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BeamOptics2D.html
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.S15 { 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: 0px 0px 4px 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; }
.S16 { margin: 15px 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: 17px; 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>2D beam optics (Section 3.3.3, 3.3.5, 3.6.1, and 3.6.2)</span></h1><div class = 'S0'><span>Volker Ziemann, 211106, CC-BY-SA-4.0</span></div><div class = 'S0'><span>In accelerators the elements, such as a magnet or the beam pipe between the magnets, follow one another and we represent them as lines in an array that describes this sequence. We describe drift space with a code=1 in the first column and thin quadrupoles by code=2. The second column contains the number the line is repeated internally, the third column displays the lenth of the element and the fourth column the strength. For a thin quadrupole the latter is specified as its focal length F. Summarizing</span></div><ul class = 'S2'><li class = 'S3'><span>First column: code, drift=1, quad=2</span></li><li class = 'S3'><span>Second column: repeat code for the element</span></li><li class = 'S3'><span>Third column: length of one segment</span></li><li class = 'S3'><span>Fourth column: strength of one segment, focal length for a thin quadrupole.</span></li></ul><div class = 'S0'><span>A simple FODO cell that starts in the middle of the drift space before the defocusing quadrupole is thus defined in the following array, named </span><span style=' font-family: monospace;'>fodo,</span><span> where the focal length is defined as</span><span style=' font-family: monospace;'> F=2.1. </span><span>Just below the defionition of fodo we define the</span><span style=' font-family: monospace;'> beamline </span><span>as 20 copies of</span><span style=' font-family: monospace;'> fodo</span><span> stacked on top of each other.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">global </span><span >beamline sigma0 </span><span style="color: rgb(2, 128, 9);">% needed for some functions.</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >F=2.1; </span><span style="color: rgb(2, 128, 9);">% focal length of the quadrupoles</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >fodo=[ 1, 5, 0.2, 0; </span><span style="color: rgb(2, 128, 9);">% 5* D(L/10)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0.0, -F; </span><span style="color: rgb(2, 128, 9);">% QD</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 10, 0.2, 0; </span><span style="color: rgb(2, 128, 9);">% 10* D(L/10) </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0.0, F; </span><span style="color: rgb(2, 128, 9);">% QF/2</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span > 1, 5, 0.2, 0] </span><span style="color: rgb(2, 128, 9);">% 5* D(L/10) </span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="F5870DE7" data-scroll-top="null" data-scroll-left="null" data-width="1326" data-testid="output_0" style="width: 1356px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier saveLoad" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1326px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">fodo = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">5×4</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":"4","totalRows":"5","charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 290px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 1.0000 5.0000 0.2000 0
2.0000 1.0000 0 -2.1000
1.0000 10.0000 0.2000 0
2.0000 1.0000 0 2.1000
1.0000 5.0000 0.2000 0
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >beamline=repmat(fodo,20,1) </span><span style="color: rgb(2, 128, 9);">% name must be 'beamline' </span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="449D2C66" data-scroll-top="null" data-scroll-left="null" data-width="1326" data-testid="output_1" style="width: 1356px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier saveLoad" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1326px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">beamline = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">100×4</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":"4","totalRows":"100","charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 290px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 1.0000 5.0000 0.2000 0
2.0000 1.0000 0 -2.1000
1.0000 10.0000 0.2000 0
2.0000 1.0000 0 2.1000
1.0000 5.0000 0.2000 0
1.0000 5.0000 0.2000 0
2.0000 1.0000 0 -2.1000
1.0000 10.0000 0.2000 0
2.0000 1.0000 0 2.1000
1.0000 5.0000 0.2000 0
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><div class = 'S0'><span>Now calculate all the transfer matrices with the function </span><span style=' font-family: monospace;'>calcmat()</span><span> that is defined in the appendix</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div></div><div class = 'S10'><span>Then we allocate memory to store the positions after each segment that we want to display later</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >data=zeros(1,nmat); </span><span style="color: rgb(2, 128, 9);">% allocate memory</span></span></div></div></div><div class = 'S10'><span>and define the input state x0, which contains the starting position and angle</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >x0=[0.001;0]; </span><span style="color: rgb(2, 128, 9);">% 1 mm offset at start</span></span></div></div></div><div class = 'S10'><span>before mapping the input x0 to the state vector x at the end of each segment along the beam line</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:nmat </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > x=Racc(:,:,k)*x0;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > data(k)=x(1); </span><span style="color: rgb(2, 128, 9);">% store the position</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S10'><span>and annotate the axes</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >plot(spos,1e3*data,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); </span><span style="color: rgb(2, 128, 9);">% 1e3 to convert to mm</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'s [m]'</span><span >); </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >ylabel(</span><span style="color: rgb(170, 4, 249);">' x [mm]'</span><span >); </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'Trajectory'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >xlim([spos(1),spos(end)])</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="1C50D4D0" data-scroll-top="null" data-scroll-left="null" data-testid="output_2" style="width: 1356px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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BFBRBARRAQRwVBEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRDAUEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBEMRQQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEX/rSl5hEDVPoC1/4Ai972cvYunUrGzduJKWUUkrjpWHK3HHHHWzevJl3vvOdrF+/nj179rBnzx727t1LSimllMZDw5T50Ic+xM9+9jP+8i//krPOOouzzjqLs846i7e97W2shForZ555JmvR5s2bmUSbN29mEm3evJlJtXnzZibR5s2bmUSbN29mEm3evJlxJomHPOQhSGIaNEyZv/u7vyMiiAgigoggInjzm9/MSui6DkmsRVu2bGESbdmyhUm0ZcsWJtWWLVuYRFu2bGESbdmyhUm0ZcsWJkGtlWnQkI4JSaSUUkorRRLTpCGtqForQ5JIKaWUVookhrquYxo0pBVnZkgipZRSWimDwQAzY1o0pBVVa6WUQtd1pJRSSiul1kophVor06AhrRhJmBlt25JSSimttJmZGSQxDRrSipHEkJlRayWllFaCJNavX0+abrVWzAwzQxKTriGtKDOjlIIkUkppJUii1kqaXpIwM8wMM0MSk64hrZiu6yilMGRmSCKllEat6zqGJJGmkyQWmRmSmHQNacVIotfrsUgSKaU0arVWhmqtpOllZgyZGV3XMeka0oqRhJkxVEpBEmk6SeLMM89EEimNmiTMjDS9uq6jlMJQr9djGjSkFSMJM2PIzBgMBqTpJQlJpDRKkhjq9/sMBgPSdJLEIjOj1sqka0grQhKSMDOGer0ekkjTSRJDkkhplCQx1Ov1kESaTpJo25ahUgqSmHQNacWYGYvMDEmk6dR1HUNd15HSKEnCzBiSRJpOktifmSGJSdaQVoQkzIxFpRRqraTpZWZIIqVRGgwGlFIopSCJNH0kIYlSCvuTxCRrSCui6zrMjANJIk2fWiuzs7PUWklplGqttG2LmSGJNJ3MjP2VUpDEJGtIK8bM2J+ZkaaXmWFmSCKlUZGEmTFkZkgiTRdJmBn7MzMGgwGTrCGtiForbduyv1IKtVbS9JGEmVFKodZKSqMgiSEzY5Ek0nSRhJmxv16vhyQmWUM6ZsyMwWBAmi6SkISZYWZ0XUdKoyAJM2NRKQVJpOkyGAwwM/ZnZkhikjWkFVFrxczYX6/XQxJp+pgZQ71ej5RGpes6zIz9DQYD0nSptdLr9dhfKYVaK5OsIY2cJMwMM+NAkkjTRRJmxlC/32d+fp6URkESZsaitm2RRJo+ZsbBSGJSNaSRk8TB9Pt9aq2k6SKJ/ZkZkkhpuSTRti1putVaMTMOZGZMsoa0IsyMQ5FEmh6DwYBSCotKKdRaSWm5aq2YGYvMjForaXpIwswwMw5USqHWyqRqSCPXdR2lFA7GzEjTRRK9Xo/9DQYDUloOSZgZZsaiUgqSSNNDEoczGAyYVA1p5CRxKKUUaq2k6SEJM2NR27ZIIqXlkISZcTCSSNPDzDiYtm2RxKRqSCMnibZtOZTBYECaHpLYXymF+fl5UlqOrusopXAgMyNNj67rKKVwKJKYVA1p5CRxKG3bIok0PSRRSmGRmTEkiZSWqtZKr9fjQKUUaq2k6SCJQymlUGtlUjWkkZKEJEopHIok0nSQhJlxIDOj1kpKy2FmpOkmibZtORgzY5I1pJEzMw6llEKtlTQdJHEwpRRSWipJ1FoppXAgM6PrOtJ0kMThmBl79uxhEjWkkZKEmXEoZkaaLmbGgdq2pes6UloqM+Nger0eaTpIQhKlFA6llMK9997LJGpII9V1HWbG4ZgZkkiTr+s6SikcyMyotbJckpifnydNF0mYGQdjZkgiTQczY1o1pJEzMw6nlEKtlTS9SilIYrk2btzIwsICabp0XUcphYMppVBrJU0+SZgZh9O2LT//+c+ZRA1ppGqttG1LSkO1Vtq25WDMDEksR62VWitputRaaduWNN26rsPMmFYNE+iWW27hcL7//e+zc+dOdu7cyc6dO9m5cyc//vGPOVbatqXrOtJ0K6VQa2Wpaq2YGWn6SOJwzAxJpMlnZhxOKYV7772XSdQwYa688kre8IY3cDjbt29nZmaGTZs2sWnTJjZt2sTXvvY1RqHWipmR0pAkzIyDaduWrutYqq7r6Pf7mBmSSNNBEkOlFA7FzKi1kiZbrZW2bTkcM2PPnj1MooYJ8cMf/pDXv/71vO997+PBfPOb3+SSSy5h165d7Nq1i127dnHOOeewXJIwM8yMwymlUGslTTZJDJkZhyKJpaq10rYtZoYk0nSQxIMxM1JadMIJJyCJSdMwIS677DJOPfVU3v72t/NgbrvtNh73uMfx/e9/nz179jAqkjgSZoYk0nTr9/vUWlkKSUiilIKZIYk0HSRhZhyOmTEYDEiTrdaKmfFgjj/+eGqtTJqGCfHmN7+Z173udTzsYQ/jcPbu3ct3vvMd3vKWt7Bhwwae/OQn88Y3vpEH4+64O+7O5ZdfzqGYGUfCzJBEmlySMDMOx8yQxNGqtWJmDJkZg8GANB4ksRyDwYBSCofT6/WQRJpckjAzzIwDXX755bg77o67c8IJJzCJGiZE0zQcibvvvptzzz2Xq6++mi984Qvs2LGDW265hQ9/+MMcTkQQEUQEW7Zs4WC6rqOUwpEwM2qtpMklCTPjcEop1Fo5WgsLC8zOzjLU6/WQRBoP69evZ35+nqWqtdK2LQ9GEmlySeJQtmzZQkQQEUQEp512Gv1+n0nTMGXOOOMM3vve93LGGWcwdPrpp/OsZz2LW2+9leWSxJEyM9JkGwwGmBmHY2Z0XcfRkEStFTNjkSTS2icJSSwsLLBUkjAzDqeUQq2VNNnMjCNxwgknMIkapsxgMOCaa65hf/fddx/HHXccyyWJtm05EmZG13WkySWJXq/H4fR6PY6WJEopmBlDpRQkkcaDmSEJSRwtSQyZGYdjZqTJ1nUdpRSmWcMU+OpXv8pdd93F0C9+8QtmZ2e5/fbbGbr77rv5zGc+w/nnn89ySeJI9Xo90mSThJlxOP1+n/n5eY5G13WUUlhkZkgirX2SMDNKKdRaOVqSMDOOhJkhiTSZJDHtGqbAZZddxuc//3mG3J1LLrmEF7zgBczMzHDeeefxile8gnPOOYflkIQkSikcCTOj1kqaXJI4EmaGJI5UrZW2bdmfmSGJtLZJYqhtWzZu3MjR6roOM+NISSJNJkm0bcs0a5gwbdtyyy23sL9t27bxvOc9j0UXXXQRO3fu5KqrrmLnzp1s3LiRUTAzjlQpBUmkySWJUgoPppRCrZUjIQlJlFJI42cwGFBKod/vY2ZI4mhIwsw4EqUUJJEmkySmXcOUapqGk046iaZpGAVJmBlHw8yQRJo8kjAzjtRgMOBILCwsUErhQKUUaq2ktU0SvV6PoVIKc3NzHA1JtG3LkRoMBqTJIwlJlFKYZg1pJCRhZhwNM0MSafJI4ki1bYskjkStlZmZGdJ4koSZMTQzM8P8/DxHo9aKmXEk2rZFEmkymRnTriGNxGAwwMw4GmaGJNJkMjOORCmF+fl5HowkJFFK4UBmRtd1pLVNEotKKZgZtVaOhCTMDDMjTTdJmBnTriGNRK2VXq/H0TAzuq4jTZ6u6yilcCTMjCFJHI4kzIyD6fV6pLVPEqUUFs3OzrKwsMCRkISZcaTMjForafJ0XYeZMe0a0siYGUej1+uR0pCZIYnDmZubo5TCwZgZkkhrlyTMjP31+33m