-
Notifications
You must be signed in to change notification settings - Fork 0
/
LongitudinalBunchTomography.html
206 lines (197 loc) · 241 KB
/
LongitudinalBunchTomography.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
<!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>Longitudinal bunch tomography (Section 5.4)</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; }
.S1 { margin: 15px 10px 5px 4px; padding: 0px; line-height: 28.8px; min-height: 0px; white-space: pre-wrap; color: rgb(213, 80, 0); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 24px; font-weight: normal; text-align: left; }
.S2 { margin: 20px 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; }
.CodeBlock { background-color: #F7F7F7; margin: 10px 0 10px 0;}
.S3 { 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: 0px none rgb(0, 0, 0); border-radius: 4px 4px 0px 0px; padding: 6px 45px 0px 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; }
.S4 { 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: 0px none rgb(0, 0, 0); border-radius: 0px; padding: 0px 45px 0px 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; }
.S5 { 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; }
.S6 { 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; }
.S7 { 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; }
.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 { 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: 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; }
.S10 { 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>Longitudinal bunch tomography (Section 5.4)</span></h1><div class = 'S0'><span>Volker Ziemann, 211112, CC-BY-SA-4.0</span></div><div class = 'S0'><span style=' font-weight: bold;'>Important:</span><span> requires the Statistics and Machine-learning Toolbox (for </span><span style=' font-family: monospace;'>hist3</span><span>).</span></div><div class = 'S0'><span style=' font-weight: bold;'>Important:</span><span> requires the elliptic package from </span><a href = "https://github.com/moiseevigor/elliptic"><span>https://github.com/moiseevigor/elliptic</span></a><span> located in a subdirectory below the present one (for the fast evaluation of elliptic functions).</span></div><div class = 'S0'><span>In tomographic reconstructions one recovers an approximation of a higher-dimensional distribution from projections in lower dimensions. Here we use one-dimensional projections of the longitudinal distribution--the bunch shape--and try to recover the two-dimesnional distribution.</span></div><div class = 'S0'><span>In the first part of this simulation we record twenty snapshots of a longitudinal particle distribution (in phase only) taken at times </span><span texencoding="T_s/20" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="38" height="20" /></span><span> apart, where </span><span texencoding="T_s" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="15" height="20" /></span><span> is the small-amplitude synchrotron period. In practice these projections could be recordings of a position-monitor sum signal on a fast oscilloscope. In the second part we back-propagate the projections, taken at time </span><span texencoding="m T_s/20" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="48.5" height="20" /></span><span> with </span><span texencoding="m=0" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="40" height="18" /></span><span> to </span><span texencoding="19" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="18" height="18" /></span><span> to time </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: normal; color: rgb(0, 0, 0);">0</span><span> and superimpose them. Since we do not know the momentum distribution at the time of the recording, we simply assume that the momenta are evenly distributed, which will show up as bands in the reconstruction, but all these bands overlap in the region, where the initial particle distribution was located, which is thereby recovered.</span></div><h2 class = 'S2'><span>Making the projections</span></h2><div class = 'S0'><span>We first add the path to the elliptic functions and define some parameters of the simulation. Then we define an initial distribution with center x0 and width dx and plot it as a cloud of green dots in the upper subplot.</span></div><div class="CodeBlock"><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 = 'S4'><span style="white-space: pre"><span >addpath </span><span style="color: rgb(170, 4, 249);">./elliptic</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >Omegas=0.25; Ts=2*pi/Omegas; dt=0.05*Ts;</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >nstep=20; </span><span style="color: rgb(2, 128, 9);">% number of projections to record</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >xbins=-pi:pi/128:pi; </span><span style="color: rgb(2, 128, 9);">% binning of the projections</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >N=1000; </span><span style="color: rgb(2, 128, 9);">% number of particles</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >x0=[1.0,0.3]; dx=[0.3,0.1]; </span><span style="color: rgb(2, 128, 9);">% center and spread of distribution</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >x1=zeros(N,2); </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:N </span><span style="color: rgb(2, 128, 9);">% initial distribution</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > x1(k,:)=x0+(rand(1,2)-0.5).*dx; </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 class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >subplot(2,1,1);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >plot(x1(:,1),x1(:,2),</span><span style="color: rgb(170, 4, 249);">'g.'