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BeamBeamTracking.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>Beam-beam tracking (Section 9.7)</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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.S8 { 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; }
.S9 { margin: 3px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: bold; text-align: left; }</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>Beam-beam tracking (Section 9.7)</span></h1><div class = 'S0'><span>Volker Ziemann, 211114, CC-BY-SA-4.0</span></div><div class = 'S0'><span style=' font-weight: bold;'>Important:</span><span> requires the Faddeeva package from </span><a href = "https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package-complex-error-functions"><span>https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package-complex-error-functions</span></a><span>.</span></div><div class = 'S0'><span>In this example we simulate a so-called </span><span style=' font-weight: bold;'>van-der-Meer scan</span><span>, where we move one beam transversely across the counter-propagating beam while they are colliding. The electro-magnetic forces cause the closed orbit of the two beams to slighly deform and couples the betatron oscillations of the two beams. We use the parameters of an early version of the B-factory in the PEP tunnel at SLAC where 9 GeV electrons collide with 3.1 GeV positrons.</span></div><div class = 'S0'><span>First we define a few quantities that we later need to post-process data. Note that we pass some quantities as </span><span style=' font-family: monospace;'>global</span><span> variables to functions.</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 >; close </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 >addpath </span><span style="color: rgb(170, 4, 249);">./Faddeeva</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 >Re Rp kapsig Ne Np egamma pgamma Relec</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >degree=pi/180;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Nfft=1024; tune=(0:Nfft/2-1)/Nfft; </span><span style="color: rgb(2, 128, 9);">% axis for fft plots</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >Relec=2.8179e-15; </span><span style="color: rgb(2, 128, 9);">% classical electron radius</span></span></div></div></div><div class = 'S5'><span>Now we define the beam parameters of the electron beam at the interaction point</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >egamma=9e9/511e3; </span><span style="color: rgb(2, 128, 9);">% 9 GeV</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Ne=3.883e10; </span><span style="color: rgb(2, 128, 9);">% particles per bunch</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >emitx=4e-8; betax=1; Qx=0.64; </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >emity=2e-9; betay=0.05; Qy=0.57;</span></span></div></div></div><div class = 'S5'><span>and those of the couter-propagating positron bunch.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >pgamma=3.1e9/511e3; </span><span style="color: rgb(2, 128, 9);">% 3.1 GeV</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Np=5.632e10; </span><span style="color: rgb(2, 128, 9);">% particles per bunch</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >pmitx=4e-8; pbetax=1; pQx=0.64; </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >pmity=2e-9; pbetay=0.05; pQy=0.57;</span></span></div></div></div><div class = 'S5'><span style=' font-family: monospace;'>Re </span><span>is the </span><span texencoding="4\times4" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="34.5" height="18" /></span><span> transfer matrix for the electron beam for one turn in the storage ring and </span><span style=' font-family: monospace;'>esigxy</span><span> is a </span><span texencoding="2\times 2" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="34.5" height="18" /></span><span>matrix with the horizontal and vertical beam sizes at the IP on the diagonal.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >Rx=[cos(2*pi*Qx),betax*sin(2*pi*Qx);-sin(2*pi*Qx)/betax,cos(2*pi*Qx)]; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Ry=[cos(2*pi*Qy),betay*sin(2*pi*Qy);-sin(2*pi*Qy)/betay,cos(2*pi*Qy)]; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Re=[Rx,zeros(2,2);zeros(2,2),Ry];</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >esigxy=[emitx*betax, 0; 0, emity*betay]; </span><span style="color: rgb(2, 128, 9);">% electron sigma_xy at IP</span></span></div></div></div><div class = 'S5'><span style=' font-family: monospace;'>Rp</span><span> and </span><span style=' font-family: monospace;'>psigxy</span><span> are the corresponding quantities for the counter-propagating positron beam.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >Rx=[cos(2*pi*pQx),pbetax*sin(2*pi*pQx);-sin(2*pi*pQx)/pbetax,cos(2*pi*pQx)]; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Ry=[cos(2*pi*pQy),pbetay*sin(2*pi*pQy);-sin(2*pi*pQy)/pbetay,cos(2*pi*pQy)]; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Rp=[Rx,zeros(2,2);zeros(2,2),Ry];</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >psigxy=[pmitx*pbetax, 0; 0, pmity*pbetay]; </span><span style="color: rgb(2, 128, 9);">% positron sigma_xy at IP</span></span></div></div></div><div class = 'S5'><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);">Σ</span><span> or </span><span style=' font-family: monospace;'>kapsig</span><span> is the sum of the transverse covariance matrices from Equation 9.20.