5+c5El3XUUrhSJVSkESaTGbGtGtII1Frxcw4GmZGrZU0eWqttG3LkSqlIInDqbXSti0HY2bUWklrlyQOppTC/Pw8D6bWSq/X42iYGZJIk6XWStu2TLuGtGySMDPMjKNRSkESKbVtS9d1HEqtFTOjlMLBmBlp7TMzDjQzM0PXdRwJMyOl9EsNadkksVRmhiTSZKm1YmYcKTNDEofSdR2lFA7HzJBEWpu6rqOUwoH6/T7z8/McjiRqrZRSOBqlFGqtpMlSa8XMmHYNaSTMjKWSRJockjAzzIwjVUqh1sqh1FqZmZnhcMwMSaTxU0phfn6ewzEzUpKEmWFmTLuGtGxd11FKYSlKKUgiJTNDEgeShCRKKRyOmSGJtDbVWmnbloOZmZmh6zoORRJmxtFq25au60iTQxLplxrSskliqcyMwWBAmhySMDOOVimFWisHqrViZjwYM2MwGJDGT7/fZ35+HkkcTNd1lFJIacjMSNCQlk0SbduyFL1eD0mkySEJM+NotW1L13UcaGFhgZmZGR5Mr9dDEmltkoSZcSj9fp9aKwdTa6VtW46WmSGJNDm6rqOUQoKGtGySWCozQxJpcgwGA8yMUZBErZVSCml8SWLIzDiUtm3puo6DkcRSlFKotZImhyR6vR4JGtKySaKUwlKUUqi1kiaHJHq9Hker3+8zPz/P/iRhZpgZD6aUQq2VNJ76/T61ViSxP0kMlVJISRJmRoKGtCySMDOWSxJpMkjCzFgKM0MSi7quo9/vcyTMDEmktUcSZsaDKaVQa2V/klgOM0MSaTJIwsxI0JCWRRJmxnKYGWlySMLMWIpSCrVWFtVaaduWoyGJtLZIwsx4MG3bMjc3x/4kYWYslZlRayWNP0lIwsxI0JCWRRLLVUqh1kqaDJIwM5bCzBgMBgxJQhKlFI6UmZHWnsFggJnxYPr9PkOSWDQYDCilsFRmRpocZkb6pYa0LIPBgFIKyzUYDEjjTxJmxlL1ej0kMbSwsICZcTRKKdRaSWuLJHq9HkeilMLc3ByLaq20bctSmRmDwYA0/iRhZqRfakjLUmul1+uxHG3bIok0/iRhZixVKYX5+XmGaq3Mzs6Sxp8kzIwjMTMzw/z8PIskYWYsVa/XQxJp/HVdh5mRfqkhLZuZsVySSMnMGKq1IolSCkfDzOi6jrS2SOJIlVIwM2qtSGLIzFgqM0MSaTKYGemXGtKy1FoxM5aj3+9TayWNv67rKKWwHGbGwsICZsbR6vV6pLVHEqUUjtTs7CwLCwtIwsxYDjOj1koaf7VW2rYl/VJDWjJJmBlmxihIIo03SSxXKYX5+XlKKRwtM0MSae2QhJlxNPr9PvPz83Rdh5mxHGZGSpOoIS2ZJEbFzEjjTxJt27Icbdsy1LYtR8vMqLWS1g5JLEUpha1bt2JmLJeZIYk03mqtmBnplxrSspgZo1BKodZKSqUUtm7dSimFo2VmpLXHzDhaMzMzDLVtyyhIIo0vSZgZZkb6pYa0ZF3XUUphVAaDAWm81VoxM5bDzJidnWWpzAxJpLWh6zpKKRytfr9Pv9/HzFiuUgqSSONLEunXNaQlk8SotG2LJI5ErZUzzzyT+fl50tohCTPDzFhNZoYk0vjbtm0bZsZymRmDwYA03syM9CsNackk0bYtoyKJw5HE3NwcGzdupN/v03UdKR3IzJBEWhtqrbRty2rq9XpIIo2vrusopZB+pSEtmSRGpZRCrZVDkcT69esZ+va3v03btkgirR2SMDNWm5kxGAxIKU0OSfR6PdKvNKQlk0QphVEwMw5GEnNzc6xfv55+v8/s7CxDZkatlbR2dF2HmbHaer0ekkhrQ60VM2M1lVKotZLGlyTMjPQrDWlJJGFmjJKZIYlFkti4cSO1Vnbs2MHs7CyLzIy09pgZKS2ShJlhZqwmM0MSaXxJwsxIv9KQlkQSZsYolVKotTI0NzfH+vXrKaWwY8cOzIwDmRmSSGtDrZVer8dqMzNqraS0P3ZyU1gAACAASURBVDNDEmn8SEISZkb6lYa0JJJYCYPBgLm5Oebn59mxYwezs7MciplRayWtHWbGaiulIIm0+iRhZqS0XGZG+nUNU+6WW25hKQaDAaUURmlmZob5+XmGvv3tb2NmHI6ZkdYOSZgZa4Uk0uqShJmxFpRSqLWSxo8kzIz06xqm2JVXXskb3vAGlqLWSq/XY5RKKXz7299mdnaWI2FmdF1HWn2SkISZsRaYGWn1DQYDzIyUlqPrOsyM9OsaptAPf/hDXv/61/O+972P5TAzVlOv1yOtHWbGWlFKodZKWl2S6PV6rAVt29J1HWltkEStFUkcCTMj/bqGKXTZZZdx6qmn8va3v52lkoSZsZrMDEmk1ScJMyOl/UnCzEjpQHNzc2zcuJEzzzyThzzkIZx55pmceeaZrF+/no0bNzI3N8fc3Bxzc3PUWmnblvTrGqbQm9/8Zl73utfxsIc9jCNxxx13cNJJJ3HSSSdx0kkn8cQnPpEhM2M1lVKotZJWnyTWEjOj6zrS6pKEmbEWmBmSSGuDJLZt28a+ffvYt28fO3bsYMeOHczOztK2LYskYWaYGUfq8ssvx91xd9ydSdUwhZqm4Wicdtpp3HDDDdxwww3ccMMNXH311ezYsYOUFg0GA0oprBW9Xo+0+iRhZqwFpRRqraS1odaKmbHIzDAzSin0+31mZ2eZnZ1l27ZtbNu2DTPjSG3ZsoWIICKICCZVQ3pQJ510EqUUSimUUiilYGasBWaGJNLqksRaYmZIIq0eSZgZa40k0uqShJlhZqSla0hjrZRCrZW0uiTRti1rhZlRayWtHkmYGWuJmZFWnyTS8jWklCaOmZHSgcyMWitp9ZkZaXka0lgzM7quI62uWiulFNYSM0MSaXV0XUcphbXEzEirr+s6Simk5WmYYm3bcssttzDOer0eaXVJwsxYiySRVock1hozYzAYkFaXJNLyNaSxZmZIIq0eSaxFpRQkkVaHJNq2ZS3p9XpIIq0uSbRtS1qehjTWSinUWkmry8xYiwaDASktMjMkkVaXJNLyNaSJIIm0Orquw8xYa9q2RRJpddRaMTPWEjOj1kpaXZIopZCWpyGNPTMjrS4zI6VFkjAzzIy1xMxIq0sSZkZavoY09kop1FpJq6PWSq/XY60xM2qtpLQ/M0MSaXVIwsxIy9eQUlo2M2OtKaUgiXTsScLMWIvMDEmk1SGJNBoNaey1bUvXdaTVIQkzY62SRDq2uq7DzFiLzAxJpNUxGAwopZCWryGltGSSkISZsRaZGWl1mBlrkZkxGAxIq6PWSq/XIy1fQxp7ZkatlbQ6zIy1qpRCrZV0bNVa6fV6rEW9Xg9JpNVjZqTla0hjr5SCJNKxJwkzI6UDmRlrVa2VtDokYWak5WtIE8HMkEQ6tiSxlpkZg8GAdGxJwsxYi/r9PkO1VtKxJYkhMyMtX0NKackGgwGlFNaqXq+HJNKxIwlJmBlr1ezsLAsLC6Q0zhrSRCilUGslHVuS6PV6rFVmhiTSsWVmrGX9fp9aK7VW0rEjCTMjjUZDmhiDwYB0bEnCzFirzIxaK+nYkYSZsdb1+30WFhZIx07XdZRSSKPRkCZC27ZIIh1bkljLzIx0bEliHMzOzjI/P48kUhpHDSmlJZHEUCmFtczMkEQ6NgaDAaUUxkG/32dubo50bNRaaduWNBoNaSKUUqi1ko6dhYUF+v0+40AS6diQxLjYtm0b8/PzpDSOGtJEMDMkkY4NSWzdupW2bVnrSilIIh0bkmjblnHR7/eZm5sjrbxaK6UU0mg0pIlhZkgirTxJmBmlFMbBYDAgpYOZmZlh69atpJUlCTMjjU5DmiiSSCtvbm6Ofr/POGjbFkmkY6PWipkxLkoplFKYn58nrRxJmBlpdBrSxCilIIm0siQhidnZWVLanyTMDDNjnMzOzjI3N0daOZJIo9WQJoaZMRgMSCur1oqZMS7MjForKR1KKQUzo9ZKWhmDwYBSCml0GtLE6PV6SCKtrIWFBWZnZxkXpRQkkVaeJMyMcTQzM8Pc3BxpZUii1+uRRqchTRRJpJUjCUmUUhg3kkgrq+s6zIxx1O/3kUStlTR6kjAz0ug0pIlRSkESaeXUWimlMG7MjHRsmBnjanZ2loWFBdLoScLMSKPTkCaGmSGJtHIWFhaYmZlh3JgZtVbSyqq10uv1GFf9fp9aK7VW0uhIQhJmRhqdhjRRzAxJpNGThCRKKYwbMyMdG2bGOOv3+ywsLJBGy8xIo9WQJoqZIYk0egsLC5RSGEdmxmAwIK0sSZgZ42x2dpb5+XkkkUZDEmZGGq2GNFHMDEmk0ZLE/Pw8MzMzjKNer4ck0sqRhCTMjHHX7/eZm5sjjUbXdZgZabQa0kQxMwaDAWm0JDFUSmEcmRmSSCvLzJgE27ZtY35+njQ6ZkYarYY0UXq9HpJIozU3N0e/32dcmRmSSCtHEmbGpOj3+8zNzZGWr9ZK27ak0WpIE0cSaXQkIYmZmRnGlZkhibRyJDFJZmZm2Lp1KymtVQ0T5I477uCmm24iIjic73//++zcuZOdO3eyc+dOdu7cyY9//GMmQSmFWitpdGqtmBlmxjgzMySRVsZgMKCUwqQopVBKYX5+nrQ8tVbMjDRaDRPik5/8JC960Yu48cYbefWrX8173vMeDmX79u3MzMywadMmNm3axKZNm/ja177GJDAz0mgtLCwwOzvLJJBEWhmS6PV6TJKZmRm6riMtnSTMDDMjjVbDBNi7dy+zs7MsLCzwrne9i2uuuYZt27YhiYP55je/ySWXXMKuXbvYtWsXu3bt4pxzzmFSmBmSSMsnCUmUUhh3pRQkkVaGJMyMSWJm1FpJSyeJtDIaJsDNN9/MKaecwuMf/3iGTj31VJ75zGfyuc99joO57bbbeNzjHsf3v/999uzZw6QxM2qtpOWrtVJKYVIMBgPSypDEpCmlIIm0PGZGGr2GCfDDH/6Q3/md32F/J598Mv/1X//Fgfbu3ct3vvMd3vKWt7Bhwwae/OQn88Y3vpEH4+64O+7O5ZdfzlpmZqTRWFhYYGZmhknQti2SSCtDEqUUJo2ZIYm0NF3XUUrhWLr88stxd9wdd2dSNUyAvXv30jQN+2uahgceeIAD3X333Zx77rlcffXVfOELX2DHjh3ccsstfPjDH+ZwIoKIICLYsmULa5mZ0XUdaXkkIYlSCpPAzJifnyeNniTMjElUSqHWSloaSfR6PY6lLVu2EBFEBBHBpGqYAA996EPZu3cv+3vggQc4/vjjOdAZZ5zBe9/7Xs444wyGTj/9dJ71rGdx6623Mil6vR5p+RYWFiilMClKKQxJIo2WJCbZYDAgLY0kzIw0eg0T4Dd/8zf5xje+wf5+8IMf8NSnPpUDDQYDrrnmGvZ33333cdxxxzEpzAxJpKWTxPz8PDMzM0wSM6PWSho9M2MStW2LJNLSSCKtjIYJ8Ad/8AcMdV3H0H//93/zhS98gT/8wz9k6Ktf/Sp33XUXQ7/4xS+YnZ3l9ttvZ+juu+/mM5/5DOeffz6TopRCrZW0dJIYKqUwSUopDAYD0mh1XYeZMakkkY6eJCRRSiGNXsMEaJqGd7/73bzhDW9gZmaGF7/4xbzjHe/gN37jNxi67LLL+PznP8+Qu3PJJZfwghe8gJmZGc477zxe8YpXcM4555DSorm5Ofr9PpOmbVskkUbPzJhE/X6fWitpacyMtDIaJsTTnvY0Pv/5z3PVVVfxpS99iT/7sz9j0bZt23je857HoosuuoidO3dy1VVXsXPnTjZu3MikMTMkkY6eJCQxMzPDpOn3+8zPz5NGq9ZK27ZMKjNDEunoSMLMSCujYcKcdNJJNE3Dg2mahpNOOommaZhEpRRqraSjV2vFzDAzJpGZIYk0OpKYdLVW0tHpug4zI62MhpTSr1lYWGB2dpZJVf4/e/Af6ld+13n86bFQjGUZqyj2n/OyurzNwNIh4kiHW88nYGECLWFhkDYW7/eCDOsfQxFswY56566l4NbC1IQOW5V8g5TsQrFIQaiMk89xOvOHGyfY2ixfU9LXaUFTAmNR0K6S7np3DJNJ8+Pem/vje895Px6lUGsl7Q7bbCqlMFalFNLOSCLtjYY0SpLo+560fbYZM0n0fU/aHbaRxJh1XUff96TtqbXSti1pbzSkUWrblrR9ttlUSmGs2rYl7Z6+7ymlkNKdSCLtjYY0SpKwTdoe20hizGazGfP5nLQ7aq2M3Ww2Yz6fk7an1ook0t5oSKNUSqHWStqevu+ZAknYJu2OruuYAtukrbGNJCSR9kZDGjXbpO0ppTB2pRRqraQHY5taK6UUxk4Saetsk/ZWQxotSaTtqbXSdR1j13Udfd+THoxtJDEFpRRqraStk0TaOw1ptEop1FpJW1drRRJTYJv0YPq+RxJTIIm+70lb0/c9pRTS3mlIKf1/tpGEJMZuNptRayU9GNuUUpiCtm1JW2ebtLca0mh1XUff96StsY0kpkIStVbSztmm6zqmoJTCfD4nbY1tuq4j7Z2GlNL/1/c9pRSmopSCbdLO2KbWSimFKZBE2jrbpL3VkEZLErVW0tbYZkq6rqPve9LOSWJKJGGbdH+2KaWQ9k7DPrp+/TrXr1/n+vXrXL9+nevXr3P9+nWuX7/O9evXuX79OtevX+f69etcv36d69evc/36ddLOlFKwTdoa23Rdx1SUUpjP56SdsY0kpqSUQq2VdG+2kUTaWw376P3vfz8rKyusrKywsrLCysoKKysrrKyssLKywsrKCisrK6ysrLCyssLKygpd15F2ThK2SfdXa0USUyGJTbZJ29f3PaUUpkQSwzCQ7s02kkh7q2Gf/Y//8T+4dOkSly5d4tKlS1y6dIlLly5x6dIlLl26xKVLl7h06RKXLl3ii1/8IintB9tIQhJTUkqh1kravlorXdcxJW3bYpt0b7ZJe69hH/3Yj/0Yb3nLWzhy5AhHjhzhyJEjHDlyhCNHjnDkyBGOHDnCkSNHOHLkCEeOHOH7v//7kUTauVIKtVbSvdlGElMjiWEYSNtXa0USUyKJWivp3oZhoJRC2lsN++j3fu/3+I//8T9y05e//GU+8IEPcOrUKU6dOsWpU6c4deoUH/jAB9h05MgR/uRP/oT0YIZhIN1b3/eUUpiaruuwTdoe20hCElNSSsE26d5qrbRtS9pbDQfkgx/8IE888QTf+MY3uHbtGteuXePatWtcu3aNa9eukXZH13XYJt1brZW2bZma2WzGfD4nbY9tJDFFkrBNujdJpL3VcED6vufTn/40fd/zwgsv8MILL/DCCy/wwgsv8Pzzz5PSfpPEFEnCNmnr+r6nlMIUlVKotZLuzjaSSHur4YC86U1v4uGHHybtrVIKtVbS3dmm1kophSkqpVBrJW1drZWu65iqYRhId2abTZJIe6vhgPzGb/wGH/7wh7lx4wZp70jCNuneJDFVXdfR9z1p62wzVV3XYZuUDlrDAXn88cd5+eWXefjhh3nkkUd45JFHeOSRR3jkkUc4duwYafdIwjbpzmwjiSmzTdoa22wqpTBVtkl3ZhtJpL3XcEAef/xxfuAHfoA//MM/5Pz585w/f57z589z/vx5PvOZz5B2l23SnfV9TymFqZrNZtRaSVtjG0lM1Ww2o9ZKurO+7ymlkPZewwF59dVX+dznPsejjz7K0aNHOXr0KEePHuXo0aMcPXqUtHtKKdgm3Vmtla7rmDJJ2CbdX9/3lFKYMknYJqWD1HBAfvAHf5Cvf/3rpL0niWEYSOluSinUWkn3V2ulbVumrtZK+m61VrquI+29hgPymc98hl/8xV/kueee4+rVq1y9epWrV69y9epVrl69Sto9bdtim/TdbFNrpZTClHVdR9/3pK2RxJSVUkjpoDUckPe9731sevbZZzlx4gQnTpzgxIkTnDhxgve85z2k3SMJ26TvZhtJTJ0k5vM56d5sY5tSClPWdR1935O+W62VUgpp7zUckL7vWSwWLBYLFosFi8WCxWLBYrHg8uXLpN1TSqHWSrozSUxdKYVNtkl3Z5uU7sY2kkj7o+EAffnLX+YDH/gAp06d4tSpU5w6dYpTp07xgQ98gLS7JGGb9EZ931NKIYEkaq2ku+v7HklM3Ww2Yz6fk97INpJI+6PhgHzwgx/kiSee4Bvf+AbXrl3j2rVrXLt2jWvXrnHt2jXS7rNNeqNaK13XkaCUwjAMpLurtVJKIb3GNul1tkn7p+GA9H3Ppz/9afq+54UXXuCFF17ghRde4IUXXuD5559nr33jG9/g+eefZ7FYMAWlFGyT3sg26TVd12GbdG9d15FAEumNhmGglELaHw0H5E1vehMPP/wwB+Hzn/8873vf+/jCF77AL//yL/PJT36SsZNE3/ek19lmUymFBLPZjPl8Troz29RaKaWQoJRCrZX0ulorbduS9kfDAfmN3/gNPvzhD3Pjxg32040bN1hfX+fcuXN8/OMf57Of/Sxnz57FNmPWti3pjWyT3kgStknfzTaSSK+RRN/3pDeSRNofDQfk8ccf5+WXX+bhhx/mkUce4ZFHHuGRRx7hkUce4dixY+yVP//zP+ehhx7iJ37iJ9j01re+lZ/92Z/li1/8ImMmiVor6XW2kUR6XSmFWivpziSRXtO2LemNaq1IIu2PhgPy+OOP8wM/8AP84R/+IefPn+f8+fOcP3+e8+fP85nPfIa98q1vfYuf/Mmf5FZvectb+Ju/+RvGrJSCbdLrhmGglEJ6nST6vid9t77vKaWQXlNKYT6fk15jG0lIIu2PhgPy6quv8rnPfY5HH32Uo0ePcvToUY4ePcrRo0c5evQoe+XGjRs0TcOtmqbhO9/5DvcSEUQEEcHp06c5jCRhm/SaWitd15Fe17Yt6c5qrXRdR3qNJNLrbLMsTp8+TUQQEUQEY9VwQH7wB3+Qr3/96+y3N7/5zdy4cYNbfec73+FNb3oT97JYLFgsFiwWC5566ikOI0nUWkmvsY0k0utmsxnz+Zz03WqtSCK9ThK2Sa+RxDJ46qmnWCwWLBYLFosFY9VwQD7zmc/wi7/4izz33HNcvXqVq1evcvXqVa5evcrVq1fZKz/8wz/MX//1X3Orv//7v+enfuqnGDtJpNfYZpMk0htJwjbpdbaRhCTS60op1FpJ0Pc9pRTS/mk4IO973/vY9Oyzz3LixAlOnDjBiRMnOHHiBO95z3vYKz/90z/Npr7v2XTlyhVefvll3vnOdzJ2XdfR9z0JbCOJ9N1KKdRaSa+zjSTSG0liGAYS2KZtW9L+aTggfd+zWCxYLBYsFgsWiwWLxYLFYsHly5fZK03T8Du/8zt85CMfYXV1lfe///389m//Nj/0Qz9Emo6+75FE+m5d19H3Pel1fd9TSiG9Udu22CaBbSSR9k/DPnrve9/LlStX2Kp/+qd/4tixY+y2n/mZn+Gll17iueee4y/+4i94/PHHmYJSCvP5nAS2kUS6M9uk19Va6bqO9EaSqLWSwDaSSPunYR/98z//M4vFgitXrnDlyhWuXLnClStXuHLlCleuXOHKlStcuXKFK1eucOXKFRaLBd/+9rfZK0eOHKFpGqZCEuk1tum6jvTdZrMZtVbS62qtSCK9USkF20ydbTZJIu2fhn3UNA0f/vCHOXnyJCdPnuTkyZOcPHmSkydPcvLkSU6ePMnJkyc5efIkJ0+e5Bd+4Rf4nu/5HtLukYRtpq7WiiTSnUnCNglsIwlJpO8mCduktN8a9tGf/umfcvnyZS5fvszly5e5fPkyly9f5vLly1y+fJnLly9z+fJlLl++zOXLl7l8+TJf+cpXSLunlEKtlSmzjSQkke6slEKtlQS2kUS6s1IKtVamzDaSSPurIU3OMAxMmW0kke6u6zr6vidB3/eUUkh3NwwDU9b3PaUU0v5qSJPSdR22mbK+7ymlkO5uNpsxn89JUGul6zrSnXVdh22mzDZp/zWkybHNlNVaaduWdG+SsM3U2Sbdm22mzDZd15H2V8MSunHjBmlvzGYzaq1MnSTSvZVSqLUyZbbZVEoh3dlsNqPWypTZRhJpfzUckOPHj/PlL3+Z2124cIH/9J/+E2lv2Waqaq2UUkj31nUdfd8zZbaRRLo3SdhmimyzSRJpfzUckHe+85088cQTfPKTn+SmD37wg/yX//Jf+IVf+AXS3pHEVNlGEun+ZrMZ8/mcKev7nlIK6f5qraS0nxoOyMc+9jH+4A/+gE996lN0Xcc73vEOXnrpJf70T/+Up59+mrR3SinUWpki20gibY0kbDNVtVbatiXdWymFqbKNJNL+azhAKysrfPjDH+batWt8+9vf5r/+1/9K27akvSWJYRiYor7vKaWQtqaUQq2VKZNEureu6+j7ninq+55SCmn/NRyQV199la7r+G//7b/xyU9+kmeeeYZf+ZVfYXV1lbS32rbFNlNUa6VtW9LWdF1H3/dMkW1sU0ohpbuxTToYDQfkP//n/8xDDz3El770JR5//HHe//7387/+1//iq1/9Kg8//DBp70jCNlMlibQ1s9mM+XzOFNkmbc1sNmM+nzNFtum6jrT/Gg7Ir/7qr/LHf/zHvPnNb+am//Af/gMvvfQSa2trpL1TSqHWytTYptZKKYW0dZKwzdT0fY8k0tbZZmpskw5GwwF573vfy9186EMfIu0tSdhmaiSRtqeUQq2Vqam1srq6StoaSUyNbWxTSiHtv4Y0WbaZEttIIm1P13X0fc+U2KbWiiTS1pRSqLUyNZJIB6MhTVIpBdtMSd/3lFJI2zObzZjP50yJbSRRSiFtjSSGYWBKbCOJdDAa0iRJou97pqTWStd1pO2ThG2mou97ZrMZaevatsU2U9L3PZJIB6MhTVLbtkyNbdLOlFKotTIVtVa6riNtnSRsMzWSSAejIU2SJGqtTIVtNpVSSNvXdR193zMFtrFNKYW0dZKotTIltVa6riMdjIY0SaUUbDMVtkk7N5vNmM/nTIFtJJG2RxJTY5t0cBrSZEnCNlNgG0mknZOEbcZuY2OD1dVV0vZJwjZTYBvblFJIB6MhTZYkaq1MwTAMlFJIO1dKodbKmNmm1ook0vZJwjZTIYl0cBrSZEliKmqtdF1H2rmu6+j7njGzjSRKKaTtk4RtpsA2kkgHpyFNVtd19H1PSlsxm82Yz+eMWd/3zGYz0s5IYhgGpqDveySRDk5DShNgG0mkByMJ24xVrZWu60g707YttpkKSaSD05Amq5TCfD5n7GyzSRLpwZRSqLUyRraxTSmFtHO2mYJaK13XkQ5OQ5osSaS0HV3X0fc9Y1RrRRJp50op2Cal/dCQJk0Sthkz20giPbjZbMZ8PmeMzp07x+rqKmnnJGGbKai1UkohHZyGNGmlFGqtjJltJJF2hyRsMya2qbUiifRgJGGbMbONJNLBakiTNwwDYzYMA5JIu6OUQq2VMbGNJEoppAdnmzGzjSTSwWpIk9Z1HbYZs1orbduSdkfXdfR9z5j0fc9sNiM9uFIKthkz20giHayGEfnGN77B888/z2Kx4H5effVVLl68yMWLF7l48SIXL17kH/7hH5gi24ydJNLumM1mzOdzxqTWStd1pAcniWEYGLNhGJBEOlgNI/H5z3+e973vfXzhC1/gl3/5l/nkJz/JvXzuc59jdXWVJ598kieffJInn3ySL33pS0zNbDaj1sqY2UYSafdIwjZjYBvblFJID65tW2wzZrVWuq4jHayGEbhx4wbr6+ucO3eOj3/843z2s5/l7Nmz2OZuvvKVr/D000/zyiuv8Morr/DKK6+wsrLCVNlmjGxjG0mk3VNKodbKGNRakUTaPbZJaa81jMCf//mf89BDD/ETP/ETbHrrW9/Kz/7sz/LFL36Ru7l8+TI//uM/zquvvsq//uu/MmWSGDNJpN3VdR193zMG586dY3V1lbQ7SinYZsxqrZRSSAerYQS+9a1v8ZM/+ZPc6i1veQt/8zd/w53cuHGDr3/96/zWb/0W73nPe3jHO97Br//6rzNVpRRqrYyRbSSRdtdsNmM+n3PY2abWiiTS7pCEbcbKNpJIB69hBG7cuEHTNNyqaRq+853vcCff/OY3+bmf+zk+/elP8/LLL3PhwgVefPFFzp8/z91EBBFBRHD69GnGRBLDMDBGtkl7QxK2OcxsI4lSCmn3SMI2Y2QbSSyz06dPExFEBBHBWDUcQh/96Ec5duwYx44d413vehdvfvObuXHjBrf6zne+w5ve9Cbu5G1vexu/+7u/y9ve9jY2/ciP/Ajvfve7+cu//EvuZrFYsFgsWCwWPPXUU4xJ27bYZoyGYaCUQtp9pRRqrRxmfd8zm81Iu882Y2SbZffUU0+xWCxYLBYsFgvGquEQOnXqFGfOnOHMmTN84hOf4Id/+If567/+a27193//9/zUT/0UdzIMA5/97Ge51b/8y7/wvd/7vUyRJGwzRrZp25a0+7quo+97DrNaK13XkXZXKQXbjNEwDJRSSAev4RB6+9vfzmOPPcZjjz3Go48+yk//9E+zqe97Nl25coWXX36Zd77zndz0V3/1V/zd3/0dm7797W+zvr7OV7/6VTZ985vf5M/+7M9473vfyxSVUqi1Mka2kUTafZKYz+ccVraxTSmFtPuGYWCMaq20bUs6eA0j0DQNv/M7v8NHPvIRVldXef/7389v//Zv80M/9EPc9Oyzz/LSSy+xKSJ4+umn+fmf/3lWV1c5ceIEv/RLv8TKygpTJQnbjI1t0t4opSAJ2xxGtVYkkXZf13XYZqwkkQ5ew0j8zM/8DC+99BLPPfccf/EXf8Hjjz/Orc6ePcsTTzzBTadOneLixYs899xzXLx4kbW1NabONmNjm1IKaW+UUqi1chidO3eO9fV1UtqOWiuSSAevYWSOHDlC0zRsRdM0HDlyhKZpmLpSCrYZE9tIIu2druvo+57Dxja1ViSRdl8phVorY2MbSUgiHbyGwbL8tQAAIABJREFUlP6NJPq+Z0xsk/aWJObzOYeNbSQhibT7JGGbsbGNJNJyaEjp37RtyxhJIu2dUgqSsM1h0vc9s9mMtHckYZsxsU1aHg0p/RtJ1FoZk77vKaWQ9pYkaq0cJrVWuq4jpe0YhoFSCmk5NKT0b0op2Cal7ZLEYWIb25RSSHunlEKtlTGptdK2LWk5NKT07yRhm7GotdJ1HWlvSWIYBg6LWiuSSHtvGAbGRhJpOTSk9O8kUWslpe1o2xbbHBbnzp1jfX2dtLe6rsM2Y1JrRRJpOTSk9O8kMSa1ViSR9p5tDgPb1FqRRErbYRtJSCIth4aU/l3XdfR9zxjYRhKSSHurlIJtDgPbSEISaW9JotbKWNgmLZeGlFJ6AJKwzWHQ9z2z2Yy090op2GZMJJGWR0NK/66Uwnw+ZwxsI4m0PyRhm5RuZ5sx6PueUgppeTSk9O8kMRZ93yOJtH9ss+xqrXRdR9ofkhgL27RtS1oeDSndYjabUWtlDCSR9kcpBdukdKtSCrVWxsA2kkjLoyGlW6yurrK2tsZhV2ulbVvS/hmGgWVnG0mktF22kURaHg0p3aKUQimFtbU1DjtJpP3RdR22WWa2sY0k0v7ouo6+7znsbLNJEml5NKR0m7Nnz2KbWiuHlW0kkdKtJJHSdtkmLZ+GlO5gfX2d48ePY5vDxja2kUTaH5KwzTKzjSTS/pFErZUxkERaLg0p3UEphWeeeYa1tTUOI0mk/VNKodbKMrNN2l+lFGxz2PV9TymFtFwaUrqL9fV1Nm1sbHCY2EYSKd1qGAZKKaT9Z5vDzDZp+TSkdA9nz57lmWeeodbKYWGbtP8kYZtlZZu2bUn7SxKHnW26riMtl4aU7kESFy5cYG1tjcNiGAZKKaT9JYlaK8vKNpJI+6uUQq2Vw8w2kkjLpSGl+yilMJvNWFtb4zCwTdu2pP0liWVmm5S2yzabJJGWS0NKW7C+vo5taq0sO9tIIu0vSQzDwLKyTSmFtL8k0fc9Ke22hpS26OzZsxw/fhzbLDPbpP3Xti22WUa2kUTaf23bcpidO3eOUgpp+TSktEWSOHv2LGtraywz25RSSPvPNsvINulgSMI2h41tNjY2mM/nrK+vk5ZPQ0rbMJvN2LSxscEyso0k0v4rpWCbZSWJtP9KKdRaOUxsc/z4cTZ97WtfQxJp+TSktE0XLlxgPp9Ta2XZ2EYSaf9JwjbLqO97JJHS/dRaOX78OLPZjPX1ddLyakhpB86ePcva2hop3UoStllGkkgHQxK2WWa22djYYG1tjQsXLrC+vk5abg0p7UAphU22WSZ931NKIaVb1Vpp25Z0MCRRa2VZ2ebcuXPUWvna176GJNLya0jpAdhmmdgmHZxSCrVWlpEk0sGQxLKyzdraGpsuXLhAOjwaUtqhUgq2WSa26bqOlG5lG0mkgyGJvu9ZNhsbGxw/fpxSCuvr66TDpSGlHZLEMAykdJMk+r5nmdjGNpJIB6NtW5bNxsYG8/mcCxcusL6+Tjp8GibuxRdfJO1M27bYZpnUWpFEOhht27KMJJEOjiRssyxqrdRa+drXvoYk0uHUMGGf+tSn+MhHPkLaOdssC9tIQhLpYEjCNsvENpJIB6eUQq2VlHZTwwR961vf4td+7df4/d//fdLOlVKwzbKwTTpYpRRqrSwT26R0q77vKaWQDreGCXr22Wd561vfysc+9jHSzknCNstEEindahgGSimkgyUJ2ywD26TDr2GCfvM3f5MPfehDfN/3fR/pwUjCNsug73skkQ6WJGyzLGyTDp4kaq0sA9t0XUc63BomqGkatisiiAgigtOnT5NeZ5tlIYl0sCRhm2Vhm67rSAdLEsvCNmN2+vRpIoKIICIYq4aR++hHP8qxY8c4duwY73rXu9ipxWLBYrFgsVjw1FNPkV5TSsE2y6DWStd1pIMlCdukdCtJDMPAMrBNKYWxeuqpp1gsFiwWCxaLBWPVMHKnTp3izJkznDlzhk984hOk3TcMAyndJIlhGFgWtVZKKaSD1bYttjlotpFEOvwaRu7tb387jz32GI899hiPPvooaXd1XYdtloFtJJEOVtu22GYZ2EYS6eBJwjYHzTaSSIdfQ0ojYJtNkkjpJtuk5SCJWisHzTZpHBomrOs6XnzxRdLOlVKotZLSTaUUaq0sC0mkgyeJZTAMA6UU0uHXkNIDkIRtDpptJJEOniRsswz6vkcSaTlIwjYHyTZt25IOv4aUHpAkbHOQbCOJtBwkYZtlIIm0HCRhm+2otbKbbCOJdPg1pLQLbHOQhmFAEindqtZK27ak5SAJ22zVfD7n+PHj1FrZLbaRRDr8GlJ6QKUUbHOQbNO2LWk5lFKotbIMJJGWgySGYWArbLOxsUEpBdvsBtvYRhLp8GtIaRcMw8BuqLXyPd/zPWyXbSSR0q1sI4m0HNq2xTb3Y5u1tTXW19cppdD3PbtFEmkcGlJ6QF3XYZvd0Pc9m+bzOdthG0mk5SCJvu85SLaxjSTS8rDN/dRa2TSbzWjblt1iG0mkcWhIaYnUWpnNZqytrbEdtpFEWg5t27IMJJGWRymFWiv3YpuNjQ3Onj3LJknUWtkNtknj0ZDSA5JErZXdsrq6SimF+XzOVthGEml5SMI2B8k2kkjLQxL3Ypu1tTXW19eRxKZSCrbZDcMwUEohjUNDSg+olIJtdkOtlVIK6+vrrK2tsRW2kURaHpKotbJTtjl+/DgPwjZp+UjCNndSa2XTbDbjVpKwzYOyTdu2pHFoSGkXSMI2D8I2kthUSqGUwnw+535sk5aLJB5ErZVaK7bZqWEYKKWQloskbHM722xsbHD27FluJ4laKw/KNpJI49CQ0pKwjSRuWl9fZ2Njg/sZhoFSCmm5SMI2O3Hu3Dk21VrZKduk5SMJ29zKNmtra6yvryOJ20liN9hGEmkcGlLaBaUUaq08iL7vKaVwUykFScznc+7FNmk52WYnbDObzej7np2yTdd1pOUiiWEYuNW5c+eQxGw24066rqPvex6EbWwjiTQODSntkmEYeBC2ud3q6irnzp3jXmzTdR1puZRSsM122WbT6uoq8/mcNC5t22Kbm2wzn89ZX19nr0kijUdDSrug6zps8yBs03Udt5rNZmyqtXI3tknLaRgGtss2kiilsMk2O1FrRRJp+dhmk23W1tZYX19HEndTSmE+n/MgbCOJNB4NKS2JWiuSuN3q6iobGxvcjW1KKaTl0nUdttmujY0NSilsKqVQa2W7bCMJSaTlUkrBNpvOnTuHJGazGfciiQdlG0mk8WhIaRdIotbKTtlGEpK43Ww2wza1Vm5nG0mkcem6jk2SGIaBNB6SsI1t5vM56+vrbIUkbLNTwzAgiTQeDSntglIKttkp20jibtbX19nY2OB2tknLSRK1VrbDNrYppbCp6zpss122kURaTpI4fvw4Z8+eRRJbUUqh1spO1Vpp25Y0Hg0p7SLb7ETf99zLbDbDNrVWbieJtHxKKdhmO2wjiZtmsxnz+Zzt6vseSaTlVUqhlMJ2DMPAg5BEGo+GlHaJJB5EKYV7WV9f59y5c9yq73tKKaTlZZut6vueUgq3koRttksSaTl97Wtf4+zZs2xH13XYZqdsI4k0Hg0p7ZJSCrVWdqLWStd13MtsNqPWSq2VdDhIYjtqrXRdx61KKdRa2Y5aK23bksbFNjthm02SSOPRkNISsM1WrK+vc+7cOW6qtdJ1HWk5SaLWylbYxjalFG7VdR1937NdkkjjMZvNqLWS0k0NKe2Sruvo+57tss2mUgr3M5vNmM/n2CYtP0lslW0kcSe22Q7bSCKNj222yzaSSOPSkNIBs812PPPMM2xsbLCp1ook0nKSxDAMbEXf95RSuN1sNqPWylbZxjaSSOMiiZ3o+x5JpHFpSGmXSKLWyk5IYqvW19eZz+fUWpGEJNJyatsW22xFrZWu67gTSdhmqySRxqeUQq2VnZBEGpeGlHZJKQXbbFff95RS2I7ZbMbGxgZpuUnCNvdjG9uUUriTUgq1VrbCNpJI4yOJYRjYrlorXdeRxqUhpV1mm+2otdJ1Hdtx9uxZaq1IIi0vSdRauR/bSOJuuq6j73vStLVti21S2tSQ0i6SxH555plnKKWQlpcktqLve0op3E0phfl8zlb0fU8phTQ+kqi1sl21ViSRxqUhpV1USqHWylbZptZKKYXtWl9fZ319nbTcJGGbe6m10nUddyOJTba5H9ukcSqlYJvtsI0kJJHGpSGlAyaJNG62uRvb2KaUwr3MZjNqrdyPbbquI42TJGyTUkNKu0gSfd+zVbaRRBqvUgq2uRvbSOJ+JNH3PWnaJFFrZatsI4k0Pg0p7aK2bdmOvu8ppZDGbRgG7qbve0op3E/btmxFrRVJpHGSxHb0fY8k0vg0pLSLJGGbrbJN27ak8eq6DtvcTa2Vruu4n9lsxnw+515sIwlJpHGSRN/3bIck0vg0jNCLL77I/bz66qtcvHiRixcvcvHiRS5evMg//MM/kB5MKYVaK1tlG0mkabJNrZVSClshCduk6Wrblu2otdJ1HWl8GkbmU5/6FB/5yEe4n8997nOsrq7y5JNP8uSTT/Lkk0/ypS99ibQ7bLMVtVYkkcZLErVW7sQ2ktiqUgq1Vu7GNpJI41VKodZKSg0j8a1vfYtf+7Vf4/d///fZiq985Ss8/fTTvPLKK7zyyiu88sorrKyskB6cJLbCNpKQRBqvUgq2uZO+75nNZmxV13X0fc/d9H2PJNJ4ScI2W1VrRRJpfBpG4tlnn+Wtb30rH/vYx9iKy5cv8+M//uO8+uqr/Ou//itp95RSqLVyP7aRRJoG29yu1krXdWyHbe5FEmncJGGb+7GNJCSRxqdhJH7zN3+TD33oQ3zf930f93Pjxg2+/vWv81u/9Vu85z3v4R3veAe//uu/Ttpffd8jiTR+kridbWqtSGKrZrMZtVbuxjZt25LGrZRCrZX7sU0ar4aRaJqGrfrmN7/Jz/3cz/HpT3+al19+mQsXLvDiiy9y/vx57iYiiAgigtOnT5PuThJ937MVkkjjJ4laK7eyjSQksR2SmM/n3IltJJHGbxgGtkISU3P69GkigoggIhirhkPoox/9KMeOHePYsWO8613vYrve9ra38bu/+7u87W1vY9OP/MiP8O53v5u//Mu/5G4WiwWLxYLFYsFTTz1Furu2bdmKWitd15HGTxK36/ueUgrbVUrhbmwjiTRuXddhm/vp+55SClPz1FNPsVgsWCwWLBYLxqrhEDp16hRnzpzhzJkzfOITn2C7hmHgs5/9LLf6l3/5F773e7+X9OAkYZv7sY0k0vhJYhgGblVrZXV1le3quo6+77kT20gijZ9t0rQ1HEJvf/vbeeyxx3jsscd49NFH2Yq/+qu/4u/+7u/Y9O1vf5v19XW++tWvsumb3/wmf/Znf8Z73/te0oMrpVBr5V5ss0kSafzatsU2t6q1shOz2Yz5fM7tbCOJNH6z2YxaK/dTa6XrOtI4NUzEs88+y0svvcSmiODpp5/m53/+51ldXeXEiRP80i/9EisrK6T9YZs0Lba5yTaSKKWwE5Kwza1sI4k0HbZJ09UwMl3X8eKLL3K7s2fP8sQTT3DTqVOnuHjxIs899xwXL15kbW2NtHskYZt7kUSahlIKtrnp3LlzSGKnSinUWknTJYn7qbVSSiGNU8OENU3DkSNHaJqGtLskUWvlbvq+p5RCmgZJ2OamWiurq6vslCT6vudWfd9TSiFNQymFWit3YxtJpPFqSGkPSOJeaq10XUeaDknYZpNtJLFTbdtyO9uk6ZDEMAzcjW3SuDWktAck0fc9Kd3ONptKKezUbDZjPp9zK9t0XUeahrZtsc29SCKNV0NKe6BtW+7GNrVWSimk6SilUGul1ookHpQkbJOmSRK2uZu+7ymlkMarIaU9IAnb3I0k0jSdO3eOUgoPqpRCrZWbaq1IIk1DKYVaK3djmzRuDSntgVIKtVbuxDaSSNPSdR1937Op6zoeVNd19H3PJttIQhJpOiRhmzuxTdd1pPFqSGmf9X1PKYU0PbaxTSmFByWJWitp2mxzJ7ZJ49aQ0h6RhG1uV2ulbVvStEii1ookdkMpBdvYxjaSSNNSSsE2d2KbUgppvBpS2iOSqLVyJ5JI01JKYVMphd0iiVortpFEmhZJ9H3P7WwjiTRuDSntEUncSa0VSaRp6rqO3VJKYRgGhmFAEmla2rblTmwjiTRuDSntEUkMw8CtbCMJSaTp+b//9/9SSmG3dF2HbWzTti1pWiRRayVNU0NKe6RtW2xzK9tIIqXdMJvNmM/n2EYSaVpKKdjmdn3fU0ohjVtDSntEEra5Vd/3SCKl3SKJWiuSSNMjCdvcyjZp/BpS2iOSqLVyK9tIIqXdUkphkyTS9Eii1sqtbNN1HWncGlLaI5K4nW26riOl3SIJSaRpksTtbJPGryGlPSQJ29xkG0mktFu6rmM2m5Gmqes6+r7nVrYppZDGrSGlPSSJWiubbLNJEintllIK6+vrpLTJNpJI49eQ0h6SxE22SSml3VRKYT6fc5NtJJHGryGlPSSJYRjYZBtJpJTSbpHErWyTpqEhpT3Uti222TQMA6UUUkppN0nCNpuGYaCUQhq/hpT2mG021Vrpuo6UUtpNpRRqrWyyTdu2pPFrSGkPlVKotbLJNimltBeGYWCTbSSRxq8hpT0kiU22sU0phZRS2k1d12GbTbaRRBq/hpT2mCRsI4mUUtptkrCNbWwjiTR+DSntMUn0fY8kUkppt5VSqLWySRJpGhpS2mOSmM/nlFJIKaW9UmtFEmkaGlLaY5KwTdu2pJTSXpBE3/ek6WhIaY+1bcsmSaSU0l4opVBrpZRCmoaGlPZJKYWUUtoLkrBN27akaWhIaY/NZjNmsxkppbRX2rZlkyTSNDSktA/Onj1LSintFUlskkSahoaUUkrpkCulMJvNkESahoaJ+upXv8rzzz/PK6+8wlSdPn2aMTp9+jRjdPr0acbq9OnTjNHp06cZo9OnT7OMzp49y4M4ffo06fBomKCPfvSjPPnkk3zhC19gY2ODU6dO8X/+z/9has6cOcMYnTlzhjE6c+YMY3XmzBnG6MyZM4zRmTNnGKMzZ86QDo+Gifnf//t/8z//5//kj/7oj/j4xz/OH//xH/OP//iPfP7znyellFJKh0PDxDz00EP89//+33nooYe46cd+7Mf427/9W1JKKaV0ODRMzI/+6I/y2GOPcdMwDFy4cIF3v/vd3M2jjz5KRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUSwKSKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAi2BQRRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEWyKCCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigk0RQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRAQRQUQQEUQEEUFEEBFEBBFBRBARRPy/9uA4tu663v/4M58WuzVNPKldJxgkQuFdsHOmtWs6oWajm9VAIhq3ds6dbZJC5wSNKFkhLSKwdC1IyaTWAaXBbAEr09QQzjxsnq49YfVQM1ckr3YuZzQaF6E9wYwwmu/xl/NHkxPg/i4B9fa7fR4Pw8wwM8wMM8PMyDEzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM3LMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzIwcM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDPDzDAzzAwzw8wwM8wMM8PMMDPMDDNj1apVnI8cF7AzZ86wdetWduzYwdVXX83/5KmnnkISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSEISkpCEJCQhCUlIQhKSkIQkJCEJSUhCEpKQhCQkIQlJSOKpp57ifOQ4z913331UV1dTXV3Nddddx4ITJ05w0003sWXLFtra2vA8z/M8Lzwc57lNmzaxd+9e9u7dy4MPPkhOMplk+/bt3HPPPWzbtg3P8zzP88LFcZ67/PLLWb16NatXr2bVqlXMzMywc+dO9uzZw5o1a5ifn2d+fp4gCPA8z/M8LxwcF5j9+/dz9uxZbr31VqqqqqiqqqKqqor7778fz/M8z/