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'Initial distribution'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >axis([-pi,pi,-0.67,0.67]);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi,-pi/2,0,pi/2,pi],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,14, </span><span style="color: rgb(14, 0, 255);">...</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > </span><span style="color: rgb(170, 4, 249);">'xticklabels'</span><span >,{</span><span style="color: rgb(170, 4, 249);">'-\pi'</span><span >,</span><span style="color: rgb(170, 4, 249);">'-\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi'</span><span >})</span></span></div></div></div><div class = 'S6'><span>In the lower subplot we display the projection of the initial distribution onto the phase axis, which is what a BPM sum signal would show, provided the bandwidth of the electronics is very high.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >projections=zeros(length(xbins),nstep); </span><span style="color: rgb(2, 128, 9);">% allocate space</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >projections(:,1)=hist(x1(:,1),xbins); </span><span style="color: rgb(2, 128, 9);">% save initial projection</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >subplot(2,1,2); bar(xbins,projections(:,1)); xlim([-pi,pi])</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi,-pi/2,0,pi/2,pi],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,14, </span><span style="color: rgb(14, 0, 255);">...</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S7'><span style="white-space: pre"><span > </span><span style="color: rgb(170, 4, 249);">'xticklabels'</span><span >,{</span><span style="color: rgb(170, 4, 249);">'-\pi'</span><span >,</span><span style="color: rgb(170, 4, 249);">'-\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi'</span><span >})</span></span></div><div class = 'S8'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="172212BF" data-scroll-top="null" data-scroll-left="null" data-testid="output_0" style="width: 1364px;"><div class="figureElement"><img class="figureImage figureContainingNode" src="data:image/png;base64,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" style="width: 560px;"></div></div></div></div></div><div class = 'S6'><span>Now we a ready to propagate the particle distribution for the time dt=Ts/20, plot the distribution in phase space in the upper subplot and use hist() to calculate the projection onto the phase axis and subsequently display it in the lower subplot.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >figure</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >m=1:nstep-1</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > subplot(2,1,1); hold </span><span style="color: rgb(170, 4, 249);">off</span><span >; </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > phi=-pi:0.01:pi; separatrix=2*Omegas*cos(0.5*phi);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > plot(phi,separatrix,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,phi,-separatrix,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > title([</span><span style="color: rgb(170, 4, 249);">'Projection '</span><span >,num2str(m+1)])</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><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 = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">parfor </span><span >k=1:N </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > x1(k,:)=pendulumtracker(x1(k,:),Omegas,dt);</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 class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > plot(x1(:,1),x1(:,2),</span><span style="color: rgb(170, 4, 249);">'r.'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > axis([-pi,pi,-0.67,0.67]);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi,-pi/2,0,pi/2,pi],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,14, </span><span style="color: rgb(14, 0, 255);">...</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(170, 4, 249);">'xticklabels'</span><span >,{</span><span style="color: rgb(170, 4, 249);">'-\pi'</span><span >,</span><span style="color: rgb(170, 4, 249);">'-\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi'</span><span >})</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > projections(:,m+1)=hist(x1(:,1),xbins); </span><span style="color: rgb(2, 128, 9);">% save projection</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > subplot(2,1,2); bar(xbins,projections(:,m+1)); xlim([-pi,pi])</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi,-pi/2,0,pi/2,pi],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,14, </span><span style="color: rgb(14, 0, 255);">...</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(170, 4, 249);">'xticklabels'</span><span >,{</span><span style="color: rgb(170, 4, 249);">'-\pi'</span><span >,</span><span style="color: rgb(170, 4, 249);">'-\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi'</span><span >})</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > pause(0.001)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S7'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div><div class = 'S8'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="370D6DE3" data-scroll-top="null" data-scroll-left="null" data-testid="output_1" style="width: 1364px;"><div class="figureElement"><img class="figureImage figureContainingNode" src="data:image/png;base64,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" style="width: 560px;"></div></div></div></div></div><div class = 'S6'><span>Once we filled the array projections() we simply write it into a data file. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >dlmwrite(</span><span style="color: rgb(170, 4, 249);">'projections.dat'</span><span >,projections,</span><span style="color: rgb(170, 4, 249);">'\t'</span><span >);</span></span></div></div></div><div class = 'S6'><span>At this point we have recorded synthetic data from our toy system, but we could equally well save real data into a file with the same format and anlyze that in the next step.