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S6'><span style="white-space: pre"><span >kapsig=1e12*(esigxy+psigxy); </span><span style="color: rgb(2, 128, 9);">% KapSigma_xy at IP, converted to micron</span></span></div></div></div><div class = 'S0'><span>Now we are ready to horizontally scan the beams across each other in a</span><span style=' font-weight: bold;'> horizontal van-der-Meer scan</span><span>. Normally this is accomplished by small dipole magnets or electro-static separators. After allocating space for a few quantities and defining the bump settings...</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >pos=zeros(Nfft,1); </span><span style="color: rgb(2, 128, 9);">% array for positions for FFT</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >y=zeros(8,1);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >bump=-1000:50:1000; </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >data=zeros(length(bump),6);</span></span></div></div></div><div class = 'S5'><span>...we a re ready to scan. For each bump setting, we first find the distorted closed orbit with the function </span><span style=' font-family: monospace;'>fitco2()</span><span>, which is defined below in the Appendix, and store the values for displaying them later. Then we track the two beams with </span><span style=' font-family: monospace;'>trak() </span><span>and store the horizontal position of beam 1 (the electrons) in the array </span><span style=' font-family: monospace;'>pos()</span><span>. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:length(bump)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > y=fitco2(y,bump(k),0); </span><span style="color: rgb(2, 128, 9);">% finds closed orbit with beambeam kick</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(k,1:4)=[y(1),y(2),y(5),y(6)]; </span><span style="color: rgb(2, 128, 9);">% store orbits for later display</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > y(1)=y(1)+10; </span><span style="color: rgb(2, 128, 9);">% excite a betatron oscillation with 10 micron amplitude</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 >m=1:Nfft </span><span style="color: rgb(2, 128, 9);">% iterate to get tunes from FFT</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > y=trak(y,bump(k),0); pos(m)=y(1);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S5'><span>From the stored position we determine the tunes of the coupled system by Fourier-transforming</span><span style=' font-family: monospace;'> pos()</span><span> with </span><span style=' font-family: monospace;'>fft()</span><span> and finding the peaks, which we store in the array </span><span style=' font-family: monospace;'>data</span><span> for later display.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > [peaks,locs]=findpeaks(2*abs(fft(pos))/Nfft,</span><span style="color: rgb(170, 4, 249);">'MinPeakHeight'</span><span >,2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(k,5)=(locs(1)-1)/Nfft; data(k,6)=(locs(2)-1)/Nfft;</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S5'><span>Once the whole range of bump settings is done, we plot the data against the bump amplitude. The upper plot shows the deflection angle of the electron and positron bunches. Note the opposite sign and the slightly different magnitudes, which is caused by the different number of particles in the bunches and the different energies of the counter-propagating bunches.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >subplot(2,1,1); plot(bump,data(:,2),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,bump,data(:,4),</span><span style="color: rgb(170, 4, 249);">'r-.'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'Horizontal bump amplitude [\mum]'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >ylabel(</span><span style="color: rgb(170, 4, 249);">'Deflection angle [\murad]'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >legend(</span><span style="color: rgb(170, 4, 249);">'Electrons'</span><span >,</span><span style="color: rgb(170, 4, 249);">'Positrons'</span><span >)</span></span></div></div></div><div class = 'S5'><span>The lower plot shows the tunes detrmined by the call to fft(). We note that for large bunch offsets the tunes are almost equal, ebcause the bunches miss each other and do not couple. But once they are close, the beam-beam interaction couples the tunes and we see that one mode stay at the unperturbed values, while the other deviates significantly. The maximum split of the two modes occurs when the beams are colliding head-on, which is used in colliders to determine the best position of the colliding beams.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >subplot(2,1,2); plot(bump,data(:,5),</span><span style="color: rgb(170, 4, 249);">'k+'</span><span >,bump,data(:,6),</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 >xlabel(</span><span style="color: rgb(170, 4, 249);">'Horizontal bump amplitude [\mum]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'Tune Q_x'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S7'><span style="white-space: pre"><span >ylim([0.3,0.4]); </span></span></div><div class = 'S8'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="F47F482C" data-scroll-top="null" data-scroll-left="null" data-testid="output_0" style="width: 1356px;"><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_6" widgetid="uniqName_333_6" 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><div class = 'S0'><span>A </span><span style=' font-weight: bold;'>vertical van-der-Meer</span><span> scan works in much the same way as the horizontal one. We first allocate variables and define the bump amplitude.