-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathSaseFreeElectronLaser.html
211 lines (201 loc) · 195 KB
/
SaseFreeElectronLaser.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
207
208
209
210
211
<!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>SASE free-electron laser (Section 10.4)</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; }
.CodeBlock { background-color: #F7F7F7; margin: 10px 0 10px 0;}
.S2 { 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; }
.S3 { 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; }
.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: 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; }
.S5 { 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; }
.S6 { border-left: 1px solid rgb(233, 233, 233); border-right: 1px solid rgb(233, 233, 233); border-top: 0px none rgb(0, 0, 0); border-bottom: 1px solid rgb(233, 233, 233); border-radius: 0px; padding: 0px 45px 4px 13px; line-height: 17.234px; min-height: 18px; white-space: nowrap; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 14px; }
.S7 { color: rgb(64, 64, 64); padding: 10px 0px 6px 17px; background: rgb(255, 255, 255) none repeat scroll 0% 0% / auto padding-box border-box; font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 14px; overflow-x: hidden; line-height: 17.234px; }
.S8 { 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 4px 0px 0px; 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; }
/* Styling that is common to warnings and errors is in diagnosticOutput.css */.embeddedOutputsErrorElement { min-height: 18px; max-height: 250px; overflow: auto;}
.embeddedOutputsErrorElement.inlineElement {}
.embeddedOutputsErrorElement.rightPaneElement {}
/* Styling that is common to warnings and errors is in diagnosticOutput.css */.embeddedOutputsWarningElement{ min-height: 18px; max-height: 250px; overflow: auto;}
.embeddedOutputsWarningElement.inlineElement {}
.embeddedOutputsWarningElement.rightPaneElement {}
/* Copyright 2015-2019 The MathWorks, Inc. *//* In this file, styles are not scoped to rtcContainer since they could be in the Dojo Tooltip */.diagnosticMessage-wrapper { font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px;}
.diagnosticMessage-wrapper.diagnosticMessage-warningType { color: rgb(255,100,0);}
.diagnosticMessage-wrapper.diagnosticMessage-warningType a { color: rgb(255,100,0); text-decoration: underline;}
.diagnosticMessage-wrapper.diagnosticMessage-errorType { color: rgb(230,0,0);}
.diagnosticMessage-wrapper.diagnosticMessage-errorType a { color: rgb(230,0,0); text-decoration: underline;}
.diagnosticMessage-wrapper .diagnosticMessage-messagePart,.diagnosticMessage-wrapper .diagnosticMessage-causePart { white-space: pre-wrap;}
.diagnosticMessage-wrapper .diagnosticMessage-stackPart { white-space: pre;}
.embeddedOutputsTextElement,.embeddedOutputsVariableStringElement { white-space: pre; word-wrap: initial; min-height: 18px; max-height: 250px; overflow: auto;}
.textElement,.rtcDataTipElement .textElement { padding-top: 3px;}
.embeddedOutputsTextElement.inlineElement,.embeddedOutputsVariableStringElement.inlineElement {}
.inlineElement .textElement {}
.embeddedOutputsTextElement.rightPaneElement,.embeddedOutputsVariableStringElement.rightPaneElement { min-height: 16px;}
.rightPaneElement .textElement { padding-top: 2px; padding-left: 9px;}
.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: 0px none rgb(0, 0, 0); border-radius: 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; }
.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>SASE free-electron laser (Section 10.4)</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 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 this simulation we numerically integrate Equation 10.32, which describes the evolution of the amplitude and phase of the electro-magnetic wave (the laser field) and an ensemble of electrons that move in the ponderomotive field of the laser. </span></div><div class = 'S0'><span>First we define the initial complex field </span><span style=' font-family: monospace;'>a</span><span> of the laser and the scaled current jcurr, which represents the peak current of the electron distribution. Moreover, we define the initial distribution of electrons in the ponderomotive field and the number N of electrons used in the simulation. From Equation 10.32 we see that the magnnitude of a, which is a0 describes the oscillation frequency </span><span texencoding="\Omega_s" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="18" height="20" /></span><span> in the ponderomotive field.