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DynamicApertureInBothPlanes.html
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DynamicApertureInBothPlanes.html
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<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>Dynamic aperture (Section 11.2)</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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.S10 { margin: 3px 10px 5px 4px; padding: 0px; line-height: 18px; min-height: 0px; white-space: pre-wrap; color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 15px; font-weight: bold; text-align: left; }
.S11 { 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>Dynamic aperture (Section 11.2)</span></h1><div class = 'S0'><span>Volker Ziemann, 211120</span></div><div class = 'S0'><span>In this example we follow particles in two transverse planes and iterate Equation 11.4 in order to find the dynamic aperture, shown in Figure 11.2, in cases where the non-linearity, a single sextupole, is well centered in the beam pipe and when it is misaligned.</span></div><div class = 'S0'><span>We determine the dynamic aperture by testing whether the particle survives </span><span style=' font-family: monospace;'>NN=1000</span><span> iterations. Then we select the horizontal and vertical tunes, </span><span style=' font-family: monospace;'>Qx</span><span> and </span><span style=' font-family: monospace;'>Qy</span><span>, respectively, and define the transfer matrix R, which is a simple rotation matrix in this case. </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 >NN=1000; </span><span style="color: rgb(2, 128, 9);">% maximum number of turns</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >Qx=0.31; Qy=0.28;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >R1D=@(mu)[cos(mu),sin(mu);-sin(mu),cos(mu)];</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >R=[R1D(2*pi*Qx),zeros(2);zeros(2),R1D(2*pi*Qy)];</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><h4 class = 'S5'><span>Sextupole not misaligned</span></h4><div class = 'S0'><span>First we consider the system without misalignment and probe the dynamic aperture along a line in the transverse </span><span texencoding="(x,y)" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="36" height="19" /></span><span> space defined by </span><span texencoding="x=r \cos\phi" style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI4AAAAkCAYAAABfegKAAAAHuUlEQVR4Xu2aBYwtRRBFDxDcNbi7S3CCuwYN7u7uQUIgWHACBAnubsHdNQR3d3eXHFJNJvPf2+k3yP+7dCU/f3enu6e7+nbVvdUzFMWKB1p4YKgWfUqX4gEKcAoIWnmgAKeV20qnApyCgVYeKMBp5bbSqQCnYCB5YE9gWOBq4NkmtxTgNHno//F8BuC5WOq0wMtNyy7AafLQ/+P5zsCxwOvAlDlLLsDJ8dLAb3MjsBxwKrBNznILcHK8NLDbDA98BowErBocp3HFBTiNLhrwDZYAbgN+AcYGvspZcQFOjpcGdpsjABXVvcDCuUttAs7owPLAPMAw8YIfKoMvG+HtKuCm3JcOgHbjA/sACwATAvrkUeA44KEu67PPjsElTAsTAW8A8guJ6ftd+s0H7BfvGCWiwgPA9zGHtu4cNYjwBcBMwJnA8cB7wKdNg/YFHMnSYsBPwN4BnLWAy2LQ3YCj4+cngTmbXjYYn88N+G8WYGbgZ2DxmM8msQEfAssA3zXMc0vgcOBQ4Oxw8mrAFcDvwLZBMqvDrA6cA9wKbAV8BIwH7AXsCnwDrA9cU3u3EeAOYOUAmI/HBa6L/lkKqDKmfGZTYAfgA+D5mK9NjDwjAhsCrwDu7z3dfNEUcVI/c6C58CJg3QhpawKHxQlyAg9mAGMl4NKMdk1NXFwCcFNbnxsZ3Cg3b7QA/B6x+UaO5IelY3O7janTPZnrARfWGj0BzBGRYJwKAAXoLbFJswG/1fodBeweYF4UMJokuxuYFRiz1mfGmKdRK9emCd9PBawD3BAgcj1GGP3j3MwuDwM/AvMDBoVBLBc42wEnRTidPU7UGh2c0LSIVXJZe8NAawOXNL2sw/OXAB1o+pUILgK4cR4MT6PFry+7jDsB8CLwakRXo0vVBLPA/ByYDPg6orSHynduBpzVYWxP+ZsRSZ4K8KWxVTuCxv5GgapdD6yY6QPXdV8cGqPYI9FPH5pFLg4wpeGc8/Sxno3/DnBEvYvS7o9w21iWzlzUf9VMvuamqh4WinSzFPArMFxMwrTczQ4CDgQOAQ7o0sh0/RbwSTxPisVffdbx9AInAttHH0954knPBP9wI+WTjp3MlOvzJjPCuneTR4oyAGhDAx8DYwGma9NuspsBo6+8zQg0iOVGHF/yBSChOjJyc9OEh7TnS0Z4F/g6zPRg9Mi1x4C5gI2AczM7HVwBmeRYHtXJNgdOjwcqHKOgJu85L37+NkB7TKS1zCn8Oa7jG9WmjoNjX0l3ohcTA+9WBnwNmCKem