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >figure</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >y=zeros(8,1);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >bump=-100:5:100;</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >data=zeros(length(bump),4);</span></span></div></div></div><div class = 'S5'><span>An then loop over the different bump settings. At each setting we first determine the closed orbit with fitco2(), store the values and follow a slightly excited bunch for Nfft turn, while storing the vertical position.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:length(bump)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > y=fitco2(y,0,bump(k)); </span><span style="color: rgb(2, 128, 9);">% finds closed orbit with beambeam kick</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(k,1:4)=[y(3),y(4),y(7),y(8)]; </span><span style="color: rgb(2, 128, 9);">% store vertical orbits</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > y(3)=y(3)+10; </span><span style="color: rgb(2, 128, 9);">% excite a vertical betatron oscillation</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 >m=1:Nfft </span><span style="color: rgb(2, 128, 9);">% iterate to get tunes from FFT</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > y=trak(y,0,bump(k)); pos(m)=y(3);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S5'><span>As before, we the determine the tunes from the FFT, but have to take care of aliasing, because the vertical tunes are above the half integer.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > [peaks,locs]=findpeaks(2*abs(fft(pos))/Nfft,</span><span style="color: rgb(170, 4, 249);">'MinPeakHeight'</span><span >,0.5);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > Q1=(locs(1)-1)/Nfft; </span><span style="color: rgb(14, 0, 255);">if </span><span >Q1>0.5 Q1=1-Q1; </span><span style="color: rgb(14, 0, 255);">end</span><span > </span><span style="color: rgb(2, 128, 9);">% avoid aliasing</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > Q2=(locs(2)-1)/Nfft; </span><span style="color: rgb(14, 0, 255);">if </span><span >Q2>0.5 Q2=1-Q2; </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(k,5)=Q1; data(k,6)=Q2;</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S5'><span>And finally, we plot the deflection angle at the interaction point in the upper plot and the tunes in the lower plot.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >subplot(2,1,1); plot(bump,data(:,2),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,bump,data(:,4),</span><span style="color: rgb(170, 4, 249);">'r-.'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'Vertical bump amplitude [\mum]'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >ylabel(</span><span style="color: rgb(170, 4, 249);">'Deflection angle [\murad]'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >legend(</span><span style="color: rgb(170, 4, 249);">'Electrons'</span><span >,</span><span style="color: rgb(170, 4, 249);">'Positrons'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >subplot(2,1,2); plot(bump,data(:,5),</span><span style="color: rgb(170, 4, 249);">'k+'</span><span >,bump,data(:,6),</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 >xlabel(</span><span style="color: rgb(170, 4, 249);">'Verical bump amplitude [\mum]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'Tune Q_y'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S7'><span style="white-space: pre"><span >ylim([0.37,0.45]); </span></span></div><div class = 'S8'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="C1049A9D" data-scroll-top="null" data-scroll-left="null" data-testid="output_1" style="width: 1356px;"><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_9" widgetid="uniqName_333_9" style="width: 100%; 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">
</div></div></div></div></div></div></div></div><h2 class = 'S9'><span>Appendix</span></h2><div class = 'S0'><span>The function</span><span style=' font-family: monospace;'> fitco2()</span><span> determines the closed orbit distortion from the combined effect of the bump and the beam-beam deflections, where the latter depend non-linearly on the positions, which makes some iterations necessary. </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 >y=fitco2(y,xbump,ybump)</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 >Re Rp kapsig Ne Np egamma pgamma Relec</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >RSe=inv(eye(4)-Re)*Re;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >RSp=inv(eye(4)-Rp)*Rp;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >ic=20; </span><span style="color: rgb(2, 128, 9);">% iteration counter</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">while </span><span >ic>0 </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > ic=ic-1;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xsep=y(1)-y(5)+xbump; </span><span style="color: rgb(2, 128, 9);">% separation between bunch centers</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > ysep=y(3)-y(7)+ybump;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > q=F0(xsep,ysep,kapsig); </span><span style="color: rgb(2, 128, 9);">% the beam beam kick</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xk=imag(q); yk=real(q); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > exdef=-2e12*Relec*Np*xk/egamma; </span><span style="color: rgb(2, 128, 9);">% electron deflection angle</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > eydef=-2e12*Relec*Np*yk/egamma; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > pxdef=2e12*Relec*Ne*xk/pgamma; </span><span style="color: rgb(2, 128, 9);">% positron deflection