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MatchTheTunes.html
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.S12 { 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 0px 4px 4px; 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; }</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>Matching the phase advances (Section 3.6.1)</span></h1><div class = 'S0'><span>Volker Ziemann, 211107, CC-BY-SA-4.0</span></div><div class = 'S0'><span style=' font-weight: bold;'>Important: </span><span>requires the functions for the 4D calculations, available in the </span><span style=' font-family: monospace;'>chap3/4D</span><span> subdirectory from the zip file with all MATLAB scripts. Needed for </span><span style=' font-family: monospace;'>calcmat()</span><span> and </span><span style=' font-family: monospace;'>plot_betas(). </span></div><div class = 'S0'><span>In this example we will start from the FODO cell that we used before and will find focal lengths of the two quadrupoles that will cause the horizontal pahse advace of one cell to be </span><span texencoding="60^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> and the vertical phase advance to be </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span>. Colloquially we sat that we set the tune per cell to 1/6 and 1/4. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span style="color: rgb(2, 128, 9);">% match the tunes in a FODO cell</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >clear </span><span style="color: rgb(170, 4, 249);">all</span><span >; close </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);">./4D</span><span > </span><span style="color: rgb(2, 128, 9);">% use the 4D software</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">global </span><span >beamline</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >F=2.1;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >fodo=[ 1, 5, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > 2, 1, 0.0, -F; </span><span style="color: rgb(2, 128, 9);">% QD</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><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, 0.0, F; </span><span style="color: rgb(2, 128, 9);">% QF</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S4'><span style="white-space: pre"><span > 1, 5, 0.2, 0] </span></span></div><div class = 'S5'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="0AFBF1CE" data-scroll-top="null" data-scroll-left="null" data-width="1334" data-testid="output_0" style="width: 1364px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1334px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">fodo = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">5×4</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":4,"totalRows":5,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 290px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 1.0000 5.0000 0.2000 0
2.0000 1.0000 0 -2.1000
1.0000 10.0000 0.2000 0
2.0000 1.0000 0 2.1000
1.0000 5.0000 0.2000 0
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div><div class="inlineWrapper"><div class = 'S6'><span style="white-space: pre"><span >beamline=fodo;</span></span></div></div></div><div class = 'S7'><span>Now we are ready to calculate the transfer matrices Racc, the periodic beam matrix sigma0 that we use as initial value for plotting the beta functions.</span></div><div class="CodeBlock"><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >[Racc,spos]=calcmat(beamline); Rend=Racc(:,:,end)</span></span></div><div class = 'S5'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="BD451E5B" data-scroll-top="null" data-scroll-left="null" data-width="1334" data-testid="output_1" style="width: 1364px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1334px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Rend = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">4×4</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":4,"totalRows":4,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 290px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 1.4989 3.5465 0 0
-0.4535 -0.4059 0 0
0 0 -0.4059 3.5465
0 0 -0.4535 1.4989
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">
</div></div></div></div></div></div></div><div class="inlineWrapper outputs"><div class = 'S10'><span style="white-space: pre"><span >Q=tunes(Rend)</span></span></div><div class = 'S5'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="0935E70C" data-scroll-top="null" data-scroll-left="null" data-width="1334" data-testid="output_3" style="width: 1364px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1334px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Q = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">1×2</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":2,"totalRows":1,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 146px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 0.1580 0.1580
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><div class = 'S7'><span>Here we use service functions to calculate the periodic beam matrix (with emittances set to 1), plotting the beta functions, drawing the magnet lattice and calculating the tunes. Note that we find the tunes to be 0.158 in both transverse planes. But we want them to be 1/6 and 1/4 instead, so we define a chisq function (see below) that varies the focal lengths of the quads and returns the squared difference between the desired and the actually acheived tunes. We then pass this function</span><span style=' font-family: monospace;'> chisq_tunes()</span><span> to</span><span style=' font-family: monospace;'> fminsearch() </span><span>to find the new focal lengths.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >f0=[2,-2]; </span><span style="color: rgb(2, 128, 9);">% starting guess</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S4'><span style="white-space: pre"><span >[f,fval]=fminsearch(@chisq_tunes,f0)</span></span></div><div class = 'S5'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="03C53446" data-scroll-top="null" data-scroll-left="null" data-width="1334" data-testid="output_4" style="width: 1364px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1334px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">f = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">1×2</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":2,"totalRows":1,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 146px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 1.8081 -1.4748