PCwXGBufPOO5GEJCQhCUl0dHTgeZ7neV44ODzP8zzP80LG4Xme53meFzIO7380MzNDPB5HEueLo0eP8k4zMzPE43EkETYnT54kHo8zMTHBO83MzBCPx5FEGEkiHo+TTqd5p5mZGeLxOJIIq+PHj/OPf/yDfDMzM8TjcSQRJrOzs6RSKVKpFKlUilQqxRtvvMGCmZkZ4vE4kgib2dlZDh8+zLFjx3inmZkZ4vE4kgiT2dlZUqkUqVSKVCpFKpUilUqRTqdZMDMzQzweRxJhk06nicfjvPLKK7zTzMwM8XgcSYSdw3tPw8PDNDc3E4vFaGtro7e3l7B79NFHaW9vJ9/w8DDNzc3EYjHa2tro7e0lLO677z5aW1uJxWL86Ec/YtOmTZw7d46c4eFhmpubicVitLW10dvbS5j85Cc/4Tvf+Q4vvPACN998M/39/SwYHh6mubmZWCxGW1sbvb29hM3JkyfZvHkzx48fZ8Hw8DDNzc3EYjHa2tro7e0lLA4ePEg0GqW1tZXW1lZaW1v505/+RM7w8DDNzc3EYjHa2tro7e0lLBKJBDfccAPPPfccPT09bN68mWw2S87w8DDNzc3EYjHa2tro7e0lLFKpFK2trbS2ttLa2kpraytbtmzhySefJGd4eJjm5mZisRhtbW309vYSFgMDA3zjG98gFovxve99j7vvvpsFw8PDNDc3E4vFaGtro7e3lzBzeO8SBAGdnZ0MDg7S3d3N0NAQAwMDpNNpwiiTybBr1y4ee+wx8gVBQGdnJ4ODg3R3dzM0NMTAwADpdJrF7pVXXuHpp5/m2Wefpbu7m9/85jf885//ZHh4mCAI6OzsZHBwkO7uboaGhhgYGCCdThMG09PTPPHEEzzzzDPs3r2bAwcO0Nvby+zsLEEQ0NnZyeDgIN3d3QwNDTEwMEA6nSYs5ufn+f73v09ZWRkLgiCgs7OTwcFBuru7GRoaYmBggHQ6TRi8/PLL3HXXXUxMTDAxMcHExATXXnstQRDQ2dnJ4OAg3d3dDA0NMTAwQDqdZrELgoBdu3bx8MMP09PTwy9/+UsymQyHDh0iCAI6OzsZHByku7uboaEhBgYGSKfThMH69euZmJhgYmKCiYkJHnnkEZYtW8Z3v/tdgiCgs7OTwcFBuru7GRoaYmBggHQ6zWKXzWbp6enhySefpLu7m2eeeYaDBw/yyiuvEAQBnZ2dDA4O0t3dzdDQEAMDA6TTacLK4b3LyMgIkUiEiooKckpLS2loaGB0dJQwevjhhyktLeWBBx4g38jICJFIhIqKCnJKS0tpaGhgdHSUxS4SidDf308kEmHBpz71Kf72t78xMjJCJBKhoqKCnNLSUhoaGhgdHSUMrrjiCg4ePEgkEiHnoosuIggC5ufnGRkZIRKJUFFRQU5paSkNDQ2Mjo4SFg899BDXX389V111FQtGRkaIRCJUVFSQU1paSkNDA6Ojo4TBn//8Z6644goi0yAWAAAL7UlEQVRmZ2eZn59nwcjICJFIhIqKCnJKS0tpaGhgdHSUxS6RSPCJT3yCVatWseC3v/0tTU1NjIyMEIlEqKioIKe0tJSGhgZGR0cJmzfffJNdu3Zx3333EYlEGBkZIRKJUFFRQU5paSkNDQ2Mjo4SBv/6179YsmQJOUuXLsU5x9tvv83IyAiRSISKigpySktLaWhoYHR0lLByeO+SyWSorKwkX0lJCVNTU4RRR0cHP/jBD1i6dCn5MpkMlZWV5CspKWFqaorF7uKLL2b16tUsOH36NEeOHGHdunVkMhkqKyvJV1JSwtTUFGHgnKOiooIgCHj66aeJRqN8+9vfZvny5WQyGSorK8lXUlLC1NQUYTA+Ps6xY8e47bbbyJfJZKisrCRfSUkJU1NTLHZBEPDqq6/y4x//mBtuuIGVK1dy9913k5PJZKisrCRfSUkJU1NTLHZzc3NceumldHR0sHLlSqqrq3n88cfJyWQyVFZWkq+kpISpqSnCZt++fVRWVnLdddeRk8lkqKysJF9JSQlTU1Msds45Ojs72bFjB729vWzevJmNGzeycuVKMpkMlZWV5CspKWFqaoqwcnjvEgQBzjnyOefIZrOEkXOO9xIEAc458jnnyGazhMmZM2fYunUrO3bs4OqrryYIApxz5HPOkc1mCZPZ2VnOnTtHeXk5Y2NjZDIZgiDAOUc+5xzZbJbF7o033qCjo4OHHnqIdwqCAOcc+ZxzZLNZFrszZ87Q2NjIz3/+c5LJJEeOHOHo0aMcOHCAIAhwzpHPOUc2m2WxO3nyJLFYjE9/+tMcP36cAwcO8LOf/YzR0VGCIMA5Rz7nHNlsljA5d+4cAwMD3HbbbSwIggDnHPmcc2SzWcIglUpRXFzMsmXLiEQi/OUvf+HNN98kCAKcc+RzzpHNZgkrh/cuRUVFBEFAvmw2S2FhIeeToqIigiAgXzabpbCwkLA4ceIEN910E1u2bKGtrY2coqIigiAgXzabpbCwkDBZtmwZW7ZsYd++fSxZsoTBwUGKiooIgoB82WyWwsJCFrs9e/ZwzTXXcPr0aRKJBLOzs7z88stIoqioiCAIyJfNZiksLGSxu+SSS3jkkUe45JJLyFm+fDnr1q3jpZdeoqioiCAIyJfNZiksLGSx++QnP8lll13Gxo0byTEz1q1bx3PPPUdRURFBEJAvm81SWFhImDz//PNceumlrFixggVFRUUEQUC+bDZLYWEhi93hw4f54x//yP79+9m0aRP9/f3kPPHEExQVFREEAfmy2SyFhYWElcN7l/LyciYnJ8k3NzdHTU0N55Py8nImJyfJNzc3R01NDWGQTCbZvn0799xzD9u2bWNBeXk5k5OT5Jubm6OmpoYwOHXqFL/4xS/I9/GPf5y///3vlJeXMzk5Sb65uTlqampY7JYtW8bZs2fZv38/+/fv569//SuJRIJkMkl5eTmTk5Pkm5ubo6amhsXu9OnTDA0Nke/tt9+moKCA8vJyJicnyTc3N0dNTQ2L3cc+9jHeyTmHc47y8nImJyfJNzc3R01NDWGSSCRYt24d+crLy5mcnCTf3NwcNTU1LHZzc3NcddVVFBQUsOCyyy5jZmaG8vJyJicnyTc3N0dNTQ1h5fDepba2lpxEIkHO9PQ0yWSS+vp6zie1tbXkJBIJcqanp0kmk9TX17PYzczMsHPnTvbs2cOaNWuYn59nfn6eIAiora0lJ5FIkDM9PU0ymaS+vp4wCIKA3bt3c+rUKXJee+01RkdHWbduHbW1teQkEglypqenSSaT1NfXs9jdfvvt9Pf309/fT39/PytWrGDHjh1s27aN2tpachKJBDnT09Mkk0nq6+tZ7N566y06Ozs5efIkOWfOnOGFF17gxhtvpLa2lpxEIkHO9PQ0yWSS+vp6Frs1a9YwOzvLkSNHyJmdneXo0aPceOON1NbWkpNIJMiZnp4mmUxSX19PmLz44ousXLmSfLW1teQkEglypqenSSaT1NfXs9hdc801jI2NcerUKXLeeOMNUqkUq1atora2lpxEIkHO9PQ0yWSS+vp6wsrhvYtzjp6eHtrb24lGo7S0tNDV1UVZWRnnE+ccPT09tLe3E41GaWlpoauri7KyMha7/fv3c/bsWW699VaqqqqoqqqiqqqK+++/H+ccPT09tLe3E41GaWlpoauri7KyMsLgyiuv5O677+arX/0q3/rWt2hsbGTLli2sXbsW5xw9PT20t7cTjUZpaWmhq6uLsrIywsw5R09PD+3t7USjUVpaWujq6qKsrIzFzsy466672LBhA9FolC996UvcfPPNXHvttTjn6Onpob29nWg0SktLC11dXZSVlbHYXXTRRezdu5d7772X5uZm1q9fz8aNG6mrq8M5R09PD+3t7USjUVpaWujq6qKsrIywyGazvP7661xzzTXkc87R09NDe3s70WiUlpYWurq6KCsrY7G7+uqraW9vZ8OGDUSjUdauXcvnP/95vva1r+Gco6enh/b2dqLRKC0tLXR1dVFWVkZYObz3VFdXx9jYGH19fYyPj9PU1ETYfeELX+Do0aPkq6urY2xsjL6+PsbHx2lqaiIM7rzzTiQhCUlIQhIdHR3k1NXVMTY2Rl9fH+Pj4zQ1NREmLS0tTExM0NXVxUsvvcQtt9zCgrq6OsbGxujr62N8fJympibCqL+/n8bGRhbU1dUxNjZGX18f4+PjNDU1ERabNm0ilUrR19dHKpVi27ZtLKirq2NsbIy+vj7Gx8dpamoiLD73uc9x5MgRBgYGOHbsGDt27GBBXV0dY2Nj9PX1MT4+TlNTE2HinEMSy5Yt453q6uoYGxujr6+P8fFxmpqaCIuNGzcyPj5OX18fx44dY9euXSyoq6tjbGyMvr4+xsfHaWpqIswc3v9XcXExzjnOd8XFxTjnON8UFxfjnCOMnHOUlZVRUFDAeykuLsY5x/mmuLgY5xxh45yjuLgY5xzvpbi4GOccYbR06VIKCgp4L8XFxTjnOB8VFxfjnCNsnHMUFxdTUFDAeykuLsY5R9g5PM/zPM/zQsbheZ7neZ4XMg7P8zzP87yQcXie53me54WMw/M8z/M8L2Qcnud5nud5IePwPM/7L7v99tvZuXMnd9xxBx/Evn372LlzJzt37uTkyZN4nnfhcXie5/2XHT58mEsvvZT169fzQdTU1HD99dfzu9/9jkwmg+d5Fx6H53ne/4GamhrWr1/PB1FdXc0Xv/hFPM+7cDk8z/P+DQ4fPszXv/51qqurWb9+PY8++ijv1y233EI8Hueb3/wm1dXVNDc3c/r0aX71q1/R2NhIbW0tu3fvxvM8b4HD8zzvQzp9+jRtbW1s3LiRkZERdu3axWOPPcbQ0BDvx+9//3s6OzvZsGEDe/fu5dy5c2zevJlDhw5x77330t7ezlNPPcWhQ4fwPM/LcXie531I6XSagoICVq9eTUlJCWvWrOHxxx9nxYoVvF/bt2/nxhtvZPXq1WzevJnXX3+dBx98kNWrV3PTTTfxmc98hj/84Q94nuflODzP8z6ka6+9lsrKShobG2lubuaRRx5hyZIlmBnv12WXXcaCpUuXsmTJEkpKSljw0Y9+lCAI8DzPy3F4nud9SAUFBQwNDfHTn/6Uyy+/nF//+td85Stf4fHHH8fzPO8/weF5nvchnTp1iueff541a9bwwAMPcPjwYbZu3cq+ffvwPM/7T3B4nud9SK+99hp33HEHx44dIyebzfLqq69y5ZVX4nme95/g8DzP+5BWrVrFjh072L59O5/97GdZuXIlZ86cYc+ePXie5/0nODzP8/4Ndu7cyYkTJ4jFYqRSKZ599lkuvvhi3g9JNDY2suDLX/4yExMT5Ovv76ejowPP87wch+d53r+Jc47ly5dTVFTE/+att97izTff5IM4d+4cZ8+exfO8C5fD8zzvv+yiiy5i165drF27lg/ihz/8IWvXruUjH/kIzjk8z7vwODzP8/7LJiYmOHHiBC+++CIfRG9vLydOnODEiRNUV1fjed6Fx+F5nud5nhcyDs/zPM/zvJBxeJ7neZ7nhYzD8zzP8zwvZBye53me53kh8/8AVGkk/iVH1SsAAAAASUVORK5CYII=" style="width: 560px;"></div></div></div></div></div><h2 class = 'S12'><span>Beta functions</span></h2><div class = 'S0'><span>Now we are ready to calculate the beta functions along the beamline. Let's first calculate the transfer matrices for a single fodo cell.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >beamline=fodo; </span><span style="color: rgb(2, 128, 9);">% just a single FODO cell</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span >Rend=Racc(:,:,end); </span><span style="color: rgb(2, 128, 9);">% the TM from start to end</span></span></div></div></div><div class = 'S10'><span>and the periodic Twiss parameters </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">α</span><span>, </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">β</span><span>, and </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">γ</span></div><div class="CodeBlock"><div class="inlineWrapper outputs"><div class = 'S13'><span style="white-space: pre"><span >[Qtune,alpha0,beta0,gamma0]=R2beta(Rend)</span></span></div><div class = 'S7'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>Qtune = 0.1580</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>alpha0 = 1.1372</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>beta0 = 4.2348</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>gamma0 = 0.5415</div></div></div></div><div class = 'S10'><span>where we observe that Qtune is 0.1580. Change the focal length </span><span style=' font-family: monospace;'>F</span><span> way up in this script to a different value and observe how </span><span style=' font-family: monospace;'>Qtune </span><span>changes. </span></div><div class = 'S0'><span>We now use the Twiss parameters to construct the </span><span style=' font-weight: bold;'>initial </span><span>beam matrix sigma0</span></div><div class="CodeBlock"><div class="inlineWrapper outputs"><div class = 'S13'><span style="white-space: pre"><span >sigma0=[beta0,-alpha0;-alpha0,gamma0]</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="A877AECB" data-scroll-top="null" data-scroll-left="null" data-width="1326" data-testid="output_7" style="width: 1356px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier saveLoad" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1326px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">sigma0 = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">2×2</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":"2","totalRows":"2","charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 146px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 4.2348 -1.1372
-1.1372 0.5415
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><div class = 'S10'><span>and map this through one FODO cell</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >data=zeros(1,nmat); </span><span style="color: rgb(2, 128, 9);">% allocate memory</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:nmat</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > sigma=Racc(:,:,k)*sigma0*Racc(:,:,k)';</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > data(k)=sigma(1,1); </span><span style="color: rgb(2, 128, 9);">% that's the beta</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S10'><span>and plot the beta function through one FODO cell</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >plot(spos,data,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'s [m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'\beta [m]'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'Beta function in one FODO cell'</span><span >)</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="2FAF2C2D" data-scroll-top="null" data-scroll-left="null" data-testid="output_8" style="width: 1356px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" style="width: 560px;"></div></div></div></div></div><div class = 'S10'><span>We observe an oscillation with aminimum at the location of the defocusing quadrupole at s=1 m and a maximum in the focusing quadrupole at s=3 m.</span></div><h2 class = 'S12'><span>Betafunction through ten FODO cells</span></h2><div class = 'S0'><span> Mapping the beta function through 10 FODO cells makes it necessary to increas the length of the</span><span style=' font-family: monospace;'> beamline</span><span> and update all transfer matrices</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >beamline=repmat(fodo,10,1);</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div></div><div class = 'S10'><span>We do not need to re-calculate sigma0, because it is periodic and we can therefore use the one determined from a single cell. Let's propagate the beta function </span><span style=' font-family: monospace;'>sigma0</span><span> through the 10 FODO cells and plot the result</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >data=zeros(1,nmat); </span><span style="color: rgb(2, 128, 9);">% allocate memory</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:nmat</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > sigma=Racc(:,:,k)*sigma0*Racc(:,:,k)';</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > data(k)=sigma(1,1); </span><span style="color: rgb(2, 128, 9);">% that's the beta</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 class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >plot(spos,data,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'s [m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'\beta [m]'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'Beta function in ten FODO cells'</span><span >)</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="78FDCB42" data-scroll-top="null" data-scroll-left="null" data-testid="output_9" style="width: 1356px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" style="width: 560px;"></div></div></div></div></div><div class = 'S10'><span>It's just ten copies of the beta function through a single cell.