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FELoscillator.html
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<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge,IE=9,chrome=1"><meta name="generator" content="MATLAB 2021a"><title>Free-electron laser oscillator (Section 10.4)</title><style type="text/css">.rtcContent { padding: 30px; } .S0 { margin: 2px 10px 9px 4px; padding: 0px; line-height: 21px; min-height: 0px; white-space: pre-wrap; color: rgb(0, 0, 0); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 14px; font-weight: normal; text-align: left; }
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.S8 { margin: 3px 10px 5px 4px; padding: 0px; line-height: 20px; min-height: 0px; white-space: pre-wrap; color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-style: normal; font-size: 20px; font-weight: bold; text-align: left; }</style></head><body><div class = rtcContent><div class = 'S0'><span>Companion software for "Volker Ziemann, </span><span style=' font-style: italic;'>Hands-on Accelerator physics using MATLAB, CRCPress, 2019</span><span>" (https://www.crcpress.com/9781138589940)</span></div><h1 class = 'S1'><span>Free-electron laser oscillator (Section 10.4)</span></h1><div class = 'S0'><span>Volker Ziemann, 211114, CC-BY-SA-4.0</span></div><div class = 'S0'><span style=' font-weight: bold;'>Important:</span><span> requires the elliptic package from </span><a href = "https://github.com/moiseevigor/elliptic"><span>https://github.com/moiseevigor/elliptic</span></a><span> located in a subdirectory below the present one (for the fast evaluation of elliptic functions).</span></div><div class = 'S0'><span>Like the example for the SASE FEL </span><span style=' font-family: monospace;'>SaseFreeElectronLaser.mlx</span><span> is this simulation based on numericall integrating Equation 10.32. The main difference is that here we operate at low current jcurr and assume that the laser field is recirculated by mirrors and meet a fresh electron bunch on the next iteration.</span></div><div class = 'S0'><span>First we define the </span><span style=' font-family: monospace;'>mirror_losses</span><span> to be 0.01, the initial complex field </span><span style=' font-family: monospace;'>a</span><span> of the laser and the scaled current </span><span style=' font-family: monospace;'>jcurr</span><span>, which represents the peak current of the electron distribution. Moreover, we define the initial distribution of electrons in the ponderomotive field and the number N of electrons used in the simulation. From Equation 10.32 we see that the magnnitude of a, which is a0 describes the oscillation frequency </span><span texencoding="\Omega_s" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="18" height="20" /></span><span> in the ponderomotive field.