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>fval = 4.7549e-11</div></div></div></div><div class = 'S7'><span>Once we have the quad settings, we update all transfer matrices, calculate the periodic beam matrix, open a new figure and plot the beta functions and a the postions of the magnets with </span><span style=' font-family: monospace;'>drawmag()</span><span>. Finally we calculate the tunes and verify that they are indeed 0.1666 and 0.25 and then write the beamline description with the new quad settings to a file called </span><span style=' font-family: monospace;'>fodo6090.bl.</span></div><div class="CodeBlock"><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >[Racc,spos]=calcmat(beamline); Rend=Racc(:,:,end)</span></span></div><div class = 'S5'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="C516B960" data-scroll-top="null" data-scroll-left="null" data-width="1334" data-testid="output_6" style="width: 1364px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1334px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Rend = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">4×4</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":4,"totalRows":4,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 290px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> -0.7312 3.6250 0 0
-0.6250 1.7311 0 0
0 0 1.2311 2.8750
0 0 -0.8750 -1.2311
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >sigma0=periodic_beammatrix(Rend,1,1);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >figure</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >plot_betas(beamline,sigma0); </span></span></div></div><div class="inlineWrapper outputs"><div class = 'S4'><span style="white-space: pre"><span >drawmag(beamline,1,1)</span></span></div><div class = 'S5'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="C99BA33B" data-scroll-top="null" data-scroll-left="null" data-testid="output_7" style="width: 1364px;"><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_4" widgetid="uniqName_333_4" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_8" widgetid="uniqName_333_8" style="width: 100%; height: auto;">
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">
</div></div></div></div></div></div></div><div class="inlineWrapper outputs"><div class = 'S10'><span style="white-space: pre"><span >Q=tunes(Rend)</span></span></div><div class = 'S5'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="94ED474F" data-scroll-top="null" data-scroll-left="null" data-width="1334" data-testid="output_8" style="width: 1364px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1334px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Q = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">1×2</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":2,"totalRows":1,"charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 146px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 0.1667 0.2500
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div><div class="inlineWrapper"><div class = 'S6'><span style="white-space: pre"><span >dlmwrite(</span><span style="color: rgb(170, 4, 249);">'fodo6090.bl'</span><span >,beamline,</span><span style="color: rgb(170, 4, 249);">'\t'</span><span >)</span></span></div></div></div><div class = 'S7'><span>If we want to work with these cells further, we simply load </span><span style=' font-family: monospace;'>fodo6090.bl </span><span>with</span><span style=' font-family: monospace;'> dlmread()</span><span> and use it as the starting point for further explorations.</span></div><h2 class = 'S11'><span>chisq_tunes()</span></h2><div class = 'S0'><span>This following function</span><span style=' font-family: monospace;'> chisq_tunes() </span><span>receives the focal lenths as input, and returns the squared difference between the desired and the actually calculated tunes. Inside the function first the focal lenths in the fourth column of entry 2 and 4 of the beamline are updated, then the tranbsfer matrices are updated and the tunes are extracted, before the difference to the desired values is determined.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >chisq=chisq_tunes(x)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">global </span><span >beamline </span><span style="color: rgb(2, 128, 9);">% need info about the beamline</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >beamline(2,4)=x(1); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >beamline(4,4)=x(2);</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 class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Rturn=Racc(:,:,end); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >[Qx,alpha0x,beta0x,gamma0x]=R2beta(Rturn(1:2,1:2));</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >[Qy,alpha0y,beta0y,gamma0y]=R2beta(Rturn(3:4,3:4));</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >chisq=(Qx-1/6)^2+(Qy-0.25)^2; </span><span style="color: rgb(2, 128, 9);">% desired tunes</span></span></div></div><div class="inlineWrapper"><div class = 'S12'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div>
<br>
<!--
##### SOURCE BEGIN #####
%%
% Companion software for "Volker Ziemann, _Hands-on Accelerator physics using
% MATLAB, CRCPress, 2019_" (https://www.crcpress.com/9781138589940)
%% Matching the phase advances (Section 3.6.1)
% Volker Ziemann, 211107, CC-BY-SA-4.0
%
% *Important:* requires the functions for the 4D calculations, available in
% the |chap3/4D| subdirectory from the zip file with all MATLAB scripts. Needed
% for |calcmat()| and |plot_betas().|
%
% In this example we will start from the FODO cell that we used before and
% will find focal lengths of the two quadrupoles that will cause the horizontal
% pahse advace of one cell to be $60^o$ and the vertical phase advance to be $90^o$.