</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></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >addpath </span><span style="color: rgb(170, 4, 249);">./elliptic</span><span > </span><span style="color: rgb(2, 128, 9);">% needed for elliptic12</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >a0=1e-8; phi=0; a=a0*exp(i*phi); </span><span style="color: rgb(2, 128, 9);">% initial amplitude and phase of laser</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >jcurr=200; </span><span style="color: rgb(2, 128, 9);">% scaled current from Equation 10.32</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >x0=[pi/2,0]; dx=[2*pi,0.3]; </span><span style="color: rgb(2, 128, 9);">% center and spread of distribution</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><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 >Omegas=sqrt(a0); </span><span style="color: rgb(2, 128, 9);">% synchrotron frequency</span></span></div></div></div><div class = 'S5'><span>Now we can plot the initial electron distribution as a cloud of green dots . We see that it is evenly distributed in phase and has a small vertical extent in the variable </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">ν</span><span> which corresponds to the difference of electron energy with respect to the resonance energy of the FEL.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >axis_scale=[-pi/2,3*pi/2,-17,17];</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >ypos=0.95*axis_scale(3)+0.05*axis_scale(4); </span><span style="color: rgb(2, 128, 9);">% where to place text</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >zeta=-pi/2:0.01:3*pi/2; separatrix=2*Omegas*cos(0.5*(zeta-pi/2+phi));</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >hold </span><span style="color: rgb(170, 4, 249);">off</span><span >; plot(zeta,separatrix,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,zeta,-separatrix,</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 >axis(axis_scale); xlabel(</span><span style="color: rgb(170, 4, 249);">'\zeta'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'\nu'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi/2,0,pi/2,pi,3*pi/2],</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 = 'S3'><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/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 style="color: rgb(170, 4, 249);">'3\pi/2'</span><span >})</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >hold </span><span style="color: rgb(170, 4, 249);">on</span><span >;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >x1(:,1)=x0(1)+(rand(N,1)-0.5)*dx(1); </span><span style="color: rgb(2, 128, 9);">% initial distribution</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >x1(:,2)=x0(2)+(rand(N,1)-0.5)*dx(2); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><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 = 'S3'><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 >pause(0.01)</span></span></div></div></div><div class = 'S5'><span>After subdividing the time for the transit through the FEL into </span><span style=' font-family: monospace;'>nstep=100</span><span> time steps, we are ready to start iterating</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >nstep=100; dt=1/nstep; tau=(1:nstep)/nstep; </span><span style="color: rgb(2, 128, 9);">% steps along the undulator</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >tic; data=zeros(nstep,4); </span><span style="color: rgb(2, 128, 9);">% storage for plot data</span></span></div></div><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 > hold </span><span style="color: rgb(170, 4, 249);">off</span><span >; </span><span style="color: rgb(2, 128, 9);">% draw new image</span></span></div></div></div><div class = 'S5'><span>As a first step we calculate </span><span texencoding="\Omega_s" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="18" height="20" /></span><span> and phase </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">ϕ</span><span> from the amplitude of the field, which enables us to plot the separatrix, whose height is thus related to the field amplitude and phase.