+ZbA8eOiefIa2T5/c0EvLxGANwVP/eyhpQ2NgDOz+yYNs3mKpd0H1TvLg+6Pf6oMtul0sDoJgCTvRCE9s6MOXgHZWYwQEiIU7Sxq9HTKGrUUjQkM0IZmQ0Wpt6/lap8sc42PwogQ3x/s6dDUekUc35KJ7nrMI15e+wm6vAcOwXYOhqaakwBncxIkC4WVTeq2KqtADjWJPFHOZCK1ujUl6X3u2ajSlUxSsJNi0YwFVQyI2pKW125ZG6qsv7ggOZppeMYwQ1ynFdtM7hUlerjnZhI24iZCKP1KksVOaZi833aFsAZXTqZAo2EmndF3hnVbeSIkkZN60CaG+7GdzOjTVJgcpZk7p8Hx9qcJQhVXzLX59+sK5muVFeDWA5wfLEL9h7D4pAhzIUqP3u1waWqVDRp06x9eAvcq10ZPrCfhFHi2Mk8XKYluUmStrbzd5VXJ7NOk2o41c8aBN2+tQ6mFRXVpJGGJMmdTHCYXt3jE4CdKo1UxJYzLFyq2lJRd7oYU0BJ1k/u5qQm4Kg2zL06XimrKlCOOwkno+mMXLLY62b9U+11ks7yVFsIbGPK1lQCMO2ZPt6uDWTKUXJ7Yq3satZEBJDyXJlu2qibFVujuqnMlJbMyrJ1F5Vf1dJB6OszCA98Ur71KOYhcgwjjXNNJiBdl7RE3lUvOfzVsBNwZNvmW9FqccgilCRJSwtMPMcJqUyqoa7NpvybfTw9hmVPYFWxtHmniiypDKu/+kNlIkisCVkFVtp6jZDMg2abEYKcSlKr5rxUMc7TSF6t1wg2D2m9/mOhUHIsF/F9nUwFbGFPXua8vNZIpqyXL1VTnYAROJJlbwz65IB14BhmHw+5p3yzjF4lagtGIUkkSq6MRrLzIdnSnJ1j2zSV1mctRJ90ul6RPHsdkQ5Z1SfWcy4P8Cq1va6w0Oh4RkOJq2k8FeZSX4HjuNKEVP4XgM7BKrRA6ybxHcN7KCv97pPlCK0aiUx7AmXeiHYC3AxiuaJPqwPHSzRfYv4U5Z1k97WAiDc9eRrqYbTpnf/1cwt2+/dVzOpxQlaYHc/UpZ/kfRbsVFp9fXJpSd+TL5/xtJvmFBpeECuTBUndTI0eYDmTz90vK9hutjK9SRkqrY1KAs9oYmZwLO/LrAv5v6A2xZ4WQMtyRxPHyRqkNBriPaAiU1n6T8Jrfce7Ki9rpRrdbua7LqwAZ4jf8390gqY5uav3Y9UvHXp+SQFOzy7r1x2s5ajcvAX3Br+TwstaYAFOlpsGTCOLhV5nyMmsGre2ApzWruuXHVMluZdrk44LLcDpl/vfatIqufRZhrWonA/vCjlu5eqB1UllZb1Is2xQ/xKxp9WWiNOTu0rj5IECnIKFVh74A11MjTQhIpbmAAAAAElFTkSuQmCC" width="71" height="18" /></span><span> and </span><span texencoding="y=r\sin\phi" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="68.5" height="18" /></span><span>. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S6'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >phi=0:pi/100:pi </span><span style="color: rgb(2, 128, 9);">% loop over angles phi</span></span></div></div></div><div class = 'S7'><span>We start by choosing </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">r</span><span> very large and then iteratively increase it by </span><span texencoding="dr=r/2" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="57.5" height="19" /></span><span> depending on whether the particle with starting coordinates </span><span texencoding="x_0=r\cos\phi" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="75" height="20" /></span><span> and </span><span texencoding="y_0=r\sin\phi" style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJEAAAAoCAYAAAD+HRieAAAIeUlEQVR4Xu2bB8xtRRHHfxCQZgAFQemgtIio9EgJSDVKLwFFxBaQIkiR3qWXSFNqQCmhVyW0IChSNAoIYkEBlQ7Su1LyI7Nf9p13v3vOPZf7vkvuTvKS9+7Z3bNn5j8z/5ndNxVFigb61MBUfc4v04sGKCAqIOhbAwVEfauwLFBAVDDQtwYKiPpWYVmggGg4MKAd3hmOrby3i08A34r9HA+83G1vBUQTa7lZgBuBjwEbA3+Y2O2Mvf17wE+Ax4C56/ZUQFSnocE+3wi4NF5xFLDHYF/XePUrgPWBs7KINO7kAqLGeh3IQCPRL4CPAl8F7hnIW3pbdBrgv8DMwObAhXXTC4jqNDR6z1cGfg28DcwRgOqqhQKi0QNJ3RcfAuwL/A5Yvm6wzwuImmhptMbcCSwHCKb9m3x6AVETLfU2Zl7ggEgFlu1zAX8BXgwPf77Dcs7xz22VZ7MDGwCbAvcCuwErAPsBKwHPBafy99d72+Zko01diwG/AqYGtou09iDwWi8l/meBdYBPA0tEeff5KPXydWTtXwY2A27uc/PDMP0jwBeBz2R/fgD8Evg4cBLwBWBP4OddNmypLjk+F/hhjJsWOBHYBpgf+Hf87ljBsQWwInAm8N1s7d2B7wCLxG/u4YGIEL+PtsCS8eySWKtXXc4JfB/YOgAzI7BeAP5wYPEg19cAO2V7n+Q91Uik17jQGtEn8PnB4Vn5RD1L1FqebtLrzmvGG06Tctou/XdAh2gqAkXH+TrwDeAtYDZAcP0GmCcWMlJo8PHkoEgBn6tUWtMDfwXWBv4WawsSm3pbxWJnVEDkzzMBLwXt+A9wN7BlGNnnAs+moCR4YcCo0VS+FA7xdEQ7daaDqIPLAdsPis5wJPBw6OjV6gu6pbO0wX8BC1Y6qoLt6viobzfddcNxdwEaoR/RYHpRr2KZfV6QSiOTyhQYawU49gb00PHkMmDDiCDqL5cfARd3AJdG0Q6dQOT8RyMlmmZWr9hhGcCopOjMqedU9902Ni8K0JkeLendw+OA0Wlb4NRYxH8/EX//JnB2LyDSCPfHBL36T5XJ5mVD88/qdvwBen4ssEsARUdR0YZy5cN17f9Ie9vHOJt1N2XfbtR5A3i2oo8ngz+NByJT2KeACyL15dPlMc5XTL8/bqBrgXcrYD9o6QzUOq4OrCwEPBR/F1xyoumAo7M0PfaqOmL9z1jQkOYCuYh6Q3/Xc5UGHzVMQ1Su6erA8H55TC+isSXApi9JtdxRHmXKGE/0ftNpGxDZrExE3feYdrrJh4A/Rlo6H/haNtj5RllBm3iYj+cDzEaKz43Gk0gdiE4AdozznTWzmSprB2Dn7DeRalUitzA86nnm/ft6scIEjtUgzwS/UNFGkqda7MfCxLQ2Q8y1glLxpodOh6xTEkQ6xSmxr2p2MV2uGtFUmyf5SlAX/91zOnOSXOC6CMOSzFTqnQ7skynZktCwLxFcJZS1bnjXallabGGTKTZFnmCV8z/AtLZXH2+WCqijnIR70Oo7LPVzmZIgSgWRNhXsSUzVOr6RyupMvpvEaGr1ltoViR+NDaiLREYXFxccAuqG6E9IOq3akkjqJI0i+Zbs998GAB3fVCaiOnNvGt2S2vS8QJN2f80HqVvTxWHRA3K4xtFIEwEiWwopshoA3FcSHf6qcCDP8RJF0f5yLqO00VUnmEzqQOSEa6M0NSSbcz0wtD+UcyH7KQJl1gBNetGhEcr1TCumJjJR1ZkltKW8hYKe10Y0TJUzGMGNcMmRJMM5R5pSkUjwXhkfZflu5ZnEHpQFgT0/M0cSK2+52v+BZaMabwWidJZipDEMik7vmiQx99vLsIch888lXXVoQvraGO39miOPS9xNDqBTtBEjjedO1dP4TwL/iAXzhqM/mR4so20JGAmr0q0602nlXEqdju1Anxxjq07t3txj3sIwxfluSX+nXuHYPptEIgmm90seAazWJNjyhiRJQaY6U14uotoyV9CJ9GGVXYFjotLRoG+23Kgg0qipgZiWsWv9SvR87LnlYnVlujinwzzH2UbxSMQrGV7NyMULY9pFqaao6ifY6DSrKEtl5XwOcEt+iwrFatzjFKs4G5A2NDtKExDZL7HhZRfX85o7KiulqwOdWu8embgpU6B5d1hFB7BLbyPNCqStCCIjmdWNKSKJPTUPM3XA/JhI3QoC7WDT0IPPXASXPEbCe3scveTPPXpSt8p4LYI0XiAbWYyE7sfmp5IilClWB5JA22x0//advCin7ceVJiBysqXvaZ16BPFhEmjTnVwpF48vDO16gG32YRSLBosH07RGSc3FNns9IviD6cKK1ehjq8N0r+HsISkSd8ttu9uLZi+SLshbfhrHGzYQjRpJBJIRU5JrL8vo7iGtIm+Rz9nLMWN0Es8GHeO5qOlTBzfKGAi8+mFx4Z48zLVCrR4Id1y0CYgkm3IEiVWnMG/PSIRfHwQ8f5HlvtVao2uWbaxW5rTSgGRfuwpmqYqA1wFsIGvLF3pZtQ5EtsZNU5K28aoribV5XWJdvcSU+JRe4xlUkeHSQHJyU5gRMx2h9LTLOhAdF6nIKNNN5AKSaKsFw2oSO9gCSG4kyIoMlwZsSdhUta2Sp82edpmDyGaUkUOiZtnpsYYITWVht4XT6bd3bszbSSSRrmsJXWT4NCAn0sFNZa079DmIZPc2l6wGjBpeieh2AStXiTnVtr5loFWOYrlvhLK97rlMkeHSgJWYjU4xYBZpfbkwB5FRyKjz5yj/vIzVi3iZzbLRvoP/6c1+iJVCfgzSy3pl7GA1YFVmkLCC9KijbW+sXNQfrJ2GenVphuDxjpO3FltLHbFuvXCZODoaKCAaHVsP7EsLiAam2tFZuIBodGw9sC8tIBqYakdn4QKi0bH1wL70XYtxvzgyAFsQAAAAAElFTkSuQmCC" width="72.5" height="20" /></span><span> survived NN turns or not. We repeat this procedure by halving the size of the interval </span><span style=' font-family: monospace;'>nmax=12</span><span> times. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > nmax=12; dr=10; r=dr;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">while </span><span >(nmax) </span><span style="color: rgb(2, 128, 9);">% scan radially</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > dr=0.5*dr;</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > x0=r*cos(phi); y0=r*sin(phi); </span><span style="color: rgb(2, 128, 9);">% new starting coordinates</span></span></div></div></div><div class = 'S7'><span>The function </span><span style=' font-family: monospace;'>survived_turns()</span><span>, defined in the Appendix, interates Equation 11.4 for a maximum on </span><span style=' font-family: monospace;'>NN</span><span> turns and returns the maximum number of turns that the particle survived.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >(survived_turns(NN,R,x0,y0,0,0)==NN), r=r+dr; </span><span style="color: rgb(14, 0, 255);">else</span><span >, r=r-dr; </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 > nmax=nmax-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 = 'S7'><span>The value of </span><span texencoding="(x_0,y_0)" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="44.5" height="20" /></span><span> thus determined show the largest starting coordinates along a line, defned by the angle </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">ϕ</span><span>for which a particles survives NN turns. We show this point by a black asterisk in transverse </span><span texencoding="(x,y)" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="36" height="19" /></span><span> space.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > plot(x0,y0,</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 style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >ylim([0,0.52]); xlim([-0.39,0.52]) </span></span></div><div class = 'S9'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="CEFB4BB5" data-scroll-top="null" data-scroll-left="null" data-testid="output_0" style="width: 1327px;"><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_105" widgetid="uniqName_333_105" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_107" widgetid="uniqName_333_107" style="width: 100%; height: auto;">