</span></div><h2 class = 'S12'><span>Adjust Qtune to 0.25</span></h2><div class = 'S0'><span>Let's go back to a single cell an adjust the quadrupoles such that the tune for one cell is Qtune=0.25. Which focal length approximatelydoes the job? Try to set the tune to 0.16666=1/6. What is F in that case?</span></div><div class="CodeBlock"><div class="inlineWrapper outputs"><div class = 'S13'><span>3.356</span><span style="white-space: pre"><span style="color: rgb(2, 128, 9);">% adjust focal length F</span></span></div><div class = 'S7'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>ans = 3.3560</div></div></div><div class="inlineWrapper"><div class = 'S14'><span style="white-space: pre"><span >F=ans; </span><span style="color: rgb(2, 128, 9);">% focal length of the quadrupoles</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >fodo=[ 1, 5, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0.0, -F; </span><span style="color: rgb(2, 128, 9);">% QD</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 10, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0.0, F; </span><span style="color: rgb(2, 128, 9);">% QF/2</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 5, 0.2, 0]; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beamline=fodo;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Rend=Racc(:,:,end); </span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >[Qtune,alpha0,beta0,gamma0]=R2beta(Rend)</span></span></div><div class = 'S7'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>Qtune = 0.0963</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>alpha0 = 1.0476</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>beta0 = 6.7193</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>gamma0 = 0.3122</div></div></div></div><h2 class = 'S12'><span>Automatic tune adjustment</span></h2><div class = 'S0'><span>Now we use fminsearch() to set the tune to a desired value. To do so we need to define a cost function that I often call </span><span texencoding="\chi^2" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="17" height="19" /></span><span> or chisq. Here we use the name </span><span style=' font-family: monospace;'>chisq_tune()</span><span>. It receives a guess for the focal length </span><span style=' font-family: monospace;'>F</span><span> and returns the difference betwen the tune value for that </span><span style=' font-family: monospace;'>F</span><span> and the desired tune, here 0.25. Such a function is defined in the appendix.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(2, 128, 9);">% global beamline % needed to make it available inside chisq_tune()</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >F0=3; </span><span style="color: rgb(2, 128, 9);">% starting guess</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >[Fnew,fval]=fminsearch(@chisq_tune,F0) </span></span></div><div class = 'S7'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>Fnew = 1.4142</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>fval = 1.9933e-11</div></div></div><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >beamline </span><span style="color: rgb(2, 128, 9);">% just look at the new beamline description</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="4DF52501" data-scroll-top="null" data-scroll-left="null" data-width="1326" data-testid="output_17" style="width: 1356px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier saveLoad" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1326px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">beamline = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">5×4</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":"4","totalRows":"5","charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 290px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 1.0000 5.0000 0.2000 0
2.0000 1.0000 0 -1.4142
1.0000 10.0000 0.2000 0
2.0000 1.0000 0 1.4142
1.0000 5.0000 0.2000 0
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><div class = 'S10'><span>Fnew is the new focal length that will give you the desired tune. let's verify that</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline); </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Rend=Racc(:,:,end); </span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >Qtune=R2beta(Rend)</span></span></div><div class = 'S7'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>Qtune = 0.2500</div></div></div></div><div class = 'S10'><span>Now look at the function chisq_tune() in the appendix and change it such that Qtune becomes 1/6. What value for the focal length do you find? </span></div><h2 class = 'S12'><span>Matching FODO cells with Qtune=0.1666 to those with Qtune=0.25</span></h2><div class = 'S0'><span>This is also called matching </span><span texencoding="60^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> cell to a </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAAmCAYAAAC76qlaAAAEGklEQVRYR+3XdahtVRAG8N+zxcZCsQO7G1QUMZ6FotitKAoWmOA/KooigmJgYGJigC0qJoqFLYrdCoqF3Xwy57Hd7HM9593HhQdn/rnn7rVmrdkz33zz7UmmU5s0ncZtFPhEV26U8VHGB8zACCoDJmqabRsr41nbBwdhMcyKr3ELzscP/xPFSjgW6+EPzIkncA7eHu8b9As8l9yONbE7HqmLdsQ1+A6T8UafAPbDZXgSu+BbLIibsD72wl19fOfBcZgdX2IbnI6Hm/v7BX419seRuLB1QQK5FV9gNXzVWt8CD1RFVsXHjfV58W4FtTFeaPmuUxU9DYkhdi4OwbLNu7oC3xBP4TcshO9bh8fnUyxShx/YWJ8Jb2FpnIFTOrJ6Nk7AM8hdPVsSz1ZVjm48z/lXYnvc03veFXggsjPeRHDaZRfjcPyOJSr72bc3riuHzfFoh/PWuL+eb4UH6/cdyP/L4POG35k4GVviobECf6fKksOD4y4LhoP12MGVkfzuvfSvCCx+6XBO/3yDVCeZjP9yValrcUDL524Efgs3q9/OeBoibDED7sV2fQLPC2U9djkOrd9ppgXwCtbo45vHaeoV8UHBKs16PY7CBQ2/pYqBzsPxzfO6Av+Rf1XjWJeH4oLHWDKyA2bDz/XsMWw2RuDpoY1qfb5imYsKKj3oZPlSbFBMlJ6bYl0Yfx9502Q+zdkLpum3fJU2z0JTKWW6PjCLBa87jRF4qtWDYZhnRryIfXFD+aVfTio6TcP/x7oCj+OetSsd3aOlpmNg8FI9uBl7YBM8Xs+C/zZWm/7NO0KL4fsMu+A9fTIz5kIYqKtPOj8k0iivYxZ8iE3xUePW4D/DJZfEMkWPqdIHArGrauL2S3peLA0eCyWGGoeyfgMohJ/BkzGfAXIFXi0IpRp/1yjPZWmsG6vJ3qvbk7UMqn52Z/VF1hfHJ0NFXU3YzydwOBFrl1YJflOJS6r7d8VfRVOZnmGkn+qwHu77nR3NEogkAUlO5sFQNjWydn58VlC6D9s2buzRYRotL9zPXsMqNWgWHSri2jw1gWdcp2mSrXVbeiPKMZUII4XmogrblgxnAKVCEV09Ihgq/mEDXx1P16Vp0MNat4VdgvdYeDp72xZ+76nN3UpUDRV0Ng8T+Nx4HuHwYDhys43N0FjUXxouAitCq22RqFnLvMhZfw4d9RCBRwlmJEc4RcMks9HkXRbMR8WFQldo8XB0Spo82jxia4poGjb4QTKeCRg9koyfhVOLTca664jSHKHFDLFgPqIryjEKMMoyFDvV1i/wZDjSNo0WdritvkIiiga1tepLZuWSDXPg5fowyN9xWVfg4e8wRyjrOUQwDc2z44pqAOdBoDLAMRO/ZRT4ROd8lPFRxgfMwAgqAyZqmm37Bwf6zSfA9ehYAAAAAElFTkSuQmCC" width="23" height="19" /></span><span> cell, because of </span><span texencoding="60^o/360^0=0.1666" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="118" height="20" /></span><span> and </span><span texencoding="90^o/360^0=0.25" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="103" height="20" /></span><span>.</span></div><div class = 'S0'><span>We found in the previous matching exercise that </span><span texencoding="F=\sqrt{2}" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="52.5" height="20" /></span><span> gave Qtune=0.25 and and </span><span texencoding="F=2" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="40" height="18" /></span><span> gave Qtune=0.1666, which allows us to define the two cells in the following way</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >F=2; </span><span style="color: rgb(2, 128, 9);">% focal length of the quadrupoles</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >fodo60=[ 1, 5, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0.0, -F; </span><span style="color: rgb(2, 128, 9);">% QD</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 10, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0.0, F; </span><span style="color: rgb(2, 128, 9);">% QF/2</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 5, 0.2, 0]; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >F=sqrt(2);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >fodo90=[ 1, 5, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0.0, -F; </span><span style="color: rgb(2, 128, 9);">% QD</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 1, 10, 0.2, 0; </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > 2, 1, 0.0, F; </span><span style="color: rgb(2, 128, 9);">% QF/2</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span > 1, 5, 0.2, 0]; </span></span></div></div></div><div class = 'S10'><span>Let's look at the beta function along that beamline. To do so we first calculate the periodic beam matrix for the </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> cell</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >beamline=fodo60;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Rend=Racc(:,:,end);</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >[Qtune,alpha60,beta60,gamma60]=R2beta(Rend)</span></span></div><div class = 'S7'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>Qtune = 0.1667</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>alpha60 = 1.1547</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>beta60 = 4.0415</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>gamma60 = 0.5774</div></div></div><div class="inlineWrapper outputs"><div class = 'S8'><span style="white-space: pre"><span >sigma60=[beta60,-alpha60;-alpha60,gamma60]</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="A9A393B1" data-scroll-top="null" data-scroll-left="null" data-width="1326" data-testid="output_23" style="width: 1356px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier saveLoad" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1326px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">sigma60 = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">2×2</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":"2","totalRows":"2","charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 146px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 4.0415 -1.1547