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >clear </span><span style="color: rgb(170, 4, 249);">all</span><span >; close </span><span style="color: rgb(170, 4, 249);">all</span><span >; tic</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >addpath </span><span style="color: rgb(170, 4, 249);">./elliptic</span><span > </span><span style="color: rgb(2, 128, 9);">% needed for elliptic12</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >mirror_losses=0.01; </span><span style="color: rgb(2, 128, 9);">% 0.01=1% extracted</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >a0=1e-8; phi=0; a=a0*exp(i*phi); </span><span style="color: rgb(2, 128, 9);">% initial amplitude and phase of laser</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >jcurr=1; </span><span style="color: rgb(2, 128, 9);">% scaled current from Equation 10.32</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >x0=[pi/2,2.6]; dx=[2*pi,0.1]; </span><span style="color: rgb(2, 128, 9);">% center and spread of distribution</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >N=1000; </span><span style="color: rgb(2, 128, 9);">% number of particles</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >Omegas=sqrt(a0); </span><span style="color: rgb(2, 128, 9);">% synchrotron frequency</span></span></div></div></div><div class = 'S5'><span>Next we need to define some parameters needed for annotating the plots. Since the increase of the field during one pass through the undulator does not grows significantly we decide to split the simulation within on pass through the unduator into </span><span style=' font-family: monospace;'>nstep=5</span><span> steps, rather than 100, as in the SASE suimulation. </span><span style=' font-family: monospace;'>Nrep</span><span>, on th other hand, specifies the number of round-trips of the laser caused by the mirrors. On each of these trips the laser interacts with a fresh electron bunch that is provided by an accelerator. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >axis_scale=[-pi/2,3*pi/2,-17,17];</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >ypos=0.95*axis_scale(3)+0.05*axis_scale(4); </span><span style="color: rgb(2, 128, 9);">% where to place text</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >zeta=-pi/2:0.01:3*pi/2; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >nstep=5; dt=1/nstep; tau=(1:nstep)/nstep; </span><span style="color: rgb(2, 128, 9);">% steps along the undulator</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span >Nrep=100; </span><span style="color: rgb(2, 128, 9);">% iterations = round-trips of the laser </span></span></div></div></div><div class = 'S5'><span>Now we start iterating and first generate a fresh electron distribution that we display as a cloud of green dots.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >data=zeros(Nrep,4);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">for </span><span >rep=1:Nrep </span><span style="color: rgb(2, 128, 9);">% iteration over round-trips</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > hold </span><span style="color: rgb(170, 4, 249);">off</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > a00=abs(a); </span><span style="color: rgb(2, 128, 9);">% needed to caluclate the gain in this iteration</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x1(:,1)=x0(1)+(rand(N,1)-0.5)*dx(1); </span><span style="color: rgb(2, 128, 9);">% initial distribution</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x1(:,2)=x0(2)+(rand(N,1)-0.5)*dx(2); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > plot(x1(:,1),x1(:,2),</span><span style="color: rgb(170, 4, 249);">'g.'