angles</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > pydef=2e12*Relec*Ne*yk/pgamma;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > y(1:4)=RSe*[0;exdef;0;eydef];</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > y(5:8)=RSp*[0;pxdef;0;pydef];</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"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S5'><span>The function trak() implements one turn of the combined system of the two counter-propagating beams including the bumps and the beam-beam interactions. It just receives the </span><span texencoding="2\times 4" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="34.5" height="18" /></span><span> input coordinates </span><span texencoding="x,x',y,y'" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="58" height="18" /></span><span> for each beam and returns those positions after one turn. </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 >y=trak(y,xbump,ybump)</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 >Re Rp kapsig Ne Np egamma pgamma Relec</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >xsep=y(1)-y(5)+xbump; </span><span style="color: rgb(2, 128, 9);">% separation between bunch centers</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >ysep=y(3)-y(7)+ybump;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >q=F0(xsep,ysep,kapsig); </span><span style="color: rgb(2, 128, 9);">% the beam beam kick</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >xk=imag(q); yk=real(q); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >exdef=-2e12*Relec*Np*xk/egamma; </span><span style="color: rgb(2, 128, 9);">% electron deflection angle</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >eydef=-2e12*Relec*Np*yk/egamma; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >pxdef=2e12*Relec*Ne*xk/pgamma; </span><span style="color: rgb(2, 128, 9);">% positron deflection angles</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >pydef=2e12*Relec*Ne*yk/pgamma;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >y(2)=y(2)+exdef; y(4)=y(4)+eydef; </span><span style="color: rgb(2, 128, 9);">% electron deflection angle</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >y(6)=y(6)+pxdef; y(8)=y(8)+pydef; </span><span style="color: rgb(2, 128, 9);">% Positron deflection angle</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >y(1:4)=Re*y(1:4); </span><span style="color: rgb(2, 128, 9);">% electron transport through the ring</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >y(5:8)=Rp*y(5:8); </span><span style="color: rgb(2, 128, 9);">% positron transport through the ring</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S5'><span>The beam-beam kick depends on the function </span><span style=' font-family: monospace;'>F0()</span><span>, defined in Equation 9.28. It uses the complex error function </span><span texencoding="w(z)" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="30.5" height="19" /></span><span> which is provided by the Faddeeva package from matlab central (</span><a href = "https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package-complex-error-functions"><span>https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package-complex-error-functions</span></a><span>).</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 >out=F0(x,y,sig)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >r=1/sqrt(2*(sig(1,1)-sig(2,2)+2*i*sig(1,2)));</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >detsig=sig(1,1)*sig(2,2)-sig(1,2)^2;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >abs(r) > 1e8 </span><span style="color: rgb(2, 128, 9);">% round beam</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > out=i*(x-i*y).*(1-exp(-0.5*(x.^2+y.^2)./sig(1,1)))./(x.^2+y.^2+1e-10);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">return</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"><div class = 'S3'><span style="white-space: pre"><span >a1=r;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >a2=i*r;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >b1=r*(sig(2,2)-i*sig(1,2))/sqrt(detsig);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >b2=i*r*(sig(1,1)+i*sig(1,2))/sqrt(detsig);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >g=0.5*(sig(2,2)*x.^2-2*sig(1,2).*x.*y+sig(1,1)*y.^2)/detsig;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >z1=a1*x+a2*y;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >z2=b1*x+b2*y;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >zz1=conj(z1);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >zz2=conj(z2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >q1=(imag(z2)>=0); </span><span style="color: rgb(2, 128, 9);">% use one or the other form , depending on sign of</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >q2=1-q1; </span><span style="color: rgb(2, 128, 9);">% imaginary part of argument of w(z)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >out1=Faddeeva_w(z1)-exp(-g).*Faddeeva_w(z2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >out1(isnan(out1))=0; out1(isinf(out1))=0;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >out2=conj(Faddeeva_w(zz1)-exp(-g).*Faddeeva_w(zz2));</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >out2(isnan(out2))=0; out2(isinf(out2))=0;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >out=sqrt(pi)*r*(q1.*out1-q2.*out2);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><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)
%% Beam-beam tracking (Section 9.7)
% Volker Ziemann, 211114, CC-BY-SA-4.0
%
% *Important:* requires the Faddeeva package from <https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package-complex-error-functions
% https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package-complex-error-functions>.