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">
</div></div></div></div></div></div></div></div><h4 class = 'S10'><span>Sextupole misaligned by dx=-0.05</span></h4><div class = 'S0'><span>Now we repat the same procedure, but horizontally displace the sextupole by </span><span style=' font-family: monospace;'>dx=-0.05</span><span>, which we pass as an argument to the function survived_turns(). In this way we find the dynamic aperture for the configuration with the misaligned sextupole, which plot as a blue plus sign. We find that the dynamic aperture, which defines the boundary between particle trajectories that are stable and those that are unstable, has become smaller.</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 >phi=0:pi/100:pi </span><span style="color: rgb(2, 128, 9);">% loop over angles phi</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > nmax=12; dr=10; r=dr;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">while </span><span >(nmax) </span><span style="color: rgb(2, 128, 9);">% scan radially</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > dr=0.5*dr;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x0=r*cos(phi); y0=r*sin(phi);</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 >(survived_turns(NN,R,x0,y0,-0.05,0)==NN), r=r+dr; </span><span style="color: rgb(14, 0, 255);">else</span><span >, r=r-dr; </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 > nmax=nmax-1;</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 = 'S3'><span style="white-space: pre"><span > plot(x0,y0,</span><span style="color: rgb(170, 4, 249);">'b+'</span><span >);</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div><div class = 'S9'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="AD617577" data-scroll-top="null" data-scroll-left="null" data-testid="output_1" style="width: 1327px;"><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_108" widgetid="uniqName_333_108" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_110" widgetid="uniqName_333_110" style="width: 100%; height: auto;">
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">
</div></div></div></div></div></div></div></div><h4 class = 'S10'><span>Sextupole misaligned by dx=-0.1</span></h4><div class = 'S0'><span>And in a third pass we increase the misalignement to </span><span style=' font-family: monospace;'>dx=-0.1</span><span>, repeat the procedure, and plot the dynamic aperture as red crosses. We observe that it has become even smaller.</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 >phi=0:pi/100:pi </span><span style="color: rgb(2, 128, 9);">% dx=-0.1, dy=0</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > nmax=12; dr=10; r=dr;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">while </span><span >(nmax)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > dr=0.5*dr;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x0=r*cos(phi); y0=r*sin(phi);</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 >(survived_turns(NN,R,x0,y0,-0.1,0)==NN), r=r+dr; </span><span style="color: rgb(14, 0, 255);">else</span><span >, r=r-dr; </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 > nmax=nmax-1;</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 = 'S3'><span style="white-space: pre"><span > plot(x0,y0,</span><span style="color: rgb(170, 4, 249);">'rx'</span><span >);</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 = 'S7'><span>After the three dynamic apertures for </span><span style=' font-family: monospace;'>dx=0,-0.05</span><span>, and</span><span style=' font-family: monospace;'> -0.1</span><span> are displayed, we annotate the axes.