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > Omegas=sqrt(abs(a)); phi=phase(a); </span><span style="color: rgb(2, 128, 9);">% needed for electron dynamics</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > separatrix=2*Omegas*cos(0.5*(zeta-pi/2+phi));</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > plot(zeta,separatrix,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,zeta,-separatrix,</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 > set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi/2,0,pi/2,pi,3*pi/2],</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 = 'S3'><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/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 style="color: rgb(170, 4, 249);">'3\pi/2'</span><span >}) </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > axis(axis_scale); xlabel(</span><span style="color: rgb(170, 4, 249);">'\zeta'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'\nu'</span><span >)</span></span></div></div></div><div class = 'S5'><span>Now we update the positions of all electrons in their phase space, which is governed by the pendulum equation and uses pendulumtracker2_phase(), which is a slightly modified version of the equivalent function from Chapter 5, but this one is centered aroudn </span><span texencoding="\pi/2" style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADYAAAAmCAYAAACPk2hGAAAD2klEQVRoQ+3YWai1YxQH8N9nnjLPUmYhc+Yxw4U5QpluiMyR4YLcIITIPCuzkCFjCSFTMkco8xAiCcmY/lrna9vf3ud993H2OcfpW5f7Wc961/9Za/3XWnuGaSozpikus4H93yI7FSI2B17DoXhlvB5wKgDbCQ9gGfw0nYDdhLlw0HiBip3JjtgC+Br74bEewOLfkdgN62FBvIWncD5+6fcYkw3sQFyEFfBnl5NJzbuxTR/nP8SeeLvX+WQDexTv4sQezj2ILXAxXsd8WB/HYrHSD+lsht+7708msETkC2yKV7scS2peik3wedfZUngBq9bvB+DOqQTsBByBtXtE6z5ch0f6pGFq7qE6uxCnTCVg6Vn34Nwup+ZGUjRtoJ+ERH4s8rsNB48V2MJYEQs1UPLL+KsFba9VRb8SPu2hn6bdZOc7LI5zcPqgwA7BSVW0Tf5+hFWalOo8zmyJ7Vvqd6vNW1QfjoiNp9sCy4tdhqMH+PAVxVhNV+LMxzgTNzQp9zkPE75YjJrozyL9WDFRStrdVVPBG0iRnloWMiXciq3x3IDO5YVTQ8vihwHvjqhfjmOqDp9oCyyAUrj314WzK4e3wvP1W6aE9Jgl8MeAzl2P1Oz+A94bUU+tv4NbRsuopj6WGe4TzInlq6CXw2dIA917QOfSZL9Cajf3xyK5Fzu79mrMIwabgO1VkUtPSc+JnIwL6rWuGtCzRCm1mEeaZVpoYSulkDLYtimNm4ClCaYZ5nVSF5E3sS5WwwctnOlUyWuHOI4b8F7U9y3CSY1+03R/NGDJ5TjxMzLG/IoNaikchNpHfFgSX9ZQ+1KTY13nOxZL71xjWOP10YBdguORYj+8LIWiz8DVOKp+WxkB2iQZXmNvjSbFrvP0uxuxyyjfyVCcJXVmevcDtnvVVkhjw5qu873HizHTDrJuLI3TkLmvSRKlpPZZTYod5xvjDuyB9/rcm7/sZoVJdv0j3cCSLpnftqvzZ6tQR/S/LYpPhG4vyk4xZ5QaTVYvx1KX2aPayDq1UJ6H9NFuie+LVua835FBPYGFhm8uC7/VStFpNLvTmh1fyACbiDVJUniHauhNujnPQzxTTbyN/kZV+zN1uyMWksiqsEgtfw93WQ1dX1kFfG1Rd5sPhz2zyl/TQjnfzvof8mojyZbsdP+SJrpvY7hJJxPLk/X63zcpj9f5RAALg4Zk9hkvp9vYGTaweWqEOgzZiidMhg0ss2RWk0zyIaMJk2EDu7fGn/w3OKEyTGCZBjLJh+YH3dn+8yMME9jmNd/lL7QJl2ECm3AwnR+cDWxSn38MH5+2EfsbtLupJyitLnQAAAAASUVORK5CYII=" width="27" height="19" /></span><span> insetead of zero. See the code below. Once all electrons coordinates are updated, we plot them as red dots superimposed to the separatrix. Note that all electrons are independent and we use parfor as a simple ay to utilize all processor cores.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > hold </span><span style="color: rgb(170, 4, 249);">on</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">parfor </span><span >k=1:N </span><span style="color: rgb(2, 128, 9);">% update electron phase space, use "for" or "parfor"</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x1(k,:)=pendulumtracker2_phase(x1(k,:),Omegas,phi,dt);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><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><div class = 'S5'><span>Now we calculate the bunching factor, which appears on the right-hand side of the equation for </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">a</span><span> in Equation 10.32 and numerically integrate that equation in order to update amplitude and phase of the laser field.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > bf=sum(exp(-i*x1(:,1)))/size(x1,1); </span><span style="color: rgb(2, 128, 9);">% bunching factor <exp(-i*zeta)></span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > a=a-jcurr*bf*dt; </span><span style="color: rgb(2, 128, 9);">% update laser field, Eq. 10.32</span></span></div></div></div><div class = 'S5'><span>Now all dynamical variables are updated for this time step and we annotate the plot and save the interesting quantities to the array </span><span style=' font-family: monospace;'>data</span><span>. The short pause at the end allows MATLAB to update the plot so we can watch the evolution in real time. Note how the seapatrix grows as the field amplitude grows and, at the same time, the phase of the separatrix shifts towards is the electrons transfer their kinetic energy to the laser field.