</span><span >)</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >(rep==1) dx0=dx(2); rms0=std(x1(:,2)); </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S5'><span>In the following loop over nstep iterations we follow the electron distribution as it passes through the undulator. In each step we update the electron coordinates and calculate the bunching factor </span><span style=' font-family: monospace;'>bf</span><span> that we subsequently use to update the field </span><span style=' font-family: monospace;'>a </span><span>before plotting the new electron coordinates as red dots. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > hold </span><span style="color: rgb(170, 4, 249);">on</span><span >; </span><span style="color: rgb(2, 128, 9);">% draw new image </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">for </span><span >m=1:nstep </span><span style="color: rgb(2, 128, 9);">% one pass through the undulator</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > Omegas=sqrt(abs(a)); phi=phase(a); </span><span style="color: rgb(2, 128, 9);">% needed for electron dynamics</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">parfor </span><span >k=1:N </span><span style="color: rgb(2, 128, 9);">% update electron phase space</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > x1(k,:)=pendulumtracker2_phase(x1(k,:),Omegas,phi,dt);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > bf=sum(exp(-i*x1(:,1)))/size(x1,1); </span><span style="color: rgb(2, 128, 9);">% bunching factor <exp(-i*zeta)></span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > a=a-jcurr*bf*dt; </span><span style="color: rgb(2, 128, 9);">% update laser field, Eq. 10.32 </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > plot(x1(:,1),x1(:,2),</span><span style="color: rgb(170, 4, 249);">'r.'</span><span >); rms1=std(x1(:,2)); </span></span></div></div></div><div class = 'S5'><span>Now we reduce the field as a consequence of the mirror losses, plot separatrix and annotate the plot.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > a=a*(1-mirror_losses);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > title([</span><span style="color: rgb(170, 4, 249);">'Iteration '</span><span >,num2str(rep),</span><span style="color: rgb(170, 4, 249);">' of '</span><span >,num2str(Nrep)])</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > separatrix=2*Omegas*cos(0.5*(zeta-pi/2+phi));</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > plot(zeta,separatrix,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,zeta,-separatrix,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > set(gca,</span><span style="color: rgb(170, 4, 249);">'xtick'</span><span >,[-pi/2,0,pi/2,pi,3*pi/2],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,14, </span><span style="color: rgb(14, 0, 255);">...