</span></div><h2 class = 'S10'><span>Analyzing the projections</span></h2><div class = 'S0'><span>In order to obviously make this part self-contained we simply clear the work space, add the path to the elliptic functions and define the same parameters as in the first part. Then we read the file with the saved projections.</span></div><div class="CodeBlock"><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 = 'S4'><span style="white-space: pre"><span >addpath </span><span style="color: rgb(170, 4, 249);">./elliptic</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >Omegas=0.25; Ts=2*pi/Omegas; dt=0.05*Ts; </span><span style="color: rgb(2, 128, 9);">% must match values in</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >xbins=-pi:pi/128:pi; nbin=length(xbins); </span><span style="color: rgb(2, 128, 9);">% the above function</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >projections=dlmread(</span><span style="color: rgb(170, 4, 249);">'projections.dat'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >nstep=size(projections,2); </span></span></div></div></div><div class = 'S6'><span>At this point we make an assumption about our ignorance of the momentum distribution while recording the projections. The above-mentioned smearing out in the momentum dimension is specified by </span><span style=' font-family: monospace;'>dp</span><span>. We also allocate space for the image </span><span style=' font-family: monospace;'>im</span><span> to which we add all back-propagated projections.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >dp=-1:0.01:1; dpbin=length(dp); </span><span style="color: rgb(2, 128, 9);">% the vertical "spread"</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >im=zeros(nbin,dpbin); </span><span style="color: rgb(2, 128, 9);">% reconstructed initial phase space image</span></span></div></div></div><div class = 'S6'><span>Now </span><span style=' font-family: monospace;'>m</span><span> loops over all the recorded projections and </span><span style=' font-family: monospace;'>kbin</span><span> over each bin of the projection. If the bin is empty, we just continue with the next one, otherwise we 'spread out' the particles in the</span><span style=' font-family: monospace;'> dp</span><span> bins with different momentum values and store these </span><span style=' font-family: monospace;'>dpbin</span><span> starting values in </span><span style=' font-family: monospace;'>x1</span><span>. Since all these starting values are independent, we can use </span><span style=' font-family: monospace;'>parfor</span><span> to use all processor-cores to back-propagate the particles to their starting time. Here </span><span style=' font-family: monospace;'>hist3() </span><span>is a very efficient way to sort these positions into the array im, which provides a continuously improving approximation of the initial distribution that we display with </span><span style=' font-family: monospace;'>contourf()</span><span> and annotate the axes.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >m=1:nstep</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">for </span><span >kbin=1:nbin</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >projections(kbin,m)==0, </span><span style="color: rgb(14, 0, 255);">continue</span><span >; </span><span style="color: rgb(14, 0, 255);">end</span><span >; </span><span style="color: rgb(2, 128, 9);">% abort, if empty</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > x1=[xbins(kbin)*ones(dpbin,1),dp'];</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">parfor </span><span >n=1:dpbin </span><span style="color: rgb(2, 128, 9);">% spread out "vertically"</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > x1(n,:)=pendulumtracker(x1(n,:),Omegas,-(m-1)*dt); </span><span style="color: rgb(2, 128, 9);">% back-propagate</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 class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > im=im+hist3(x1,{xbins,dp})*projections(kbin,m); </span><span style="color: rgb(2, 128, 9);">% add to image</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 class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > contourf(xbins,dp,im')</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi,-pi/2,0,pi/2,pi],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,14, </span><span style="color: rgb(14, 0, 255);">...</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(170, 4, 249);">'xticklabels'</span><span >,{</span><span style="color: rgb(170, 4, 249);">'-\pi'</span><span >,</span><span style="color: rgb(170, 4, 249);">'-\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi'</span><span >})</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > title([</span><span style="color: rgb(170, 4, 249);">'Projection '</span><span >,num2str(m),</span><span style="color: rgb(170, 4, 249);">' of '</span><span >,num2str(nstep)]);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > pause(0.2)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S7'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div><div class = 'S8'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="136B67AA" data-scroll-top="null" data-scroll-left="null" data-testid="output_2" style="width: 1364px;"><div class="figureElement"><img class="figureImage figureContainingNode" src="data:image/png;base64,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" style="width: 560px;"></div></div></div></div></div><div class = 'S6'><span>Now we can calculate the projections of the image im onto the respective axes and can, for example, compare the upper subplot with the initial distribution, shown at the start of the simulation by the green cloud of dots.