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > text(-1.4,ypos,[</span><span style="color: rgb(170, 4, 249);">'bf = '</span><span >,num2str(bf,</span><span style="color: rgb(170, 4, 249);">'%6.3f'</span><span >),</span><span style="color: rgb(170, 4, 249);">' '</span><span >],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,16) </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > text(pi,ypos,[</span><span style="color: rgb(170, 4, 249);">'\tau = '</span><span >,num2str(tau(m),4),</span><span style="color: rgb(170, 4, 249);">' '</span><span >],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,16) </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(m,1)=abs(a);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(m,2)=phase(a)*180/pi;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(m,3)=abs(bf);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(m,4)=(abs(a)-a0)/a0;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > title([</span><span style="color: rgb(170, 4, 249);">' abs(a) = '</span><span >,num2str(abs(a),3),</span><span style="color: rgb(170, 4, 249);">' gain = ' </span><span >num2str(data(m,4),3)])</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > pause(0.01)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="87943469" data-scroll-top="null" data-scroll-left="null" data-testid="output_0" 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_45" widgetid="uniqName_333_45" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_47" widgetid="uniqName_333_47" style="width: 100%; height: auto;">
<canvas class="ImageView" data-dojo-attach-point="canvasViewNode" draggable="false" ondragstart="return false;" style="width: 100%; height: auto; display: none;"></canvas>
<img class="ImageView figureImage" data-dojo-attach-point="imageViewNode" draggable="false" ondragstart="return false;" style="width: 100%; height: auto; display: inline;" src="data:image/png;base64,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">
</div></div></div></div></div><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="629E2AB9" data-scroll-top="null" data-scroll-left="null" data-testid="output_1" 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_50" widgetid="uniqName_333_50" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_53" widgetid="uniqName_333_53" style="width: 100%; height: auto;">
<canvas class="ImageView" data-dojo-attach-point="canvasViewNode" draggable="false" ondragstart="return false;" style="width: 100%; height: auto; display: none;"></canvas>
<img class="ImageView figureImage" data-dojo-attach-point="imageViewNode" draggable="false" ondragstart="return false;" style="width: 100%; height: auto; display: inline;" src="data:image/png;base64,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">
</div></div></div></div></div></div></div></div><div class = 'S5'><span>Once the simulation is complete, we calculate the theoretical exponential gain from Equation 10.33 and also from a fit to the final part of the numerically determined growth of</span><span style=' font-family: monospace;'> a</span><span>. The upper plot shows latter growth and also shows the theoretical and experimentally determined growth rate in the title.</span></div><div class="CodeBlock"><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >toc; growth_theo=0.5*sqrt(3)*(jcurr/2)^(1/3);</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsTextElement" uid="1A95E648" data-scroll-top="null" data-scroll-left="null" data-width="1334" data-height="18" data-hashorizontaloverflow="false" data-testid="output_2" style="max-height: 261px; width: 1364px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="textElement" style="white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Elapsed time is 14.680380 seconds.</div></div></div></div><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >mm=0.3*nstep:nstep; p=polyfit(tau(mm)',log(data(mm,1)),1);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >growth_rate=p(1);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >figure; </span><span style="color: rgb(2, 128, 9);">% second figure with evaolution along the undulator tau=s/L</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >subplot(4,1,1); plot(tau,data(:,1),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'abs(a)'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >title([</span><span style="color: rgb(170, 4, 249);">'Growth rate [theo/exp] = '</span><span >,num2str(growth_theo,3),</span><span style="color: rgb(170, 4, 249);">' / '</span><span >, </span><span style="color: rgb(14, 0, 255);">...</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > num2str(growth_rate,3)])</span></span></div></div></div><div class = 'S5'><span>The second and third plot show the evolution of the phase </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">ϕ</span><span> and the bunching factor, whereas the fourth shows the gain </span><span texencoding="(a-a_0)/a_0" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="71.5" height="20" /></span><span> as the simulation progresses.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >subplot(4,1,2); plot(tau,data(:,2),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'phase(a) [deg]'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >subplot(4,1,3); plot(tau,data(:,3),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'<exp(-i\zeta)>'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >subplot(4,1,4); plot(tau,data(:,4),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'Gain'</span><span >);</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'\tau = s/L_u'</span><span >)</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="F6849998" data-scroll-top="null" data-scroll-left="null" data-testid="output_3" 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_51" widgetid="uniqName_333_51" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_55" widgetid="uniqName_333_55" style="width: 100%; height: auto;">