%
% In this example we simulate a so-called *van-der-Meer scan*, where we move
% one beam transversely across the counter-propagating beam while they are colliding.
% The electro-magnetic forces cause the closed orbit of the two beams to slighly
% deform and couples the betatron oscillations of the two beams. We use the parameters
% of an early version of the B-factory in the PEP tunnel at SLAC where 9 GeV electrons
% collide with 3.1 GeV positrons.
%
% First we define a few quantities that we later need to post-process data.
% Note that we pass some quantities as |global| variables to functions.
clear all; close all;
addpath ./Faddeeva
global Re Rp kapsig Ne Np egamma pgamma Relec
degree=pi/180;
Nfft=1024; tune=(0:Nfft/2-1)/Nfft; % axis for fft plots
Relec=2.8179e-15; % classical electron radius
%%
% Now we define the beam parameters of the electron beam at the interaction
% point
egamma=9e9/511e3; % 9 GeV
Ne=3.883e10; % particles per bunch
emitx=4e-8; betax=1; Qx=0.64;
emity=2e-9; betay=0.05; Qy=0.57;
%%
% and those of the couter-propagating positron bunch.
pgamma=3.1e9/511e3; % 3.1 GeV
Np=5.632e10; % particles per bunch
pmitx=4e-8; pbetax=1; pQx=0.64;
pmity=2e-9; pbetay=0.05; pQy=0.57;
%%
% |Re| is the $4\times4$ transfer matrix for the electron beam for one turn
% in the storage ring and |esigxy| is a $2\times 2$matrix with the horizontal
% and vertical beam sizes at the IP on the diagonal.
Rx=[cos(2*pi*Qx),betax*sin(2*pi*Qx);-sin(2*pi*Qx)/betax,cos(2*pi*Qx)];
Ry=[cos(2*pi*Qy),betay*sin(2*pi*Qy);-sin(2*pi*Qy)/betay,cos(2*pi*Qy)];
Re=[Rx,zeros(2,2);zeros(2,2),Ry];
esigxy=[emitx*betax, 0; 0, emity*betay]; % electron sigma_xy at IP
%%
% |Rp| and |psigxy| are the corresponding quantities for the counter-propagating
% positron beam.
Rx=[cos(2*pi*pQx),pbetax*sin(2*pi*pQx);-sin(2*pi*pQx)/pbetax,cos(2*pi*pQx)];
Ry=[cos(2*pi*pQy),pbetay*sin(2*pi*pQy);-sin(2*pi*pQy)/pbetay,cos(2*pi*pQy)];
Rp=[Rx,zeros(2,2);zeros(2,2),Ry];
psigxy=[pmitx*pbetax, 0; 0, pmity*pbetay]; % positron sigma_xy at IP
%%
% $\Sigma$ or |kapsig| is the sum of the transverse covariance matrices from
% Equation 9.20.
kapsig=1e12*(esigxy+psigxy); % KapSigma_xy at IP, converted to micron
%%
% Now we are ready to horizontally scan the beams across each other in a *horizontal
% van-der-Meer scan*. Normally this is accomplished by small dipole magnets or
% electro-static separators. After allocating space for a few quantities and
% defining the bump settings...