</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(170, 4, 249);">'xticklabels'</span><span >,{</span><span style="color: rgb(170, 4, 249);">'-\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi/2'</span><span >,</span><span style="color: rgb(170, 4, 249);">'\pi'</span><span >,</span><span style="color: rgb(170, 4, 249);">'3\pi/2'</span><span >}) </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > axis(axis_scale); xlabel(</span><span style="color: rgb(170, 4, 249);">'\zeta'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'\nu'</span><span >) </span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span > text(-pi/4,ypos,[</span><span style="color: rgb(170, 4, 249);">'abs(a) = '</span><span >,num2str(abs(a),3),</span><span style="color: rgb(170, 4, 249);">' '</span><span >],</span><span style="color: rgb(170, 4, 249);">'fontsize'</span><span >,16) </span></span></div></div></div><div class = 'S5'><span>Before the next iteration, we save a number of interesting parameters for later plots to the array </span><span style=' font-family: monospace;'>data</span><span>.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span > data(rep,1)=abs(a);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(rep,2)=phase(a)*180/pi;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(rep,3)=(abs(a)-a00)/a00;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > data(rep,4)=rms1/rms0; </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > pause(0.001);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >(mod(rep,100)==0) toc; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="3EE38F99" data-scroll-top="null" data-scroll-left="null" data-testid="output_0" style="width: 1364px;"><div class="figureElement"><div class="figureContainingNode" style="width: 560px; max-width: 100%; display: inline-block;"><div class="GraphicsView" data-dojo-attach-point="graphicsViewNode,backgroundColorNode" id="uniqName_333_54" widgetid="uniqName_333_54" style="width: 100%; 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rRpLFmyhMOZMWMGkyZNom7btm38+Z//OWeeeSannHIKv/3tb2nYvXs3da7r0pCmKdOmTeOmm27i9Xz5y1/G8zzqdu7cycc//nHa2tr4zGc+w/PPP0/d1VdfzXnnnUczWbhwIbNnz6Zu06ZNnHzyySxatIiGG2+8kYaFCxcye/Zs6jZt2sTJJ5/MokWLaLjxxhs5nC9/+ct4nkfdzp07+fjHP05bWxuf+cxneP7556m7+uqrOe+883i7LFy4kNmzZ1O3adMmTj75ZBYtWkTDjTfeSMPChQuZPXs2dZs2beLkk09m0aJFNNx4440Y02wcjDGvctppp3HppZcy0v79+6mbMmUKmzZtYvbs2dQNDQ0xNDTEqFGjWLRoEQ8++CBjx47lcBzHYf369Zx88snUPf/882zatIlzzjmHp556ijFjxlD3/e9/n7rTTjuNSy+9lJH279/P63EchwcffJDrrruOE088kZE+8IEPcOedd/KNb3yDZrRu3TouuOACRo0aRcOJJ57ImjVrOPfccxlp3bp1XHDBBYwaNYqGE088kTVr1nDuuedyOI7j8OCDD3Lddddx4oknMtIHPvAB7rzzTr7xjW/wdlu3bh0XXHABo0aNouHEE09kzZo1nHvuuYy0bt06LrjgAkaNGkXDiSeeyJo1azj33HMxptk4GHMMu+2226jVatRqNT772c8y0q233sru3bvZsGEDzzzzDKtWraLhL/7iL9i4cSO///3v+clPfkKapuzfv5+enh7a29tp6OnpoVarUavVOOecczjYlClTePLJJ9m2bRsbNmzg+eefZ926dUyePJlKpUKtVuPBBx+k4dZbb2X37t1s2LCBZ555hlWrVlF3+eWXU6vVqNVqLFiwgJEcx+Haa69l165dbNu2jQ0bNvDMM8+wY8cOgiBgpH/5l3+hVqtRq9VYsGABI332s5+lVqtRq9VYuHAhb6Wenh5qtRq1Wo1zzjmHQznhhBPo7e3lxRdfZMOGDWzZsoVdu3Yxf/58DnbCCSfQ29vLiy++yIYNG9iyZQu7du1i/vz5vFGO43Dttdeya9cutm3bxoYNG3jmmWfYsWMHQRBwsHe9613UajVqtRo/+MEP+EP19PRQq9Wo1Wqcc845HMoJJ5xAb28vL774Ihs2bGDLli3s2rWL+fPnc7ATTjiB3t5eXnzxRTZs2MCWLVvYtWsX8+fPx5hm5GCMeU0TJ06ks7OTyZMncyjjxo3D933mzJnD6NGj+b+aMmUKnZ2dtLe3czgTJ06ks7OTyZMn84eaMmUKnZ2dTJ48maPFhAkT6Ozs5JRTTuFwJkyYQGdnJ6eccgp/jClTptDZ2cnkyZM5EkyYMIHOzk5OOeUUDmfChAl0dnZyyimnYEwzczDGGGOMaTIOxhhjjDFNxsEYY4wxpsk4GGOMMcY0GQdjjDHGmCbjYIwxxhjTZByMMcYYY5qMgzmshQsXIiKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIsHDhQo5GDuawNm/ejKqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCp1qoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqdaqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqrUqSqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqqKqqCqqiqqiqqgqqoqqoqqoKqqKqrJ582aORg7GGGOMMU3GwRhjjDGmyTgYc5S58sorMc3lyiuvxDSPK6+8EmP+1ByMOcosXrwY01wWL16MaR6LFy/GmD81B2OMMcaYJuNgjDHGGNNkHIwxxhhjmoyDMcYYY0yTcTDGGGOMaTIOxhhjjDFNxsEYY4wxpsk4HEWee+45vvCFLzA8PMzBfvGLX7B27VrWrl3L2rVrWbt2LWvXrmXt2rUMDAxgjDHGmObhcJTYt28fV199NevXr6darXKwm2++maVLl7J06VKWLl3K0qVLWbp0KUuXLiXPc4wxxhjTPByOAs899xylUon+/n5ey+bNm5k9eza9vb309vbS29tLb28vvb29TJ06FWOMMcY0D4cm19PTw9y5c9m+fTtTpkzhUHbu3EmlUuEjH/kI06dPZ/r06UyfPp3p06czffp0xo0bhzHGGGOah0OTu+mmm5g1axb33Xcf06ZN41C2bt1Kneu6GGOMMab5OTS5733ve3z7299m4sSJvJZt27ZR9+STT3L22WczdepUZs2axQ033MDevXsxxhhjTHNxaHKTJk3icJ555hnq1qxZw9y5c1m2bBmu63L77bdz0UUXUa1WORwRQUQQEVauXIkxxhhzJFq5ciUigoggIhytHI4B733ve/nUpz7FD3/4Q5YsWUJXVxerV6/m/PPP57HHHmP16tUcjqqiqqgqixcvxhhjjDkSLV68GFVFVVFVjlYOx4BrrrmGr3/960yYMIGRPv/5z1P385//HGOMMcY0D4dj2Dvf+U5aWloYGhrCGGOMMc3D4Sj33HPPsWzZMr7zne9wsL1791KpVBg3bhzGGGOMaR4OR7n29nYeeOAB7rjjDoaGhhipt7eXurPOOgtjjDHGNA+Ho5zjOCxZsoSdO3dy6aWXsnnzZrZv384tt9zCjTfeyBlnnMG8efMwxhhjTPNwOAYEQcDy5ct54oknWLhwIR/72MdYuXIl8+fP59Zbb8UYY4wxzcXhKLJixQpUlTFjxnCwrq4uNm/ezLp161i1ahW/+tWvWLFiBePGjcMYY4wxzcXhGOI4DiLCGWecwahRozDGGGNMc3IwxhhjjGkyDsYYY4wxTcbBGGOMMabJOBhjjDHGNBkHY4wxxpgm42CMMcYY02QcjDHGGGOajIMxxhhjTJNxMMYYY4xpMg7GGGOMMU3GwRhjjDGmyTgYY4wxxjQZB2OMMcaYJuNgjDHGGNNkHIwxxhhjmoyDMcYYY0yTcTDGGGOMaTIOxhhjjDFNxsEYY4wxpsk4GGOMMcY0GQdjjDHGmCbjYIwxxhjTZByMMcYYY5qMgzHGGGNMk3EwxhhjjGkyDsYYY4wxTcbBGGOMMabJOBhjjDHGNBkHY4wxxpgm42CMMcYY02QcjDHGGGOajIMxxhhjTJNxMMYYY4xpMg5Hkeeee44vfOELDA8PcyiPPPIIX/nKV/iHf/gHenp6+N3vfocxxhhjmo/DUWLfvn1cffXVrF+/nmq1ysGuu+46Fi1axJYtW3jxxRf553/+Zz7+8Y+za9cujDHGGNNcHI4Czz33HKVSif7+fg6lr6+P3t5eLrroIn74wx9y2223sW7dOvbu3cvSpUsxxhhjTHNxaHI9PT3MnTuX7du3M2XKFA7lO9/5DmPHjuULX/gCDZMnT6arq4vNmzfz7LPPYowxxpjm4dDkbrrpJmbNmsV9993HtGnTOJRNmzbR0dHBmDFjGGnatGnUbd68GWOMMcY0D4cm973vfY9vf/vbTJw4kUMZHBzkpZde4s/+7M842Ic+9CHqnnzySYwxxhjTPBya3KRJk3g9TzzxBHUtLS0c7LjjjqPuwIEDHI6IICKICCtXrsQYY4w5Eq1cuRIRQUQQEY5WDke54eFhDmd4eJjDUVVUFVVl8eLFGGOMMUeixYsXo6qoKqrK0crhKNfe3s5rqVar1I0ZMwZjjDHGNA+Ho5zrutT9/ve/52C7du2i7l3vehfGGGOMaR4OR7kxY8bwnve8h//8z//kYE8//TR1p5xyCsYYY4xpHg7HgI9+9KP09/eT5zkjffe732Xs2LHMnj0bY4wxxjQPh2PAxRdfzPjx47n44ovZuHEjeZ6zYsUKHnroIT73uc8xbtw4jDHGGNM8HI4BEydO5Pbbb6fu4osv5m/+5m+4++67ufzyy7nsssswxhhjTHNxOIqsWLECVWXMmDEc7C//8i/5j//4D9avX89dd93F448/zpIlSzDGGGNM83E4xkyePJkZM2YwatQojDHGGNOcHIwxxhhjmoyDMcYYY0yTcTDGGGOMaTIOxhhjjDFNxsEYY4wxpsk4GGOMMcY0GQdjjDHGmCbjYIwxxhjTZByMMcYYY5qMgzHGGGNMk3EwxhhjjGkyDsYYY4wxTcbBGGOMMabJOBhjjDHGNBkHY4wxxpgm42CMMcYY02QcjDHGGGOajIMxxpgjX7kM5TKkKS8rl6FchiiCKIJyGfKcl5XLUC5DmvKyNIU0hTTFmKOFgzHGmDdXnkOaQprysiiCIH81VLIAACAASURBVIAo4n9FERSLUChAoQCFApTLvKaeHggCCAJeFgQQBNDdDd3dEASQprwsiiAIIIp4WRSB74Pv84ZEEQQBBAGkKaQppCnkOeQ5xhwJHIwxxrwxeQ55DmkKaQp5zsvSFIpFKBYhTaGnB3wffB/yHNIUymUol/lfeQ55zhGpXIZyGcpl6OkB3wffh2IRikUoFKBQgCDAmD8VB2OMMW9MsQjFIvg++D6kKS/Lc8hzyHPeMNcld11y1yX3PFLXJd2xgzRNKZfLlMtlyuUy5XKZcrlM2fMol0qUPY80TSmXSpRLJcqlEuVSiXKpRHnHDsrlMmXPI+3uJvU80jQl9Tzy7m7y7m7eFlEEhQIUCuD7EAQQBJDnGPNmcTDGmGNRnkOe82bIgdx1SYFyTw9lIHJdAiCIInzA9zyKQLFYpFAoUOjuxgd8wM9zItclSlOiKKKnp4e+vj76+vro6+ujr6+PvjynD+gDenp66AP6gD6gD+gD+vKcvr4++oAoTYnSlCiKCMpl/HIZv1ymUChQKBQoFosUi0WKxSK+7xMEAUEQEEURUalEOY5Jk4S8qwviGOIYuruhVIJSCUolmDOHw0pTKJehXIY8x5g3i4MxxhyLikUoFiEIOJw8z0nTlLLrUnZdAsAH/CiiUChQDAJ8IHBdevKcvjwn9zzmxDFz5swhDEPCMCSOY5IkoVarUavVyLKMLMvIsowkSUiShCRJSJKEOI6J45g4jonjmDiOieOYOI6J45g4jonjmDiOieOYOI6J45g4jonjmCRJSJKEJEnIsowsy8iyjFqtRq1WI0kSkiQhjmPCMGTOnDm4rktDX18fURThBwGFIKAQBBTLZfw8JwAi1yXasYM0TcnznFeYMwc8DzyPNyxNoVCAQgGKRfB9SFPIc8hzjDmYgzHGGPI8J01TyuUyQRDg+z6+71MoFPB9nyAI6PM8+jyPOXFMVxwTxjFZllGr1ciyjCzLSJKEOI6J45hSqUSpVMLzPDzPw/M8XNflSOC6Lq7r4nkenudRKpUIw5AwDAnDkDiOSZKELMuo1WpkWUaSJIRhyJw5c6jL85woivB9n0KhQLFYxPd9gp4eIs+j3NVFGseQZZBl4Hm8IXkOaQp5DsUiFIsQRRgzkoMxxjSjPIc0hXIZggCCANKUw8nznHK5TNl1CQA/TSkUCvi+TxRF9PX1MWfOHLq6ugjDkFqtRpZlZFlGHMfEcUypVKJUKuF5Hq7rcixwXRfXdfE8j1KpRBiGxHFMkiRkWUatViNJEsIwxHVd6np6eoh6eigUixR9H9/3iaKIKIpI05RXcF3wPPA8cF1wXQ7L98H3wfehXIY0xRw7HIwxppkEARSL4Pvg+xAEUC5DuQx9fTTkeU6appTLZYIgwPd9CoUCvu/T09NDn+cxJ44J45harUaWZSRJQhzHlEolSqUSnudh3jjXdfE8jzAMCcOQJElIkoRarUaSJIRhSF2e50RRRKFQoFgs4vs+UU8P5a4uSBLIMsgyKJWguxu6u2HOHF4lTSFNIU0hCMD3oVAA34cggHIZc/RyMMaYZlIuQ55DntOQAylQTlOCIMD3fXzfJwgC+vr6mDNnDmEYUqvVyLKMJEmI45hSqYTneZi3nuu6eJ5HGIbEcUySJNRqNZIkoauri7qenh4KhQLFYhHf94miiIj/EYbgebyK64Lr8ippCuUyBAEUClAoQJ5DmkKaYo4ODsYYc6TIcwgC8H0oFKBQgDxnpBzIgTIQAD7guy6B69LnusyZM4cwDMmyjCzLiOOYUqmE53mYI4/rupRKJcIwJEkSarUaSZIQhiF1aZpSKBQoFov4vk8URaRpysuyDLIMkgS6u6FUAs/jkHp6wPfB9yHPeVmaQppCnmOaj4MxxhxJymVIUxryPCdNU6Iowvd9ioDvuvSVSsyJY8IkIcsysiwjjmNKpRKe52Gal+u6eJ5HGIYkSUKtViNJErq6uqiLoohCoUCxWCSKIqK+PvKuLohjiGPIMsgyiGMolaBU4pB8H3wfikUoFiGKIE0xzcHBGGPeTlEExSIUixAEHCwHykAA+IAfBERRRJ7ndHV1UavVyLKMOI4plUp4noc5+rmuS6lUIgxDkiShVquRJAl1aZpSLBYpFosEUUTU00Oa51AqQRxDHENXF8QxxDG4Lq+S59DdDb4PxSL4PkQR5DnmyORgjDFvlTyHNIUgAN+HIIByGfIc8py6PM8pl8sEQYAfBPiuS4/n4XZ3EyYJWZaRJAlxHFMqlTCmwXVdwjAkSRJqtRpJkuC6LnW+71MsFgmCgCiKyPkfpRKUSvyv7m4olXiVPIc0he5u8H0oFqFYhDTFHDkcjDHmrZKm4PtQLkOaQpqSAykQAX6a4vs+PT09uK5LGIZkWUaSJIRhiOd5GPNGua5LGIaEYUitViNJElzXpa5YLFIsFomiiCiKeFkYQhxDrQZJAt3dUCqB6/K/8hzyHPIc8hyiCHwffB/zp+VgjDFvsRwoA36eU8xzAtclL5UI45gsy0iShDAM8TwPY94srusShiFhGFKr1UiShLo0TSkUChSLRaIoIk1T8DwIQ4hjSBLIMsgycF1eIc8hTSFNIc+hWIRiEXwfymXIc8zbw+EY8Ytf/IK1a9eydu1a1q5dy9q1a1m7di1r165lYGAAY8ybJ89z0jQl6OnBB3zXpa9UoiuOqdVqZFlGHMd4nocxbxfXdQnDkCRJqNVqJElCXRAEFItFfN8niiJwXXBdcF3IMqjVoFaDUglcF1wXXJeX5TnkOaQpBAEUi5i3h8Mx4uabb2bp0qUsXbqUpUuXsnTpUpYuXcrSpUvJ8xxjzGHkOZTLUC5DnnOwPM8pl8sEQUCxWCQIAlzPI0wSsiwjjmNKpRLGHClc1yUMQ7IsI0kSPM8jz3MKhQLFYpEoikjTlFcIQ8gyyDJwXXBdXlOeQxRBFEEUQZpi3jwOx4jNmzcze/Zsent