<canvas class="ImageView" data-dojo-attach-point="canvasViewNode" draggable="false" ondragstart="return false;" style="width: 100%; height: auto; display: none;"></canvas>
<img class="ImageView figureImage" data-dojo-attach-point="imageViewNode" draggable="false" ondragstart="return false;" style="width: 100%; height: auto; display: inline;" src="data:image/png;base64,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">
</div></div></div></div></div></div></div></div><h2 class = 'S10'><span>Appendix</span></h2><div class = 'S0'><span>The function pendulumtracker2_phase() integrates the equations of motion for a mathematical pendulum in terms of Jacobi elliptic functions. It is very similar to the one used in Chapter 5 (see those examples), exept this one takes the phase of the ponderomotive force </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">ϕ</span><span> into account.</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 >xout=pendulumtracker2_phase(x,omega,phi,dt)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >x(1)=x(1)-pi/2+phi; </span><span style="color: rgb(2, 128, 9);">% adjust to new phase</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><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 = 'S3'><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 = 'S3'><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 = 'S3'><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 = 'S3'><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 = 'S3'><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; check this part next</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > kelf=ellipke(1/k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > trev=2*kelf/(k*omega);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > t0=mod(dt,trev);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><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 = 'S3'><span style="white-space: pre"><span > [sn,cn,dn]=ellipj(tmp,1/k2); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >(abs(tmp) > kelf) sn=-sn; </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 > xout(1)=2*asin(sn);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xout(2)=2*s1*omega*k*dn;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><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 = 'S3'><span style="white-space: pre"><span > trev=4*ellipke(k2)/omega;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > t0=mod(dt,trev);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><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 = 'S3'><span style="white-space: pre"><span > tmp=s1*omega*t0+s*elliptic12(z0,k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > [sn,cn,dn]=ellipj(tmp,k2); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xout(1)=2*asin(k*sn);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xout(2)=2*s1*omega*k*cn;</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 >x(1)=x(1)+pi/2-phi; </span><span style="color: rgb(2, 128, 9);">% adjust phase back</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >xout(1)=xout(1)+pi/2-phi;</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 >(xout(1)>3*pi/2) xout(1)=xout(1)-2*pi; </span><span style="color: rgb(14, 0, 255);">end</span><span > </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 >(xout(1)<-pi/2) xout(1)=xout(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);">end</span></span></div></div></div><div class = 'S5'></div>
<br>
<!--
##### SOURCE BEGIN #####
%%
% Companion software for "Volker Ziemann, _Hands-on Accelerator physics using
% MATLAB, CRCPress, 2019_" (https://www.crcpress.com/9781138589940)
%% SASE free-electron laser (Section 10.4)
% Volker Ziemann, 211114, CC-BY-SA-4.0
%
% *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 this simulation we numerically integrate Equation 10.32, which describes
% the evolution of the amplitude and phase of the electro-magnetic wave (the laser
% field) and an ensemble of electrons that move in the ponderomotive field of
% the laser.