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >figure(2); </span><span style="color: rgb(2, 128, 9);">% display the projections</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >subplot(2,1,1); plot(xbins,sum(im,2),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); xlim([-pi,pi]);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi,-pi/2,0,pi/2,pi],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,14, </span><span style="color: rgb(14, 0, 255);">...</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(170, 4, 249);">'xticklabels'</span><span >,{</span><span style="color: rgb(170, 4, 249);">'-\pi'</span><span >,</span><span style="color: rgb(170, 4, 249);">'-\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi'</span><span >})</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S7'><span style="white-space: pre"><span >subplot(2,1,2); plot(dp,sum(im,1),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >)</span></span></div><div class = 'S8'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="98387178" data-scroll-top="null" data-scroll-left="null" data-testid="output_3" style="width: 1364px;"><div class="figureElement"><img class="figureImage figureContainingNode" src="data:image/png;base64,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" style="width: 560px;"></div></div></div></div></div><div class = 'S6'><span>Now play with the simulation by increasing the number </span><span style=' font-family: monospace;'>nstep</span><span> of recorded projections, the definition of the momentum-smearing </span><span style=' font-family: monospace;'>dp</span><span>, or any other parameter.</span></div><h2 class = 'S10'><span>Appendix </span></h2><div class = 'S0'><span>The function</span><span style=' font-family: monospace;'> pendulumtracker()</span><span> receives the phase-space coordinates </span><span style=' font-family: monospace;'>x</span><span> at the start, the small-amplitude synchrotron frequency </span><span style=' font-family: monospace;'>omega</span><span>, and the integration time </span><span style=' font-family: monospace;'>dt</span><span> as input and returns the phase-space coordinates </span><span style=' font-family: monospace;'>xout</span><span>. Internally, it integrates the equations of motion for a mathematical pendulum in closed form using Jacobi elliptic functions. This is much faster than numerically integration, expecially for extremely large times, such as thousands or even millions of synchrotron periods. The coding closely follows Section 5.4, especially Equations 5.50 to 5.54. Here we use the elliptic functions from </span><a href = "https://github.com/moiseevigor/elliptic"><span>https://github.com/moiseevigor/elliptic</span></a><span>.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >xout=pendulumtracker(x,omega,dt)</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >k2=(0.5*x(2)/omega)^2+sin(0.5*x(1))^2; k=sqrt(k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >(x(1)>pi) x(1)=x(1)-2*pi; </span><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);">if </span><span >(x(1)<-pi) x(1)=x(1)+2*pi; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >s=1; </span><span style="color: rgb(14, 0, 255);">if </span><span >(x(1)<0) s=-s; x(1)=-x(1); </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >s1=1; </span><span style="color: rgb(14, 0, 255);">if </span><span >(x(2)<0) s1=-s1; </span><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);">if </span><span >(k>1) </span><span style="color: rgb(2, 128, 9);">% outside separatrix</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > kelf=ellipke(1/k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > trev=2*kelf/(k*omega);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > t0=mod(dt,trev);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > tmp=s1*k*omega*t0+s*elliptic12(0.5*x(1),1/k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > [sn,cn,dn]=ellipj(tmp,1/k2); </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >(abs(tmp) > kelf) sn=-sn; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > xout(1)=2*asin(sn);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > xout(2)=2*s1*omega*k*dn;</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">else</span><span > </span><span style="color: rgb(2, 128, 9);">% inside separatrix</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > trev=4*ellipke(k2)/omega;</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > t0=mod(dt,trev);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > z0=asin(min(1,sin(0.5*x(1))/k));</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > tmp=s1*omega*t0+s*elliptic12(z0,k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > [sn,cn,dn]=ellipj(tmp,k2); </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > xout(1)=2*asin(k*sn);</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > xout(2)=2*s1*omega*k*cn;</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 class="inlineWrapper"><div class = 'S5'><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)
%% Longitudinal bunch tomography (Section 5.4)
% Volker Ziemann, 211112, CC-BY-SA-4.0
%
% *Important:* requires the Statistics and Machine-learning Toolbox (for |hist3|).
%
% *Important:* requires the elliptic package from <https://github.com/moiseevigor/elliptic
% https://github.com/moiseevigor/elliptic> located in a subdirectory below the
% present one (for the fast evaluation of elliptic functions).
%
% In tomographic reconstructions one recovers an approximation of a higher-dimensional
% distribution from projections in lower dimensions. Here we use one-dimensional
% projections of the longitudinal distributionREPLACE_WITH_DASH_DASHthe bunch shapeREPLACE_WITH_DASH_DASHand try to recover
% the two-dimesnional distribution.