76e3tpbe3l97eXnp7e5k6dSrGmMPIcwgCCAJIU+ryPCeKInzfx/d9+vr6mDNnDrVajSzLCMMQz/Mw5kjnui5hGBLHMbVajSRJqAuCgGKxSBRFpGnKq2QZZBl0d0N3N3R38wrd3dDdDd3d4PtQLEIQQJ5j/jgOx4CdO3dSqVT4yEc+wvTp05k+fTrTp09n+vTpTJ8+nXHjxmGM+f+lKaQp5DmHkgNRTw++7+P7PnmeE4YhWZYRxzGlUgljmp3ruoRhSJZlJElCXRRFFItFgiAgiiL+l+tCGEIYQhjyuvIcymUIAiiXIYqgXMb84RyOAVu3bqXOdV2MMa+hXIYgAN8H34cgoC7Pc9I0Jerrowj4rgueRxiGZFlGHMd4nocxRyvXdQnDkCRJSJIE13VJ05RCoYDv+0RRxCG5LmQZdHdDqcQrpCkEAXR3QxRBnkOeQ55j3hiHY8C2bduoe/LJJzn77LOZOnUqs2bN4oYbbmDv3r0YY/5HXx+Uy9TlQJrnBEFAsVgkCALq4iQhyzLCMMTzPIw51riuSxiGJElClmV4nkeaphQKBYrFIlEU8QquC2EIcQy1GsQxxDF4Hq+Q51AsQrEIxSL4PkQR5Dnm0ByOAc888wx1a9asYe7cuSxbtgzXdbn99tu56KKLqFarGHPMSFOIIogiyHNGyoEI8IEAcF2XJEnIsowwDPE8D2PM/8d1XcIwJEkSsiyjVCqR5zmFQgHf94miiFcplaBUgjiGOIY4hjDkFfIc0hS6u6FYBN/HvJrDMeC9730vn/rUp/jhD3/IkiVL6OrqYvXq1Zx//vk89thjrF69msMREUQEEWHlypUY07T6+qC7G7q7qcvznCiKKKYpvutCdzdxkpBlGWEY4nkexpjX57ouYRgSxzFZluF5HmmaUigU8H2fcrnMK7gulEpQKkGpBK4LpRJ4Hq+SplAoQKEAQQDlMpTLkOccysqVKxERRAQR4WjlcAy45ppr+PrXv86ECRMY6fOf/zx1P//5zzkcVUVVUVUWL16MMc0sByLADwJ836cujmOyLCMMQzzPwxjzf+O6LmEYkiQJWZbheR49PT0Ui0WiKCJNU17FdSGOIUkgyyDLwPPAdXmFchmCAIIAfB+CgIMtXrwYVUVVUVWOVg7HsHe+8520tLQwNDSEMUe7PM8pl8v45TK+65KXSoRhSJZlhGGI53kYY95crusShiFJkpAkCXVBEFAsFomiiDzPeRXXBdeFJIEsgySBUglKJV4hzyFNIc+hXIZymWOJw1HuueeeY9myZXznO9/hYHv37qVSqTBu3DiMORrleU65XCYIAnzfp6+vj64wJMsy4jjG8zyMMW8P13UJw5Asy0iShLpisUixWCSKIl6T50EcQxxDdzd4Hq+QphAEEARQKIDvcyxwOMq1t7fzwAMPcMcddzA0NMRIvb291J111lkcUp5DnvO+AwcwppnkeU4URfi+TxRFuK5LlmXEcUypVMIY86flui5hGFKr1UiShLpCoYDv+5TLZV5TGEKSQJZBlkGW8SppCsUiFIsQBHzyd7+DcpmjjcNRznEclixZws6dO7n00kvZvHkz27dv55ZbbuHGG2/kjDPOYN68eRxSnkOxyE+yDIpF8H0olzHmSJTnOeVyGd/38X2fujiOybKMMAwxxhyZXNclDEOyLMPzPKIoolgsEkUReZ5zSK4LrsvLPA+SBLq7oVQC14U8hzyHcpnrd++GIIA852jicAwIgoDly5fzxBNPsHDhQj72sY+xcuVK5s+fz6233sobkueQphAEUCxCEGDM2yrPwffB96FcpiHPc4IgwPd9+vr66OrqIssywjDE8zyMMc3BdV3CMCTLMpIkoa5YLFIsFomiiNfkuuB5EIYQx1AqgedxtHM4RnR1dbF582bWrVvHqlWr+NX/Yw9uQofb7oNQP/9/OZKmpQhBU6iBtaBwQFDRYh0Y6V53og5E40zh+q4tEVRuEcSKgrLWkgo67h0ICmsfrx+gUCHFgSB3r7QgGslApZUrwv6VVNuBFYlpHMT6v7715tycnOTk63y+736ef/Nv/PiP/7gPf/jDvq6U6N1/eOUVbxDBcfDwQClEuN3eFWuxlvj0p40xlFKUUqSUnOdpzqnW6na7fbCllLTWPD09Oc9TRMg5G2OICG+pNc6T86R3P/GRjzAnKXmRPHqJPD4+evXVV/3wD/+w7/qu7/INpURr/sJHP0rvpORN1iKCtViLtdxu37Hj4DhYy+tSsrCjrCUitNZc16W1JqXkdru9eFJK5pzO8/RcKUXO2RjDW9o2WvN/fuQj1OpF8+j2DX3mwx+mNa6LOendG4xBKZRCKew7x+F2+5aNQSnsO/vOGCLCGEPO2Z6S1Lvrusw5bdvmdru9HFJKWmuu63Kep4jw8PBgjCEivGwe3b41tdIa18V18fRESt7gONh3joPj4DiIcLt9QxGs5bnAvpZSiogw53Rdl9aa2+32ckspmXO6rstzpRQ5Z2MML4tHt29PSqTk1zx7xpzU6g0+/Wn2nX1nDCKIcLt9PYEDBSUlqXfXdZlz2rbN7Xa7faWUktaa67qc5yki5JyNMUSEF9mj23du26iV1uidWqnVGxwHOZMzDw+MQYTb7bmIMMZQ1vLpWrXzdF2X1prb7Xb7ZqSUzDmd5+m5nLOcs89//vNeRI9ubykiXNdljOEbSonWmJM5efaM3tk2b9I7r73GGES4vXwiwnEcSilKKZ47z9Oc07Ztbrfb7duRUtJa8/T0pNbqi1/8ohfRo9tbSin5Tb/pN3nu4eHBGENE+KZsG63RGrV6k97pnVI4DreXQ0QYYyilGGN49uyZ67q01qSU3G6329ulteb7v//7vYge3b6hV155RWvNdV2eyznLORtj+KZsG3MyJ72zbd4ggn3n4YHjcHsxRYQxhlKKiDDndF2XWqvb7Xa7fWse3b5pKSWtNU9PT1prjuOQczbG8E2pldaYk95JyZvsOw8PrOX2wRcRjuNQSlFK8dx5nuactm1zu91ut2/Po9u3pdbqui7neXru4eHBGENE+IZSojWui23zNZXCvrt9MEWEMYZSijGGZ8+eua5La01Kye12u92+M49u35GUktaa67o