%
% First we define the initial complex field |a| of the laser and the scaled
% current jcurr, which represents the peak current of the electron distribution.
% Moreover, we define the initial distribution of electrons in the ponderomotive
% field and the number N of electrons used in the simulation. From Equation 10.32
% we see that the magnnitude of a, which is a0 describes the oscillation frequency
% $\Omega_s$ in the ponderomotive field.
clear all; close all
addpath ./elliptic % needed for elliptic12
a0=1e-8; phi=0; a=a0*exp(i*phi); % initial amplitude and phase of laser
jcurr=200; % scaled current from Equation 10.32
x0=[pi/2,0]; dx=[2*pi,0.3]; % center and spread of distribution
N=1000; % number of particles
Omegas=sqrt(a0); % synchrotron frequency
%%
% Now we can plot the initial electron distribution as a cloud of green dots
% . We see that it is evenly distributed in phase and has a small vertical extent
% in the variable $\nu$ which corresponds to the difference of electron energy
% with respect to the resonance energy of the FEL.
axis_scale=[-pi/2,3*pi/2,-17,17];
ypos=0.95*axis_scale(3)+0.05*axis_scale(4); % where to place text
zeta=-pi/2:0.01:3*pi/2; separatrix=2*Omegas*cos(0.5*(zeta-pi/2+phi));
hold off; plot(zeta,separatrix,'k',zeta,-separatrix,'k')
axis(axis_scale); xlabel('\zeta'); ylabel('\nu')
set(gca,'xtick',[-pi/2,0,pi/2,pi,3*pi/2],'fontsize',14, ...
'xticklabels',{'-\pi/2','0','\pi/2','\pi','3\pi/2'})
hold on;
x1(:,1)=x0(1)+(rand(N,1)-0.5)*dx(1); % initial distribution
x1(:,2)=x0(2)+(rand(N,1)-0.5)*dx(2);
plot(x1(:,1),x1(:,2),'g.')
title('Initial Distribution')
pause(0.01)
%%
% After subdividing the time for the transit through the FEL into |nstep=100|
% time steps, we are ready to start iterating
nstep=100; dt=1/nstep; tau=(1:nstep)/nstep; % steps along the undulator
tic; data=zeros(nstep,4); % storage for plot data
for m=1:nstep
hold off; % draw new image
%%
% As a first step we calculate $\Omega_s$ and phase $\phi$ from the amplitude
% of the field, which enables us to plot the separatrix, whose height is thus
% related to the field amplitude and phase.
Omegas=sqrt(abs(a)); phi=phase(a); % needed for electron dynamics
separatrix=2*Omegas*cos(0.5*(zeta-pi/2+phi));
plot(zeta,separatrix,'k',zeta,-separatrix,'k');
set(gca,'xtick',[-pi/2,0,pi/2,pi,3*pi/2],'fontsize',14, ...