% Colloquially we sat that we set the tune per cell to 1/6 and 1/4.
% match the tunes in a FODO cell
clear all; close all
addpath ./4D % use the 4D software
global beamline
F=2.1;
fodo=[ 1, 5, 0.2, 0;
2, 1, 0.0, -F; % QD
1, 10, 0.2, 0;
2, 1, 0.0, F; % QF
1, 5, 0.2, 0]
beamline=fodo;
%%
% Now we are ready to calculate the transfer matrices Racc, the periodic beam
% matrix sigma0 that we use as initial value for plotting the beta functions.
[Racc,spos]=calcmat(beamline); Rend=Racc(:,:,end)
sigma0=periodic_beammatrix(Rend,1,1);
plot_betas(beamline,sigma0);
drawmag(beamline,1,1)
Q=tunes(Rend)
%%
% Here we use service functions to calculate the periodic beam matrix (with
% emittances set to 1), plotting the beta functions, drawing the magnet lattice
% and calculating the tunes. Note that we find the tunes to be 0.158 in both transverse
% planes. But we want them to be 1/6 and 1/4 instead, so we define a chisq function
% (see below) that varies the focal lengths of the quads and returns the squared
% difference between the desired and the actually acheived tunes. We then pass
% this function |chisq_tunes()| to |fminsearch()| to find the new focal lengths.
f0=[2,-2]; % starting guess
[f,fval]=fminsearch(@chisq_tunes,f0)
%%
% Once we have the quad settings, we update all transfer matrices, calculate
% the periodic beam matrix, open a new figure and plot the beta functions and
% a the postions of the magnets with |drawmag()|. Finally we calculate the tunes
% and verify that they are indeed 0.1666 and 0.25 and then write the beamline
% description with the new quad settings to a file called |fodo6090.bl.|
[Racc,spos]=calcmat(beamline); Rend=Racc(:,:,end)
sigma0=periodic_beammatrix(Rend,1,1);
figure
plot_betas(beamline,sigma0);
drawmag(beamline,1,1)
Q=tunes(Rend)
dlmwrite('fodo6090.bl',beamline,'\t')
%%
% If we want to work with these cells further, we simply load |fodo6090.bl|
% with |dlmread()| and use it as the starting point for further explorations.
%% chisq_tunes()
% This following function |chisq_tunes()| receives the focal lenths as input,
% and returns the squared difference between the desired and the actually calculated
% tunes. Inside the function first the focal lenths in the fourth column of entry
% 2 and 4 of the beamline are updated, then the tranbsfer matrices are updated
% and the tunes are extracted, before the difference to the desired values is
% determined.
function chisq=chisq_tunes(x)
global beamline % need info about the beamline
beamline(2,4)=x(1);
beamline(4,4)=x(2);
[Racc,spos]=calcmat(beamline);
Rturn=Racc(:,:,end);
[Qx,alpha0x,beta0x,gamma0x]=R2beta(Rturn(1:2,1:2));
[Qy,alpha0y,beta0y,gamma0y]=R2beta(Rturn(3:4,3:4));
chisq=(Qx-1/6)^2+(Qy-0.25)^2; % desired tunes
end
##### SOURCE END #####
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