pos=zeros(Nfft,1); % array for positions for FFT
y=zeros(8,1);
bump=-1000:50:1000;
data=zeros(length(bump),6);
%%
% ...we a re ready to scan. For each bump setting, we first find the distorted
% closed orbit with the function |fitco2()|, which is defined below in the Appendix,
% and store the values for displaying them later. Then we track the two beams
% with |trak()| and store the horizontal position of beam 1 (the electrons) in
% the array |pos()|.
for k=1:length(bump)
y=fitco2(y,bump(k),0); % finds closed orbit with beambeam kick
data(k,1:4)=[y(1),y(2),y(5),y(6)]; % store orbits for later display
y(1)=y(1)+10; % excite a betatron oscillation with 10 micron amplitude
for m=1:Nfft % iterate to get tunes from FFT
y=trak(y,bump(k),0); pos(m)=y(1);
end
%%
% From the stored position we determine the tunes of the coupled system by Fourier-transforming
% |pos()| with |fft()| and finding the peaks, which we store in the array |data|
% for later display.
[peaks,locs]=findpeaks(2*abs(fft(pos))/Nfft,'MinPeakHeight',2);
data(k,5)=(locs(1)-1)/Nfft; data(k,6)=(locs(2)-1)/Nfft;
end
%%
% Once the whole range of bump settings is done, we plot the data against the
% bump amplitude. The upper plot shows the deflection angle of the electron and
% positron bunches. Note the opposite sign and the slightly different magnitudes,
% which is caused by the different number of particles in the bunches and the
% different energies of the counter-propagating bunches.
subplot(2,1,1); plot(bump,data(:,2),'k',bump,data(:,4),'r-.');
xlabel('Horizontal bump amplitude [\mum]')
ylabel('Deflection angle [\murad]')
legend('Electrons','Positrons')
%%
% The lower plot shows the tunes detrmined by the call to fft(). We note that
% for large bunch offsets the tunes are almost equal, ebcause the bunches miss
% each other and do not couple. But once they are close, the beam-beam interaction
% couples the tunes and we see that one mode stay at the unperturbed values, while
% the other deviates significantly. The maximum split of the two modes occurs
% when the beams are colliding head-on, which is used in colliders to determine
% the best position of the colliding beams.
subplot(2,1,2); plot(bump,data(:,5),'k+',bump,data(:,6),'k+');
xlabel('Horizontal bump amplitude [\mum]'); ylabel('Tune Q_x')
ylim([0.3,0.4]);
%%
% A *vertical van-der-Meer* scan works in much the same way as the horizontal
% one. We first allocate variables and define the bump amplitude.
figure
y=zeros(8,1);
bump=-100:5:100;
data=zeros(length(bump),4);
%%
% An then loop over the different bump settings. At each setting we first determine
% the closed orbit with fitco2(), store the values and follow a slightly excited
% bunch for Nfft turn, while storing the vertical position.
for k=1:length(bump)
y=fitco2(y,0,bump(k)); % finds closed orbit with beambeam kick
data(k,1:4)=[y(3),y(4),y(7),y(8)]; % store vertical orbits
y(3)=y(3)+10; % excite a vertical betatron oscillation
for m=1:Nfft % iterate to get tunes from FFT
y=trak(y,0,bump(k)); pos(m)=y(3);
end
%%
% As before, we the determine the tunes from the FFT, but have to take care
% of aliasing, because the vertical tunes are above the half integer.
[peaks,locs]=findpeaks(2*abs(fft(pos))/Nfft,'MinPeakHeight',0.5);
Q1=(locs(1)-1)/Nfft; if Q1>0.5 Q1=1-Q1; end % avoid aliasing
Q2=(locs(2)-1)/Nfft; if Q2>0.5 Q2=1-Q2; end
data(k,5)=Q1; data(k,6)=Q2;
end
%%
% And finally, we plot the deflection angle at the interaction point in the
% upper plot and the tunes in the lower plot.