'xticklabels',{'-\pi/2','0','\pi/2','\pi','3\pi/2'})
axis(axis_scale); xlabel('\zeta'); ylabel('\nu')
%%
% Now we update the positions of all electrons in their phase space, which is
% governed by the pendulum equation and uses pendulumtracker2_phase(), which is
% a slightly modified version of the equivalent function from Chapter 5, but this
% one is centered aroudn $\pi/2$ insetead of zero. See the code below. Once all
% electrons coordinates are updated, we plot them as red dots superimposed to
% the separatrix. Note that all electrons are independent and we use parfor as
% a simple ay to utilize all processor cores.
hold on
parfor k=1:N % update electron phase space, use "for" or "parfor"
x1(k,:)=pendulumtracker2_phase(x1(k,:),Omegas,phi,dt);
end
plot(x1(:,1),x1(:,2),'r.');
%%
% Now we calculate the bunching factor, which appears on the right-hand side
% of the equation for $a$ in Equation 10.32 and numerically integrate that equation
% in order to update amplitude and phase of the laser field.
bf=sum(exp(-i*x1(:,1)))/size(x1,1); % bunching factor <exp(-i*zeta)>
a=a-jcurr*bf*dt; % update laser field, Eq. 10.32
%%
% Now all dynamical variables are updated for this time step and we annotate
% the plot and save the interesting quantities to the array |data|. The short
% pause at the end allows MATLAB to update the plot so we can watch the evolution
% in real time. Note how the seapatrix grows as the field amplitude grows and,
% at the same time, the phase of the separatrix shifts towards is the electrons
% transfer their kinetic energy to the laser field.
text(-1.4,ypos,['bf = ',num2str(bf,'%6.3f'),' '],'fontsize',16)
text(pi,ypos,['\tau = ',num2str(tau(m),4),' '],'fontsize',16)
data(m,1)=abs(a);
data(m,2)=phase(a)*180/pi;
data(m,3)=abs(bf);
data(m,4)=(abs(a)-a0)/a0;
title([' abs(a) = ',num2str(abs(a),3),' gain = ' num2str(data(m,4),3)])
pause(0.01)
end
%%
% Once the simulation is complete, we calculate the theoretical exponential
% gain from Equation 10.33 and also from a fit to the final part of the numerically
% determined growth of |a|. The upper plot shows latter growth and also shows
% the theoretical and experimentally determined growth rate in the title.
toc; growth_theo=0.5*sqrt(3)*(jcurr/2)^(1/3);
mm=0.3*nstep:nstep; p=polyfit(tau(mm)',log(data(mm,1)),1);
growth_rate=p(1);
figure; % second figure with evaolution along the undulator tau=s/L
subplot(4,1,1); plot(tau,data(:,1),'k'); ylabel('abs(a)');
title(['Growth rate [theo/exp] = ',num2str(growth_theo,3),' / ', ...
num2str(growth_rate,3)])
%%
% The second and third plot show the evolution of the phase $\phi$ and the bunching
% factor, whereas the fourth shows the gain $(a-a_0)/a_0$ as the simulation progresses.
subplot(4,1,2); plot(tau,data(:,2),'k'); ylabel('phase(a) [deg]');
subplot(4,1,3); plot(tau,data(:,3),'k'); ylabel('<exp(-i\zeta)>');
subplot(4,1,4); plot(tau,data(:,4),'k'); ylabel('Gain');
xlabel('\tau = s/L_u')
%% Appendix
% The function pendulumtracker2_phase() integrates the equations of motion for
% a mathematical pendulum in terms of Jacobi elliptic functions. It is very similar
% to the one used in Chapter 5 (see those examples), exept this one takes the
% phase of the ponderomotive force $\phi$ into account.
function xout=pendulumtracker2_phase(x,omega,phi,dt)
x(1)=x(1)-pi/2+phi; % adjust to new phase
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; check this part next
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
x(1)=x(1)+pi/2-phi; % adjust phase back
xout(1)=xout(1)+pi/2-phi;
if (xout(1)>3*pi/2) xout(1)=xout(1)-2*pi; end
if (xout(1)<-pi/2) xout(1)=xout(1)+2*pi; end
end
%%
%
##### SOURCE END #####
-->
</div></body></html>