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >plot([0,0.4],[0,0.4],</span><span style="color: rgb(170, 4, 249);">'k:'</span><span >,</span><span style="color: rgb(170, 4, 249);">'LineWidth'</span><span >,2)</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);">'$\hat x$'</span><span >,</span><span style="color: rgb(170, 4, 249);">'interpreter'</span><span >,</span><span style="color: rgb(170, 4, 249);">'latex'</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);">'$\hat y$'</span><span >,</span><span style="color: rgb(170, 4, 249);">'interpreter'</span><span >,</span><span style="color: rgb(170, 4, 249);">'latex'</span><span >);</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >set(gca,</span><span style="color: rgb(170, 4, 249);">'FontSize'</span><span >,16);</span></span></div><div class = 'S9'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="DD44DF69" data-scroll-top="null" data-scroll-left="null" data-testid="output_2" style="width: 1327px;"><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_111" widgetid="uniqName_333_111" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_113" widgetid="uniqName_333_113" style="width: 100%; height: auto;">
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">
</div></div></div></div></div></div></div></div><h4 class = 'S10'><span>Survived turns along </span><span texencoding="\phi=45^o" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="65.5" height="25" /></span></h4><div class = 'S0'><span>Now we want to determine the number of turns that a particle survives as a function of its starting coordinates located on a line with coordinates </span><span texencoding="x_0=r\cos\phi" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="75" height="20" /></span><span> and </span><span texencoding="y_0=r\sin\phi" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="72.5" height="20" /></span><span> where </span><span texencoding="\phi=45^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="52" height="19" /></span><span>. The starting positions are indicated on the previous plot by the diagonal dotted line. Here we therefore define the angle </span><span style=' font-family: monospace;'>phi</span><span> and the starting values for</span><span style=' font-family: monospace;'> r</span><span> and allocate an array </span><span style=' font-family: monospace;'>turns</span><span> in which we store the survived turns for each starting coordinate. We do so for the same misalignments </span><span style=' font-family: monospace;'>dx</span><span> considered above.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >phi=45*pi/180;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >r=2:-0.0001:0.1; </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >turns=zeros(3,length(r));</span></span></div></div></div><div class = 'S7'><span>Now we loop over the radial positions r, define starting coordinates x0 and y0 and use the function survived_turns() to store the found value in the array turns.</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(r)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x0=r(k)*cos(phi); y0=r(k)*sin(phi);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > turns(1,k)=survived_turns(NN,R,x0,y0,0,0); </span><span style="color: rgb(2, 128, 9);">% dx=0</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > turns(2,k)=survived_turns(NN,R,x0,y0,-0.05,0); </span><span style="color: rgb(2, 128, 9);">% dx=-0.05</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > turns(3,k)=survived_turns(NN,R,x0,y0,-0.1,0); </span><span style="color: rgb(2, 128, 9);">% dx=-0.1</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 = 'S7'><span>Once the loop completes, we open a new figure, plot the number of survived turns for the three cases on double-logarithmic scales, and annotate the axes. Note that the radial coordinate </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">r</span><span> where the respective curves start to deviate from </span><span texencoding="10^3" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> correspond to the intersection of the dotted black line on the previous figure with the three dynamic apertures.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >figure(2)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >loglog(r,turns(1,:),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,r,turns(2,:),</span><span style="color: rgb(170, 4, 249);">'b--'</span><span >,r,turns(3,:),</span><span style="color: rgb(170, 4, 249);">'r-.'</span><span >,</span><span style="color: rgb(170, 4, 249);">'LineWidth'</span><span >,2)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >axis([0.1,2,2,1700])</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);">'d_x = 0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'d_x = -0.05'</span><span >,</span><span style="color: rgb(170, 4, 249);">'d_x = -0.1'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'Starting position r'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'Survived turns'</span><span >)</span></span></div><div class = 'S9'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="8D2D6837" data-scroll-top="null" data-scroll-left="null" data-testid="output_3" style="width: 1327px;"><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_114" widgetid="uniqName_333_114" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_116" widgetid="uniqName_333_116" style="width: 100%; height: auto;">
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">
</div></div></div></div></div></div></div></div><div class = 'S7'><span>Note how fast the survived number of turns drops once the dynamic aperture is exceeded.</span></div><h2 class = 'S11'><span>Appendix</span></h2><div class = 'S0'><span>The function</span><span style=' font-family: monospace;'> survived_turns()</span><span> receives the maximum number of turns to probe </span><span style=' font-family: monospace;'>N</span><span>, the transfer matrix </span><span style=' font-family: monospace;'>R</span><span>, the starting coordinates </span><span style=' font-family: monospace;'>x0</span><span> and </span><span style=' font-family: monospace;'>y0</span><span>, as well as the misalignments </span><span style=' font-family: monospace;'>dx</span><span> and </span><span style=' font-family: monospace;'>dy</span><span> of the sextupole as input and returns the survived number of turns as</span><span style=' font-family: monospace;'> out</span><span>. Inside the function the starting coordinates and the default return value </span><span style=' font-family: monospace;'>out</span><span> are initialized . Then we calculate the sextupole kick angles </span><span style=' font-family: monospace;'>thetax</span><span> and </span><span style=' font-family: monospace;'>thetay</span><span> from Equation 11.4, but with misalignment added.</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=survived_turns(N,R,x0,y0,dx,dy)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >x=[x0;0;y0;0]; out=N;</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 >k=1:N</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > thetax=(x(1)-dx)^2-(x(3)-dy)^2; </span><span style="color: rgb(2, 128, 9);">% sextupole kick, horizontal</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > thetay=-2*(x(1)-dx)*(x(3)-dy); </span><span style="color: rgb(2, 128, 9);">% sextupole kick, vertical </span></span></div></div></div><div class = 'S7'><span>In the next line we implement Equation 11.4 and update the particle coordinates by adding the kicks and transporting with the transfer matrix R. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S6'><span style="white-space: pre"><span > x=R*[x(1);x(2)-thetax;x(3);x(4)-thetay];</span></span></div></div></div><div class = 'S7'><span>Finally, we test whether one coordinate exceeds a large value, here we chose 3. If that happens we set the return value </span><span style=' font-family: monospace;'>out</span><span> to the present turn number</span><span style=' font-family: monospace;'> k</span><span> and exit the function.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >((abs(x(1))>3) || (abs(x(3))>3)), out=k; </span><span style="color: rgb(14, 0, 255);">return</span><span >; </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);">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>
<br>
<!--
##### SOURCE BEGIN #####
%%
% Companion software for "Volker Ziemann, _Hands-on Accelerator physics using
% MATLAB, CRCPress, 2019_" (https://www.crcpress.com/9781138589940)
%% Dynamic aperture (Section 11.2)
% Volker Ziemann, 211120
%
% In this example we follow particles in two transverse planes and iterate Equation
% 11.4 in order to find the dynamic aperture, shown in Figure 11.2, in cases where
% the non-linearity, a single sextupole, is well centered in the beam pipe and
% when it is misaligned.
%
% We determine the dynamic aperture by testing whether the particle survives
% |NN=1000| iterations. Then we select the horizontal and vertical tunes, |Qx|
% and |Qy|, respectively, and define the transfer matrix R, which is a simple
% rotation matrix in this case.
clear all; close all
NN=1000; % maximum number of turns
Qx=0.31; Qy=0.28;
R1D=@(mu)[cos(mu),sin(mu);-sin(mu),cos(mu)];
R=[R1D(2*pi*Qx),zeros(2);zeros(2),R1D(2*pi*Qy)];
hold on
% Sextupole not misaligned
% First we consider the system without misalignment and probe the dynamic aperture
% along a line in the transverse $(x,y)$ space defined by $x=r \cos\phi$ and $y=r\sin\phi$.
for phi=0:pi/100:pi % loop over angles phi
%%
% We start by choosing $r$ very large and then iteratively increase it by $dr=r/2$
% depending on whether the particle with starting coordinates $x_0=r\cos\phi$
% and $y_0=r\sin\phi$ survived NN turns or not. We repeat this procedure by halving
% the size of the interval |nmax=12| times.
nmax=12; dr=10; r=dr;
while (nmax) % scan radially
dr=0.5*dr;
x0=r*cos(phi); y0=r*sin(phi); % new starting coordinates
%%
% The function |survived_turns()|, defined in the Appendix, interates Equation
% 11.4 for a maximum on |NN| turns and returns the maximum number of turns that
% the particle survived.
if (survived_turns(NN,R,x0,y0,0,0)==NN), r=r+dr; else, r=r-dr; end
nmax=nmax-1;
end
%%
% The value of $(x_0,y_0)$ thus determined show the largest starting coordinates
% along a line, defned by the angle $\phi$for which a particles survives NN turns.
% We show this point by a black asterisk in transverse $(x,y)$ space.
plot(x0,y0,'k*');
end
ylim([0,0.52]); xlim([-0.39,0.52])
% Sextupole misaligned by dx=-0.05
% Now we repat the same procedure, but horizontally displace the sextupole by
% |dx=-0.05|, which we pass as an argument to the function survived_turns(). In
% this way we find the dynamic aperture for the configuration with the misaligned
% sextupole, which plot as a blue plus sign. We find that the dynamic aperture,
% which defines the boundary between particle trajectories that are stable and
% those that are unstable, has become smaller.