-1.1547 0.5774
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div></div></div></div><div class = 'S10'><span>Now let's build a long beamline, starting with two fodo60, followed by six fodo90 cells and display the betafunction along this beam line, if we start with the input beam sigma60</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >beamline=[fodo60;fodo60;repmat(fodo90,6,1)];</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >data=zeros(1,nmat); </span><span style="color: rgb(2, 128, 9);">% allocate memory</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:nmat</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > sigma=Racc(:,:,k)*sigma60*Racc(:,:,k)';</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > data(k)=sigma(1,1); </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 class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >plot(spos,data,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); xlabel(</span><span style="color: rgb(170, 4, 249);">'s [m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'\beta [m]'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'Unmatched fodo60 to fodo90 transition'</span><span >)</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="8F9428E9" data-scroll-top="null" data-scroll-left="null" data-testid="output_24" style="width: 1356px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" style="width: 560px;"></div></div></div></div></div><div class = 'S0'><span>We observe that the beam that is matched for the fodo60 cell does not show a regular pattern once it enters the fodo90 cells. We therefore try to adjust the two quadrupoles in the second fodo60 cell to try to minimize the irregularity. Note that these two quads are now in line 7 and 9, respectively. The second cell we refer to as the </span><span style=' font-style: italic;'>matching cell.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >beamline(7,4)=</span></span><span>-2.044</span><span style="white-space: pre"><span >;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beamline(9,4)=</span></span><span>2.0934</span><span style="white-space: pre"><span >;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >data=zeros(1,nmat); </span><span style="color: rgb(2, 128, 9);">% allocate memory</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:nmat</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > sigma=Racc(:,:,k)*sigma60*Racc(:,:,k)';</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > data(k)=sigma(1,1); </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 class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >plot(spos,data,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); xlabel(</span><span style="color: rgb(170, 4, 249);">'s [m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'\beta [m]'</span><span >); ylim([0,10])</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'Matching by hand'</span><span >)</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="9D886997" data-scroll-top="null" data-scroll-left="null" data-testid="output_25" style="width: 1356px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" style="width: 560px;"></div></div></div></div></div><div class = 'S10'><span>Did you manage to get a smooth and periodic beta function through the downstream part of the beamline? If not, try out the following code, which uses </span><span style=' font-family: monospace;'>fminsearch()</span><span> to adjust the two quads such that </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">α</span><span> and </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">β</span><span> at the start become those of the downstream </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> cells at the start of the third cell a s=8 m, which is the first </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> cell.</span></div><h2 class = 'S12'><span>Automatic matching</span></h2><div class = 'S0'><span>Let us first find out what </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">α</span><span> and </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">β</span><span> at the start of the </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> cells is</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >beamline=fodo90;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Rend=Racc(:,:,end);</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >[Qtune,alpha90,beta90,gamma90]=R2beta(Rend)</span></span></div><div class = 'S7'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>Qtune = 0.2500</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>alpha90 = 1.4142</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>beta90 = 3</div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>gamma90 = 1.0000</div></div></div></div><div class = 'S10'><span>We find that </span><span texencoding="\beta=3" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="37.5" height="18" /></span><span>m and </span><span texencoding="\alpha=\sqrt{2}" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="50" height="20" /></span><span>. Now we need to define a </span><span style=' font-family: monospace;'>chisq_beta()</span><span> function that takes the two focal lengths for the two quadrupoles as input and returns the squared difference between the calculated beta function at the end of the matching cell and those of the downstrem </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> cells. Let's base the matching cell on the </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAAmCAYAAAC76qlaAAAEGklEQVRYR+3XdahtVRAG8N+zxcZCsQO7G1QUMZ6FotitKAoWmOA/KooigmJgYGJigC0qJoqFLYrdCoqF3Xwy57Hd7HM9593HhQdn/rnn7rVmrdkz33zz7UmmU5s0ncZtFPhEV26U8VHGB8zACCoDJmqabRsr41nbBwdhMcyKr3ELzscP/xPFSjgW6+EPzIkncA7eHu8b9As8l9yONbE7HqmLdsQ1+A6T8UafAPbDZXgSu+BbLIibsD72wl19fOfBcZgdX2IbnI6Hm/v7BX419seRuLB1QQK5FV9gNXzVWt8CD1RFVsXHjfV58W4FtTFeaPmuUxU9DYkhdi4OwbLNu7oC3xBP4TcshO9bh8fnUyxShx/YWJ8Jb2FpnIFTOrJ6Nk7AM8hdPVsSz1ZVjm48z/lXYnvc03veFXggsjPeRHDaZRfjcPyOJSr72bc3riuHzfFoh/PWuL+eb4UH6/cdyP/L4POG35k4GVviobECf6fKksOD4y4LhoP12MGVkfzuvfSvCCx+6XBO/3yDVCeZjP9yValrcUDL524Efgs3q9/OeBoibDED7sV2fQLPC2U9djkOrd9ppgXwCtbo45vHaeoV8UHBKs16PY7CBQ2/pYqBzsPxzfO6Av+Rf1XjWJeH4oLHWDKyA2bDz/XsMWw2RuDpoY1qfb5imYsKKj3oZPlSbFBMlJ6bYl0Yfx9502Q+zdkLpum3fJU2z0JTKWW6PjCLBa87jRF4qtWDYZhnRryIfXFD+aVfTio6TcP/x7oCj+OetSsd3aOlpmNg8FI9uBl7YBM8Xs+C/zZWm/7NO0KL4fsMu+A9fTIz5kIYqKtPOj8k0iivYxZ8iE3xUePW4D/DJZfEMkWPqdIHArGrauL2S3peLA0eCyWGGoeyfgMohJ/BkzGfAXIFXi0IpRp/1yjPZWmsG6vJ3qvbk7UMqn52Z/VF1hfHJ0NFXU3YzydwOBFrl1YJflOJS6r7d8VfRVOZnmGkn+qwHu77nR3NEogkAUlO5sFQNjWydn58VlC6D9s2buzRYRotL9zPXsMqNWgWHSri2jw1gWdcp2mSrXVbeiPKMZUII4XmogrblgxnAKVCEV09Ihgq/mEDXx1P16Vp0MNat4VdgvdYeDp72xZ+76nN3UpUDRV0Ng8T+Nx4HuHwYDhys43N0FjUXxouAitCq22RqFnLvMhZfw4d9RCBRwlmJEc4RcMks9HkXRbMR8WFQldo8XB0Spo82jxia4poGjb4QTKeCRg9koyfhVOLTca664jSHKHFDLFgPqIryjEKMMoyFDvV1i/wZDjSNo0WdritvkIiiga1tepLZuWSDXPg5fowyN9xWVfg4e8wRyjrOUQwDc2z44pqAOdBoDLAMRO/ZRT4ROd8lPFRxgfMwAgqAyZqmm37Bwf6zSfA9ehYAAAAAElFTkSuQmCC" width="23" height="19" /></span><span> cell</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >sigma0=sigma60; </span><span style="color: rgb(2, 128, 9);">% use sigma60 as starting matrix "global sigma0"</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beamline=fodo90;</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >F0=[-2,2]; </span><span style="color: rgb(2, 128, 9);">% initial guesses</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >[F,fval]=fminsearch(@chisq_beta,F0)</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="654DADBF" data-scroll-top="null" data-scroll-left="null" data-width="1326" data-testid="output_30" style="width: 1356px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="matrixElement veSpecifier saveLoad" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="veVariableName variableNameElement double" style="width: 1326px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="headerElementClickToInteract" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><span style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">F = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">1×2</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":"2","totalRows":"1","charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 146px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> -2.0294 1.6602
</div><div class="horizontalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div><div class="verticalEllipsis hide" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"></div></div></div></div><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>fval = 2.3561e-09</div></div></div><div class="inlineWrapper"><div class = 'S15'><span style="white-space: pre"><span >matching=beamline; </span><span style="color: rgb(2, 128, 9);">% save the resulting beamline as matching cell</span></span></div></div></div><div class = 'S10'><span>And now we can reassemble the beamline consisting of one fodo60 cell, a matching cell, and four fodo90 cells, calculate the transfer matrices and plot the beta functions.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >beamline=[fodo60;matching;repmat(fodo90,4,1)];</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >data=zeros(1,nmat); </span><span style="color: rgb(2, 128, 9);">% allocate memory</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >k=1:nmat</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > sigma=Racc(:,:,k)*sigma60*Racc(:,:,k)';</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > data(k)=sigma(1,1); </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 class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >plot(spos,data,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); xlabel(</span><span style="color: rgb(170, 4, 249);">'s [m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'\beta [m]'</span><span >); ylim([0,10])</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'After automatic matching'</span><span >)</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="43CAAF0E" data-scroll-top="null" data-scroll-left="null" data-testid="output_32" style="width: 1356px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" style="width: 560px;"></div></div></div></div></div><div class = 'S10'><span>And that concludes this quick tutorial. Please do also have a look at the service functions in the Appendix below. They generate the transfer matrices, translate a transfer matrix to Twiss parameters, and calculate the chisq for the automatic matching of the tune and the beta function, respectively.