%
% In the first part of this simulation we record twenty snapshots of a longitudinal
% particle distribution (in phase only) taken at times $T_s/20$ apart, where $T_s$
% is the small-amplitude synchrotron period. In practice these projections could
% be recordings of a position-monitor sum signal on a fast oscilloscope. In the
% second part we back-propagate the projections, taken at time $m T_s/20$ with
% $m=0$ to $19$ to time $0$ and superimpose them. Since we do not know the momentum
% distribution at the time of the recording, we simply assume that the momenta
% are evenly distributed, which will show up as bands in the reconstruction, but
% all these bands overlap in the region, where the initial particle distribution
% was located, which is thereby recovered.
%% Making the projections
% We first add the path to the elliptic functions and define some parameters
% of the simulation. Then we define an initial distribution with center x0 and
% width dx and plot it as a cloud of green dots in the upper subplot.
clear all; close all
addpath ./elliptic
Omegas=0.25; Ts=2*pi/Omegas; dt=0.05*Ts;
nstep=20; % number of projections to record
xbins=-pi:pi/128:pi; % binning of the projections
N=1000; % number of particles
x0=[1.0,0.3]; dx=[0.3,0.1]; % center and spread of distribution
x1=zeros(N,2);
for k=1:N % initial distribution
x1(k,:)=x0+(rand(1,2)-0.5).*dx;
end
subplot(2,1,1);
plot(x1(:,1),x1(:,2),'g.')
title('Initial distribution')
axis([-pi,pi,-0.67,0.67]);
set(gca,'xtick',[-pi,-pi/2,0,pi/2,pi],'fontsize',14, ...
'xticklabels',{'-\pi','-\pi/2','0','\pi/2','\pi'})
%%
% In the lower subplot we display the projection of the initial distribution
% onto the phase axis, which is what a BPM sum signal would show, provided the
% bandwidth of the electronics is very high.
projections=zeros(length(xbins),nstep); % allocate space
projections(:,1)=hist(x1(:,1),xbins); % save initial projection
subplot(2,1,2); bar(xbins,projections(:,1)); xlim([-pi,pi])
set(gca,'xtick',[-pi,-pi/2,0,pi/2,pi],'fontsize',14, ...
'xticklabels',{'-\pi','-\pi/2','0','\pi/2','\pi'})
%%
% Now we a ready to propagate the particle distribution for the time dt=Ts/20,
% plot the distribution in phase space in the upper subplot and use hist() to
% calculate the projection onto the phase axis and subsequently display it in
% the lower subplot.
figure
for m=1:nstep-1
subplot(2,1,1); hold off;
phi=-pi:0.01:pi; separatrix=2*Omegas*cos(0.5*phi);
plot(phi,separatrix,'k',phi,-separatrix,'k');
title(['Projection ',num2str(m+1)])
hold on
parfor k=1:N
x1(k,:)=pendulumtracker(x1(k,:),Omegas,dt);
end
plot(x1(:,1),x1(:,2),'r.')
axis([-pi,pi,-0.67,0.67]);
set(gca,'xtick',[-pi,-pi/2,0,pi/2,pi],'fontsize',14, ...
'xticklabels',{'-\pi','-\pi/2','0','\pi/2','\pi'})
projections(:,m+1)=hist(x1(:,1),xbins); % save projection
subplot(2,1,2); bar(xbins,projections(:,m+1)); xlim([-pi,pi])
set(gca,'xtick',[-pi,-pi/2,0,pi/2,pi],'fontsize',14, ...
'xticklabels',{'-\pi','-\pi/2','0','\pi/2','\pi'})
pause(0.001)
end
%%
% Once we filled the array projections() we simply write it into a data file.
dlmwrite('projections.dat',projections,'\t');
%%
% At this point we have recorded synthetic data from our toy system, but we
% could equally well save real data into a file with the same format and anlyze
% that in the next step.