for phi=0:pi/100:pi % loop over angles phi
nmax=12; dr=10; r=dr;
while (nmax) % scan radially
dr=0.5*dr;
x0=r*cos(phi); y0=r*sin(phi);
if (survived_turns(NN,R,x0,y0,-0.05,0)==NN), r=r+dr; else, r=r-dr; end
nmax=nmax-1;
end
plot(x0,y0,'b+');
end
% Sextupole misaligned by dx=-0.1
% And in a third pass we increase the misalignement to |dx=-0.1|, repeat the
% procedure, and plot the dynamic aperture as red crosses. We observe that it
% has become even smaller.
for phi=0:pi/100:pi % dx=-0.1, dy=0
nmax=12; dr=10; r=dr;
while (nmax)
dr=0.5*dr;
x0=r*cos(phi); y0=r*sin(phi);
if (survived_turns(NN,R,x0,y0,-0.1,0)==NN), r=r+dr; else, r=r-dr; end
nmax=nmax-1;
end
plot(x0,y0,'rx');
end
%%
% After the three dynamic apertures for |dx=0,-0.05|, and |-0.1| are displayed,
% we annotate the axes.
plot([0,0.4],[0,0.4],'k:','LineWidth',2)
xlabel('$\hat x$','interpreter','latex');
ylabel('$\hat y$','interpreter','latex');
set(gca,'FontSize',16);
% Survived turns along $\phi=45^o$
% Now we want to determine the number of turns that a particle survives as a
% function of its starting coordinates located on a line with coordinates $x_0=r\cos\phi$
% and $y_0=r\sin\phi$ where $\phi=45^o$. The starting positions are indicated
% on the previous plot by the diagonal dotted line. Here we therefore define
% the angle |phi| and the starting values for |r| and allocate an array |turns|
% in which we store the survived turns for each starting coordinate. We do so
% for the same misalignments |dx| considered above.
phi=45*pi/180;
r=2:-0.0001:0.1;
turns=zeros(3,length(r));
%%
% Now we loop over the radial positions r, define starting coordinates x0 and
% y0 and use the function survived_turns() to store the found value in the array
% turns.
for k=1:length(r)
x0=r(k)*cos(phi); y0=r(k)*sin(phi);
turns(1,k)=survived_turns(NN,R,x0,y0,0,0); % dx=0
turns(2,k)=survived_turns(NN,R,x0,y0,-0.05,0); % dx=-0.05
turns(3,k)=survived_turns(NN,R,x0,y0,-0.1,0); % dx=-0.1
end
%%
% Once the loop completes, we open a new figure, plot the number of survived
% turns for the three cases on double-logarithmic scales, and annotate the axes.
% Note that the radial coordinate $r$ where the respective curves start to deviate
% from $10^3$ correspond to the intersection of the dotted black line on the previous
% figure with the three dynamic apertures.
figure(2)
loglog(r,turns(1,:),'k',r,turns(2,:),'bREPLACE_WITH_DASH_DASH',r,turns(3,:),'r-.','LineWidth',2)
axis([0.1,2,2,1700])
legend('d_x = 0','d_x = -0.05','d_x = -0.1')
xlabel('Starting position r'); ylabel('Survived turns')
%%
% Note how fast the survived number of turns drops once the dynamic aperture
% is exceeded.
%% Appendix
% The function |survived_turns()| receives the maximum number of turns to probe
% |N|, the transfer matrix |R|, the starting coordinates |x0| and |y0|, as well
% as the misalignments |dx| and |dy| of the sextupole as input and returns the
% survived number of turns as |out|. Inside the function the starting coordinates
% and the default return value |out| are initialized . Then we calculate the
% sextupole kick angles |thetax| and |thetay| from Equation 11.4, but with misalignment
% added.
function out=survived_turns(N,R,x0,y0,dx,dy)
x=[x0;0;y0;0]; out=N;
for k=1:N
thetax=(x(1)-dx)^2-(x(3)-dy)^2; % sextupole kick, horizontal
thetay=-2*(x(1)-dx)*(x(3)-dy); % sextupole kick, vertical
%%
% In the next line we implement Equation 11.4 and update the particle coordinates
% by adding the kicks and transporting with the transfer matrix R.
x=R*[x(1);x(2)-thetax;x(3);x(4)-thetay];
%%
% Finally, we test whether one coordinate exceeds a large value, here we chose
% 3. If that happens we set the return value |out| to the present turn number
% |k| and exit the function.
if ((abs(x(1))>3) || (abs(x(3))>3)), out=k; return; end
end
end
##### SOURCE END #####
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