</span></div><h2 class = 'S12'><span>Appendix</span></h2><h3 class = 'S16'><span>Transfer matrix for a drift space </span><span style=' font-family: monospace;'>D(L)</span></h3><div class = 'S0'><span>The following receives the length</span><span style=' font-family: monospace;'> L </span><span>of a drift space and resturns the 2x2 transfer matrix</span><span style=' font-family: monospace;'> out</span><span> for a drift space</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >out=D(L)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > out=[1,L;0,1];</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><h3 class = 'S16'><span>Transfer matrix for a thin-lens quadrupole </span><span style=' font-family: monospace;'>Q(F)</span></h3><div class = 'S0'><span>The following receives the length</span><span style=' font-family: monospace;'> L </span><span>of a drift space and resturns the 2x2 transfer matrix</span><span style=' font-family: monospace;'> out</span><span> for a drift space</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >out=Q(F)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >out=eye(2);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >abs(F)<1e-8, </span><span style="color: rgb(14, 0, 255);">return</span><span >; </span><span style="color: rgb(14, 0, 255);">end</span><span > </span><span style="color: rgb(2, 128, 9);">% turn off, if F=0</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >out=[1,0;-1/F,1]; </span><span style="color: rgb(2, 128, 9);">% transfer matrix</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><h3 class = 'S16'><span>The function </span><span style=' font-family: monospace;'>calcmat()</span><span> to calculate all transfer matrices</span></h3><div class = 'S0'><span>The following function receives the </span><span style=' font-family: monospace;'>beamline</span><span> description as input and returns</span></div><ul class = 'S2'><li class = 'S3'><span>Racc(2,2,nmat): transfer matrices from the start to the each of each segment, such that R(:,:,end) is the transfer matrix from the start to the end of the beamline.</span></li><li class = 'S3'><span>spos: position along the beamline after each segment, useful when plotting.</span></li><li class = 'S3'><span>nmat: number of segments </span></li><li class = 'S3'><span>nlines: number of lines in the beamline </span></li></ul><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(2, 128, 9);">% calcmat.m, calculate the transfer-matrices</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >[Racc,spos,nmat,nlines]=calcmat(beamline)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >ndim=size(D(1),1); </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >nlines=size(beamline,1); </span><span style="color: rgb(2, 128, 9);">% number of lines in beamline</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >nmat=sum(beamline(:,2))+1; </span><span style="color: rgb(2, 128, 9);">% sum over repeat-count in column 2</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Racc=zeros(ndim,ndim,nmat); </span><span style="color: rgb(2, 128, 9);">% matrices from start to element-end</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Racc(:,:,1)=eye(ndim); </span><span style="color: rgb(2, 128, 9);">% initialize first with unit matrix</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >spos=zeros(nmat,1); </span><span style="color: rgb(2, 128, 9);">% longitudinal position</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >ic=1; </span><span style="color: rgb(2, 128, 9);">% element counter</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >line=1:nlines </span><span style="color: rgb(2, 128, 9);">% loop over input elements</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">for </span><span >seg=1:beamline(line,2) </span><span style="color: rgb(2, 128, 9);">% loop over repeat-count </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > ic=ic+1; </span><span style="color: rgb(2, 128, 9);">% next element </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > Rcurr=eye(2); </span><span style="color: rgb(2, 128, 9);">% matrix in next element</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">switch </span><span >beamline(line,1) </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">case </span><span >1 </span><span style="color: rgb(2, 128, 9);">% drift</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > Rcurr=D(beamline(line,3));</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">case </span><span >2 </span><span style="color: rgb(2, 128, 9);">% thin quadrupole</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > Rcurr=Q(beamline(line,4)); </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">otherwise</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > disp(</span><span style="color: rgb(170, 4, 249);">'unsupported code'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">end</span><span > </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > Racc(:,:,ic)=Rcurr*Racc(:,:,ic-1); </span><span style="color: rgb(2, 128, 9);">% concatenate </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > spos(ic)=spos(ic-1)+beamline(line,3); </span><span style="color: rgb(2, 128, 9);">% position of element </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span > </span><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 class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><h3 class = 'S16'><span>R2beta()</span></h3><div class = 'S0'><span>The function R2beta() receives a transfer matrix </span><span style=' font-family: monospace;'>R</span><span> as input and returns the "tune" </span><span texencoding="Q=\mu/2\pi" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="65" height="19" /></span><span> for the transfer matrix R, as well as the periodic Twiss parameters </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">α</span><span>, </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">β</span><span>, and </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">γ</span><span>.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >[Q,alpha,beta,gamma]=R2beta(R)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >mu=acos(0.5*(R(1,1)+R(2,2)));</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >(R(1,2)<0), mu=2*pi-mu; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Q=mu/(2*pi);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beta=R(1,2)/sin(mu);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >alpha=(0.5*(R(1,1)-R(2,2)))/sin(mu);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >gamma=(1+alpha^2)/beta;</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><h3 class = 'S16'><span>chisq_tune()</span></h3><div class = 'S0'><span>This function receives a guess for the focal length F and calculates the squared difference between the desired tune and tune for this F. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >chisq=chisq_tune(F)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">global </span><span >beamline sigma0</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beamline(2,4)=-F; </span><span style="color: rgb(2, 128, 9);">% set the two quadrupoles, here QD</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beamline(4,4)=F; </span><span style="color: rgb(2, 128, 9);">% and here QF</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline); </span><span style="color: rgb(2, 128, 9);">% update transfer matrices</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Rend=Racc(:,:,end); </span><span style="color: rgb(2, 128, 9);">% the last one</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Qtune,alpha0,beta0,gamma0]=R2beta(Rend); </span><span style="color: rgb(2, 128, 9);">% get Qtune</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >chisq=(Qtune-0.25)^2; </span><span style="color: rgb(2, 128, 9);">% difference to minimize</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><h3 class = 'S16'><span>chisq_beta()</span></h3><div class = 'S0'><span>This function receives the focal lengths of the two quads in the matching cell and returns the aquared difference between </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">α</span><span> and </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">β</span><span> for the </span><span texencoding="90^o" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="19" /></span><span> cell and the one derived from the provided quad values</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >chisq=chisq_beta(F)</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">global </span><span >beamline sigma0</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beamline(2,4)=F(1); </span><span style="color: rgb(2, 128, 9);">% set the two quadrupoles, here QD</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beamline(4,4)=F(2); </span><span style="color: rgb(2, 128, 9);">% and here QF</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >[Racc,spos,nmat,nlines]=calcmat(beamline); </span><span style="color: rgb(2, 128, 9);">% update transfer matrices</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >Rend=Racc(:,:,end); </span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >sigma=Rend*sigma0*Rend';</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beta=sigma(1,1); alpha=-sigma(1,2);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >beta90=3; alpha90=sqrt(2);</span></span></div></div><div class="inlineWrapper"><div class = 'S5'><span style="white-space: pre"><span >chisq=(beta-beta90)^2+(alpha-alpha90)^2;</span></span></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S10'><span></span></div><div class = 'S0'></div>
<br>
<!--
##### SOURCE BEGIN #####
%%
% Companion software for "Volker Ziemann, _Hands-on Accelerator physics using
% MATLAB, CRCPress, 2019_" (https://www.crcpress.com/9781138589940)
%% 2D beam optics (Section 3.3.3, 3.3.5, 3.6.1, and 3.6.2)
% Volker Ziemann, 211106, CC-BY-SA-4.0
%
% In accelerators the elements, such as a magnet or the beam pipe between the
% magnets, follow one another and we represent them as lines in an array that
% describes this sequence. We describe drift space with a code=1 in the first
% column and thin quadrupoles by code=2. The second column contains the number
% the line is repeated internally, the third column displays the lenth of the
% element and the fourth column the strength. For a thin quadrupole the latter
% is specified as its focal length F. Summarizing
%%
% * First column: code, drift=1, quad=2
% * Second column: repeat code for the element
% * Third column: length of one segment
% * Fourth column: strength of one segment, focal length for a thin quadrupole.