%% Analyzing the projections
% In order to obviously make this part self-contained we simply clear the work
% space, add the path to the elliptic functions and define the same parameters
% as in the first part. Then we read the file with the saved projections.
clear all; close all
addpath ./elliptic
Omegas=0.25; Ts=2*pi/Omegas; dt=0.05*Ts; % must match values in
xbins=-pi:pi/128:pi; nbin=length(xbins); % the above function
projections=dlmread('projections.dat');
nstep=size(projections,2);
%%
% At this point we make an assumption about our ignorance of the momentum distribution
% while recording the projections. The above-mentioned smearing out in the momentum
% dimension is specified by |dp|. We also allocate space for the image |im| to
% which we add all back-propagated projections.
dp=-1:0.01:1; dpbin=length(dp); % the vertical "spread"
im=zeros(nbin,dpbin); % reconstructed initial phase space image
%%
% Now |m| loops over all the recorded projections and |kbin| over each bin of
% the projection. If the bin is empty, we just continue with the next one, otherwise
% we 'spread out' the particles in the |dp| bins with different momentum values
% and store these |dpbin| starting values in |x1|. Since all these starting values
% are independent, we can use |parfor| to use all processor-cores to back-propagate
% the particles to their starting time. Here |hist3()| is a very efficient way
% to sort these positions into the array im, which provides a continuously improving
% approximation of the initial distribution that we display with |contourf()|
% and annotate the axes.
for m=1:nstep
for kbin=1:nbin
if projections(kbin,m)==0, continue; end; % abort, if empty
x1=[xbins(kbin)*ones(dpbin,1),dp'];
parfor n=1:dpbin % spread out "vertically"
x1(n,:)=pendulumtracker(x1(n,:),Omegas,-(m-1)*dt); % back-propagate
end
im=im+hist3(x1,{xbins,dp})*projections(kbin,m); % add to image
end
contourf(xbins,dp,im')
set(gca,'xtick',[-pi,-pi/2,0,pi/2,pi],'fontsize',14, ...
'xticklabels',{'-\pi','-\pi/2','0','\pi/2','\pi'})
title(['Projection ',num2str(m),' of ',num2str(nstep)]);
pause(0.2)
end
%%
% Now we can calculate the projections of the image im onto the respective axes
% and can, for example, compare the upper subplot with the initial distribution,
% shown at the start of the simulation by the green cloud of dots.
figure(2); % display the projections
subplot(2,1,1); plot(xbins,sum(im,2),'k'); xlim([-pi,pi]);
set(gca,'xtick',[-pi,-pi/2,0,pi/2,pi],'fontsize',14, ...
'xticklabels',{'-\pi','-\pi/2','0','\pi/2','\pi'})
subplot(2,1,2); plot(dp,sum(im,1),'k')
%%
% Now play with the simulation by increasing the number |nstep| of recorded
% projections, the definition of the momentum-smearing |dp|, or any other parameter.
%% Appendix
% The function |pendulumtracker()| receives the phase-space coordinates |x|
% at the start, the small-amplitude synchrotron frequency |omega|, and the integration
% time |dt| as input and returns the phase-space coordinates |xout|. Internally,
% it integrates the equations of motion for a mathematical pendulum in closed
% form using Jacobi elliptic functions. This is much faster than numerically integration,
% expecially for extremely large times, such as thousands or even millions of
% synchrotron periods. The coding closely follows Section 5.4, especially Equations
% 5.50 to 5.54. Here we use the elliptic functions from <https://github.com/moiseevigor/elliptic
% https://github.com/moiseevigor/elliptic>.
function xout=pendulumtracker(x,omega,dt)
k2=(0.5*x(2)/omega)^2+sin(0.5*x(1))^2; k=sqrt(k2);
if (x(1)>pi) x(1)=x(1)-2*pi; end
if (x(1)<-pi) x(1)=x(1)+2*pi; end
s=1; if (x(1)<0) s=-s; x(1)=-x(1); end
s1=1; if (x(2)<0) s1=-s1; end
if (k>1) % outside separatrix
kelf=ellipke(1/k2);
trev=2*kelf/(k*omega);
t0=mod(dt,trev);
tmp=s1*k*omega*t0+s*elliptic12(0.5*x(1),1/k2);
[sn,cn,dn]=ellipj(tmp,1/k2);
if (abs(tmp) > kelf) sn=-sn; end
xout(1)=2*asin(sn);
xout(2)=2*s1*omega*k*dn;
else % inside separatrix
trev=4*ellipke(k2)/omega;
t0=mod(dt,trev);
z0=asin(min(1,sin(0.5*x(1))/k));
tmp=s1*omega*t0+s*elliptic12(z0,k2);
[sn,cn,dn]=ellipj(tmp,k2);
xout(1)=2*asin(k*sn);
xout(2)=2*s1*omega*k*cn;
end
end
##### SOURCE END #####
-->
</div></body></html>