fixed by slightly changing the quadrupole excitations.
##### SOURCE END #####
-->
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