%%
% A simple FODO cell that starts in the middle of the drift space before the
% defocusing quadrupole is thus defined in the following array, named |fodo,|
% where the focal length is defined as |F=2.1.| Just below the defionition of
% fodo we define the |beamline| as 20 copies of |fodo| stacked on top of each
% other.
global beamline sigma0 % needed for some functions.
F=2.1; % focal length of the quadrupoles
fodo=[ 1, 5, 0.2, 0; % 5* D(L/10)
2, 1, 0.0, -F; % QD
1, 10, 0.2, 0; % 10* D(L/10)
2, 1, 0.0, F; % QF/2
1, 5, 0.2, 0] % 5* D(L/10)
beamline=repmat(fodo,20,1) % name must be 'beamline'
%%
% Now calculate all the transfer matrices with the function |calcmat()| that
% is defined in the appendix
[Racc,spos,nmat,nlines]=calcmat(beamline);
%%
% Then we allocate memory to store the positions after each segment that we
% want to display later
data=zeros(1,nmat); % allocate memory
%%
% and define the input state x0, which contains the starting position and angle
x0=[0.001;0]; % 1 mm offset at start
%%
% before mapping the input x0 to the state vector x at the end of each segment
% along the beam line
for k=1:nmat
x=Racc(:,:,k)*x0;
data(k)=x(1); % store the position
end
%%
% and annotate the axes
plot(spos,1e3*data,'k'); % 1e3 to convert to mm
xlabel('s [m]');
ylabel(' x [mm]');
title('Trajectory')
xlim([spos(1),spos(end)])
%% Beta functions
% Now we are ready to calculate the beta functions along the beamline. Let's
% first calculate the transfer matrices for a single fodo cell.
beamline=fodo; % just a single FODO cell
[Racc,spos,nmat,nlines]=calcmat(beamline);
Rend=Racc(:,:,end); % the TM from start to end
%%
% and the periodic Twiss parameters $\alpha$, $\beta$, and $\gamma$
[Qtune,alpha0,beta0,gamma0]=R2beta(Rend)
%%
% where we observe that Qtune is 0.1580. Change the focal length |F| way up
% in this script to a different value and observe how |Qtune| changes.
%%
% We now use the Twiss parameters to construct the *initial* beam matrix sigma0
sigma0=[beta0,-alpha0;-alpha0,gamma0]
%%
% and map this through one FODO cell
data=zeros(1,nmat); % allocate memory
for k=1:nmat
sigma=Racc(:,:,k)*sigma0*Racc(:,:,k)';
data(k)=sigma(1,1); % that's the beta
end
%%
% and plot the beta function through one FODO cell
plot(spos,data,'k')
xlabel('s [m]'); ylabel('\beta [m]')
title('Beta function in one FODO cell')
%%
% We observe an oscillation with aminimum at the location of the defocusing
% quadrupole at s=1 m and a maximum in the focusing quadrupole at s=3 m.
%% Betafunction through ten FODO cells
% Mapping the beta function through 10 FODO cells makes it necessary to increas
% the length of the |beamline| and update all transfer matrices
beamline=repmat(fodo,10,1);
[Racc,spos,nmat,nlines]=calcmat(beamline);
%%
% We do not need to re-calculate sigma0, because it is periodic and we can therefore
% use the one determined from a single cell. Let's propagate the beta function
% |sigma0| through the 10 FODO cells and plot the result
data=zeros(1,nmat); % allocate memory
for k=1:nmat
sigma=Racc(:,:,k)*sigma0*Racc(:,:,k)';
data(k)=sigma(1,1); % that's the beta
end
plot(spos,data,'k')
xlabel('s [m]'); ylabel('\beta [m]')
title('Beta function in ten FODO cells')
%%
% It's just ten copies of the beta function through a single cell.
%% Adjust Qtune to 0.25
% Let's go back to a single cell an adjust the quadrupoles such that the tune
% for one cell is Qtune=0.25. Which focal length approximatelydoes the job? Try
% to set the tune to 0.16666=1/6. What is F in that case?
3.356% adjust focal length F
F=ans; % focal length of the quadrupoles
fodo=[ 1, 5, 0.2, 0;
2, 1, 0.0, -F; % QD
1, 10, 0.2, 0;
2, 1, 0.0, F; % QF/2
1, 5, 0.2, 0];
beamline=fodo;
[Racc,spos,nmat,nlines]=calcmat(beamline);
Rend=Racc(:,:,end);
[Qtune,alpha0,beta0,gamma0]=R2beta(Rend)
%% Automatic tune adjustment
% Now we use fminsearch() to set the tune to a desired value. To do so we need
% to define a cost function that I often call $\chi^2$ or chisq. Here we use the
% name |chisq_tune()|. It receives a guess for the focal length |F| and returns
% the difference betwen the tune value for that |F| and the desired tune, here
% 0.25. Such a function is defined in the appendix.
% global beamline % needed to make it available inside chisq_tune()
F0=3; % starting guess
[Fnew,fval]=fminsearch(@chisq_tune,F0)
beamline % just look at the new beamline description
%%
% Fnew is the new focal length that will give you the desired tune. let's verify
% that
[Racc,spos,nmat,nlines]=calcmat(beamline);
Rend=Racc(:,:,end);
Qtune=R2beta(Rend)
%%
% Now look at the function chisq_tune() in the appendix and change it such that
% Qtune becomes 1/6. What value for the focal length do you find?
%% Matching FODO cells with Qtune=0.1666 to those with Qtune=0.25
% This is also called matching $60^o$ cell to a $90^o$ cell, because of $60^o/360^0=0.1666$
% and $90^o/360^0=0.25$.
%
% We found in the previous matching exercise that $F=\sqrt{2}$ gave Qtune=0.25
% and and $F=2$ gave Qtune=0.1666, which allows us to define the two cells in
% the following way
F=2; % focal length of the quadrupoles
fodo60=[ 1, 5, 0.2, 0;
2, 1, 0.0, -F; % QD
1, 10, 0.2, 0;
2, 1, 0.0, F; % QF/2
1, 5, 0.2, 0];
F=sqrt(2);
fodo90=[ 1, 5, 0.2, 0;
2, 1, 0.0, -F; % QD
1, 10, 0.2, 0;
2, 1, 0.0, F; % QF/2
1, 5, 0.2, 0];
%%
% Let's look at the beta function along that beamline. To do so we first calculate
% the periodic beam matrix for the $90^o$ cell
beamline=fodo60;
[Racc,spos,nmat,nlines]=calcmat(beamline);
Rend=Racc(:,:,end);
[Qtune,alpha60,beta60,gamma60]=R2beta(Rend)
sigma60=[beta60,-alpha60;-alpha60,gamma60]
%%
% Now let's build a long beamline, starting with two fodo60, followed by six
% fodo90 cells and display the betafunction along this beam line, if we start
% with the input beam sigma60
beamline=[fodo60;fodo60;repmat(fodo90,6,1)];
[Racc,spos,nmat,nlines]=calcmat(beamline);
data=zeros(1,nmat); % allocate memory
for k=1:nmat
sigma=Racc(:,:,k)*sigma60*Racc(:,:,k)';
data(k)=sigma(1,1);
end
plot(spos,data,'k'); xlabel('s [m]'); ylabel('\beta [m]')
title('Unmatched fodo60 to fodo90 transition')
%%
% We observe that the beam that is matched for the fodo60 cell does not show
% a regular pattern once it enters the fodo90 cells. We therefore try to adjust
% the two quadrupoles in the second fodo60 cell to try to minimize the irregularity.
% Note that these two quads are now in line 7 and 9, respectively. The second
% cell we refer to as the _matching cell._
beamline(7,4)=-2.044;
beamline(9,4)=2.0934;
[Racc,spos,nmat,nlines]=calcmat(beamline);
data=zeros(1,nmat); % allocate memory
for k=1:nmat
sigma=Racc(:,:,k)*sigma60*Racc(:,:,k)';
data(k)=sigma(1,1);
end
plot(spos,data,'k'); xlabel('s [m]'); ylabel('\beta [m]'); ylim([0,10])
title('Matching by hand')
%%
% Did you manage to get a smooth and periodic beta function through the downstream
% part of the beamline? If not, try out the following code, which uses |fminsearch()|
% to adjust the two quads such that $\alpha$ and $\beta$ at the start become those
% of the downstream $90^o$ cells at the start of the third cell a s=8 m, which
% is the first $90^o$ cell.
%% Automatic matching
% Let us first find out what $\alpha$ and $\beta$ at the start of the $90^o$
% cells is
beamline=fodo90;
[Racc,spos,nmat,nlines]=calcmat(beamline);
Rend=Racc(:,:,end);
[Qtune,alpha90,beta90,gamma90]=R2beta(Rend)
%%
% We find that $\beta=3$m and $\alpha=\sqrt{2}$. Now we need to define a |chisq_beta()|
% function that takes the two focal lengths for the two quadrupoles as input and
% returns the squared difference between the calculated beta function at the
% end of the matching cell and those of the downstrem $90^o$ cells. Let's base
% the matching cell on the $90^o$ cell
sigma0=sigma60; % use sigma60 as starting matrix "global sigma0"
beamline=fodo90;
F0=[-2,2]; % initial guesses
[F,fval]=fminsearch(@chisq_beta,F0)
matching=beamline; % save the resulting beamline as matching cell
%%
% And now we can reassemble the beamline consisting of one fodo60 cell, a matching
% cell, and four fodo90 cells, calculate the transfer matrices and plot the beta
% functions.
beamline=[fodo60;matching;repmat(fodo90,4,1)];
[Racc,spos,nmat,nlines]=calcmat(beamline);
data=zeros(1,nmat); % allocate memory
for k=1:nmat
sigma=Racc(:,:,k)*sigma60*Racc(:,:,k)';
data(k)=sigma(1,1);
end
plot(spos,data,'k'); xlabel('s [m]'); ylabel('\beta [m]'); ylim([0,10])
title('After automatic matching')
%%
% And that concludes this quick tutorial. Please do also have a look at the
% service functions in the Appendix below. They generate the transfer matrices,
% translate a transfer matrix to Twiss parameters, and calculate the chisq for
% the automatic matching of the tune and the beta function, respectively.
%% Appendix
% Transfer matrix for a drift space |D(L)|
% The following receives the length |L| of a drift space and resturns the 2x2
% transfer matrix |out| for a drift space
function out=D(L)
out=[1,L;0,1];
end
% Transfer matrix for a thin-lens quadrupole |Q(F)|
% The following receives the length |L| of a drift space and resturns the 2x2
% transfer matrix |out| for a drift space
function out=Q(F)
out=eye(2);
if abs(F)<1e-8, return; end % turn off, if F=0
out=[1,0;-1/F,1]; % transfer matrix
end
% The function |calcmat()| to calculate all transfer matrices
% The following function receives the |beamline| description as input and returns
%%
% * Racc(2,2,nmat): transfer matrices from the start to the each of each segment,
% such that R(:,:,end) is the transfer matrix from the start to the end of the
% beamline.
% * spos: position along the beamline after each segment, useful when plotting.
% * nmat: number of segments
% * nlines: number of lines in the beamline
% calcmat.m, calculate the transfer-matrices
function [Racc,spos,nmat,nlines]=calcmat(beamline)
ndim=size(D(1),1);
nlines=size(beamline,1); % number of lines in beamline
nmat=sum(beamline(:,2))+1; % sum over repeat-count in column 2
Racc=zeros(ndim,ndim,nmat); % matrices from start to element-end
Racc(:,:,1)=eye(ndim); % initialize first with unit matrix
spos=zeros(nmat,1); % longitudinal position
ic=1; % element counter
for line=1:nlines % loop over input elements
for seg=1:beamline(line,2) % loop over repeat-count
ic=ic+1; % next element
Rcurr=eye(2); % matrix in next element
switch beamline(line,1)
case 1 % drift
Rcurr=D(beamline(line,3));
case 2 % thin quadrupole
Rcurr=Q(beamline(line,4));
otherwise
disp('unsupported code')
end
Racc(:,:,ic)=Rcurr*Racc(:,:,ic-1); % concatenate
spos(ic)=spos(ic-1)+beamline(line,3); % position of element
end
end
end
% R2beta()
% The function R2beta() receives a transfer matrix |R| as input and returns
% the "tune" $Q=\mu/2\pi$ for the transfer matrix R, as well as the periodic Twiss
% parameters $\alpha$, $\beta$, and $\gamma$.
function [Q,alpha,beta,gamma]=R2beta(R)
mu=acos(0.5*(R(1,1)+R(2,2)));
if (R(1,2)<0), mu=2*pi-mu; end
Q=mu/(2*pi);
beta=R(1,2)/sin(mu);
alpha=(0.5*(R(1,1)-R(2,2)))/sin(mu);
gamma=(1+alpha^2)/beta;
end
% chisq_tune()
% This function receives a guess for the focal length F and calculates the squared
% difference between the desired tune and tune for this F.
function chisq=chisq_tune(F)
global beamline sigma0
beamline(2,4)=-F; % set the two quadrupoles, here QD
beamline(4,4)=F; % and here QF
[Racc,spos,nmat,nlines]=calcmat(beamline); % update transfer matrices
Rend=Racc(:,:,end); % the last one
[Qtune,alpha0,beta0,gamma0]=R2beta(Rend); % get Qtune
chisq=(Qtune-0.25)^2; % difference to minimize
end
% chisq_beta()
% This function receives the focal lengths of the two quads in the matching
% cell and returns the aquared difference between $\alpha$ and $\beta$ for the
% $90^o$ cell and the one derived from the provided quad values
function chisq=chisq_beta(F)
global beamline sigma0
beamline(2,4)=F(1); % set the two quadrupoles, here QD
beamline(4,4)=F(2); % and here QF
[Racc,spos,nmat,nlines]=calcmat(beamline); % update transfer matrices
Rend=Racc(:,:,end);
sigma=Rend*sigma0*Rend';
beta=sigma(1,1); alpha=-sigma(1,2);
beta90=3; alpha90=sqrt(2);
chisq=(beta-beta90)^2+(alpha-alpha90)^2;
end
%%
%
%
%
##### SOURCE END #####
-->
</div></body></html>