subplot(2,1,1); plot(bump,data(:,2),'k',bump,data(:,4),'r-.');
xlabel('Vertical bump amplitude [\mum]')
ylabel('Deflection angle [\murad]')
legend('Electrons','Positrons')
subplot(2,1,2); plot(bump,data(:,5),'k+',bump,data(:,6),'k+');
xlabel('Verical bump amplitude [\mum]'); ylabel('Tune Q_y')
ylim([0.37,0.45]);
%% Appendix
% The function |fitco2()| determines the closed orbit distortion from the combined
% effect of the bump and the beam-beam deflections, where the latter depend non-linearly
% on the positions, which makes some iterations necessary.
function y=fitco2(y,xbump,ybump)
global Re Rp kapsig Ne Np egamma pgamma Relec
RSe=inv(eye(4)-Re)*Re;
RSp=inv(eye(4)-Rp)*Rp;
ic=20; % iteration counter
while ic>0
ic=ic-1;
xsep=y(1)-y(5)+xbump; % separation between bunch centers
ysep=y(3)-y(7)+ybump;
q=F0(xsep,ysep,kapsig); % the beam beam kick
xk=imag(q); yk=real(q);
exdef=-2e12*Relec*Np*xk/egamma; % electron deflection angle
eydef=-2e12*Relec*Np*yk/egamma;
pxdef=2e12*Relec*Ne*xk/pgamma; % positron deflection angles
pydef=2e12*Relec*Ne*yk/pgamma;
y(1:4)=RSe*[0;exdef;0;eydef];
y(5:8)=RSp*[0;pxdef;0;pydef];
end
end
%%
% The function trak() implements one turn of the combined system of the two
% counter-propagating beams including the bumps and the beam-beam interactions.
% It just receives the $2\times 4$ input coordinates $x,x',y,y'$ for each beam
% and returns those positions after one turn.
function y=trak(y,xbump,ybump)
global Re Rp kapsig Ne Np egamma pgamma Relec
xsep=y(1)-y(5)+xbump; % separation between bunch centers
ysep=y(3)-y(7)+ybump;
q=F0(xsep,ysep,kapsig); % the beam beam kick
xk=imag(q); yk=real(q);
exdef=-2e12*Relec*Np*xk/egamma; % electron deflection angle
eydef=-2e12*Relec*Np*yk/egamma;
pxdef=2e12*Relec*Ne*xk/pgamma; % positron deflection angles
pydef=2e12*Relec*Ne*yk/pgamma;
y(2)=y(2)+exdef; y(4)=y(4)+eydef; % electron deflection angle
y(6)=y(6)+pxdef; y(8)=y(8)+pydef; % Positron deflection angle
y(1:4)=Re*y(1:4); % electron transport through the ring
y(5:8)=Rp*y(5:8); % positron transport through the ring
end
%%
% The beam-beam kick depends on the function |F0()|, defined in Equation 9.28.
% It uses the complex error function $w(z)$ which is provided by the Faddeeva
% package from matlab central (<https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package-complex-error-functions
% https://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package-complex-error-functions>).
function out=F0(x,y,sig)
r=1/sqrt(2*(sig(1,1)-sig(2,2)+2*i*sig(1,2)));
detsig=sig(1,1)*sig(2,2)-sig(1,2)^2;
if abs(r) > 1e8 % round beam
out=i*(x-i*y).*(1-exp(-0.5*(x.^2+y.^2)./sig(1,1)))./(x.^2+y.^2+1e-10);
return
end
a1=r;
a2=i*r;
b1=r*(sig(2,2)-i*sig(1,2))/sqrt(detsig);
b2=i*r*(sig(1,1)+i*sig(1,2))/sqrt(detsig);
g=0.5*(sig(2,2)*x.^2-2*sig(1,2).*x.*y+sig(1,1)*y.^2)/detsig;
z1=a1*x+a2*y;
z2=b1*x+b2*y;
zz1=conj(z1);
zz2=conj(z2);
q1=(imag(z2)>=0); % use one or the other form , depending on sign of
q2=1-q1; % imaginary part of argument of w(z)
out1=Faddeeva_w(z1)-exp(-g).*Faddeeva_w(z2);
out1(isnan(out1))=0; out1(isinf(out1))=0;
out2=conj(Faddeeva_w(zz1)-exp(-g).*Faddeeva_w(zz2));
out2(isnan(out2))=0; out2(isinf(out2))=0;
out=sqrt(pi)*r*(q1.*out1-q2.*out2);
end
##### SOURCE END #####
-->
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