8l3OWc3Ych2/KnPTuazoOjsPtfeo4GIPj8GURYYyhlCIizDld16XW6na73W5vn0e3t0VKSWvN09OTWqsxhpyzMYa3lBKtMScpeZN9Z9+JcHufGYPeee01EWHfd6UUz53nac5p2za32+12e/s9ur3tWmuu63Kep4iQczbG8JZq5bro3ZscB6UQ4fYeWYtSKIUxfNmBspZSipSS67q01qSU3G632+2d8+j2jkkpmXM6z9NzDw8PxhgiwtfVGrV6kwjWcnuPvPYaa7GWOA7HccgYKXk2p+u6tNbcbrfb7d3x6PaWQvj8Jz4vy7KsKJbluaIoiqLIsizLsizLsqLIspKKaMFF1+Wc5ZKVKHa73W4YsizL8ly+pn2XZVk2DFmWZVmWZVmWZUWRZVm22w3DbrfbFUWWZVlR7Ha73eGwLLtdURRFlmVZlhVFlmVZlmVZlmVZURwOw7DbZVmWZVmWFcVuNwzDsNvtdsOw2xVFURRFlmVZlmVZlmVZUWRZlmVZURRFURRFURRFUex2u12WZVmWZVmWZVmWZVmWZVmWFUVRZFmWHQ7DMAzDsCyBgRxh//QuZnAx6rDb7XZZlmVZVhRZlmVFURRZlmW7XZZlWVFkWZZlWVEURVEMwzAMwzAcDsNQFEVRFEVRFEWx2xVFlmVZUex2RVEUWZZlWZZlWVYUWZZlWZZlWVYURVEURVEUu91ul2VZlmVZVhRFURRFURRZlmVFkWVZVhTDcDgURVFkWZZlWVEURVEURVEURZZlWZbtdrtdlmVZUWRZlg3Dsjx3OBRFURRFUWRZlh0ORVEURVEURVEURVEURVEURVEUWZZlu91ut9vtdkWRZVmWZVlWFFmWZVmWZVmWZUWRZVmWZVmWZVk2DLvdbrfb7XZZlmW73W632xVFlmVZlmVZlmVZlmVZlmVZlmXZbjcMw7AsRZFlWZZlh8Mw7Ha73TDsdlmWZVmWZUWx2+12u91ut9sNw+GQZVmWZVmWZUVRFEVRFIfDbpdlWZZlw7DbFUVRHA4hHA6Hw7LsdlmWZVmWZVmWZUVRFEVRFFmWZVlWFFmWZVlWFFmWZbtdlmVZlhVFURTFblcURZFlWZZlWZZlWZZlu93hMAzDcDgURZZl2W5XFEWx22VZlu12WZZlWZZlWZZlWZZlWVYURVEURVEUu91uVxRFURRFsdvtdrvdMCzLL/8fv2wYQniRPLq9pWH4pb/2S0IIYVmK4sGDZVmWZQkhhBBCCGFZQgjhcJDQcBFbWGU58uE4Dl0XQgghlNPXFEIIXRdCCCGEEEIIyxJCCIdD1x0Oh8OyhBDCshwOh8NuVxSHw7IsSwghhLAsIYQQQgghhLAsu13XHQ4hhBBCCMtyOHRd1x0Oh0PXHQ7LsizLEkIIIYQQQgjLEkIIISzLsizLsizLsizL4XA4hBBCCCGEEEIIIYQQQgjLsiwhhLDbdV3X9eh2ISd6xYmJjRBCOBwOhxBCCGFZQghhWZYlhBAOhxBCWJYQQghhWZZlWbqu67qu63a7rluWZVmWZVmWZTkcliWEEJblcFiWZQkhhBBCCGFZQgghhBBCWJZlWZZlWZbD4XAIIYQQQliWZVmWZVmWEEJYlhBCWJau2+2WZVlCCCGEZVmWZVmWZVmWEEII4XA4HEIIYVlCCKHrdrvnft7PW5ZlWZZlCSGE3W5ZlmVZlmVZlmVZlmVZlmVZliWEEA6Hw+FwOByWJYQQQghhWUIIIYQQQghhWUIIIYQQQgih6w6Hw+FwOBxCCOFwOBwOh2UJIYQQQgghhBBCCCGEEEI4HLqu64piWUIIIYTdrusOh8Oh6w6HEEIIIYRlORwOh8PhcDgcum63CyGEEEIIYVmWZVmWZbc7HEIIIYSuOxyWZVmGIYTdbrcrisMhhBBCCCGEEJZlWZZlWUIIIYRlCSGEEJYlhBAOhxBCCGFZlmVZDodlWZYQQgghhBBCCOFw2O26rut2u2UJIYTDYVmW5XAIIYTDIYQQQgghhBBCCCGEZVmWZVmWZTkcDodlWZZlWZbD4XA4HLquKH75R39Z14XwInl0e/clNFyoGMgYXrc2X1MKt+9Qkny1etAH9fD/C+woRMKJic3tXZAkSXK73W5fy6PbW3rmme//C99vmrqu66qqqrpumrquqqqq67qu66qqqqqq606naZqm06nraqvqVdWz2tZGxqDrpOSrVVVVdd00TVPXVVVVVVVVVVXXdV3XVVVVTVPXdV1VVVVVVVVVVVVVdd3pNE3T1HVd13Vd13XT1HVdV1VddzpVVVVVVVVVVVVVVVVVVVVVVVVVVVVdLtPUdV3XdV3XdV03TZdL13VdVVVVVVVVVXXdNHVdVXVd11VVVVVV03RdVVVV182RtE57Ldlio5BKUlPVr663rqaqqqqqqk6nruu6ruu6qqqqrpumruu6aTqdpmmapmmapqnruq7rum6auq7rum6auq6qqqrruq6qqqrrqqqqqqrruq6qqqqqqqqqqqqqqqqqqqqqum6auq6qqqqqqqqquq6qqqqqqqrrpqnruq7ruq6qqqqquq7ruq6qqqqquq7rqqqqqqrruq7rpulyuVyePDmdqqqqqqqqqqqqqqqquu50mqbnnnlmmqap67qu66qqqqqq66qqqqqqqk6nrquqqqqqqjqdpqmqqqqqqqqquq7ruq7rum6auq6qqqqqqqqqqqqqqmqapmmauq6qqqqqqqrruq7ruq6qqmqaLpeuq6qu67qu67ppmqbLpeuqqqqqqqq6ruuqqqq6bpqmqaqqquu6rqqqquu6bpq6ruuqqqqqquum6XTquq6bptPpcqmqqqqqqqqqquq6ruu6rquqzWazOZ2qqqqqqqqqapq6ruuqqqq6ruu6rqqqquu6rqqqappOp66rqqqapmmapmmapsvldDqdpqmqqqqqum6aLpeqqqqqqqqqqqqu67rTaZq6brPZbDabruu6ruu6qqqqquq6aZqmaZqmaeq6qqqqqqqqqqqqqqqqy+V06rquq6rv+0ffp6qS5EXy6PaWNpvv+0ffp6qapmmmaZqapqqaZpqmqWmapmmmaZqmqWk2m6qqqs2maaZpmmaazvN0nZca1ZEPI8IbpKRppqlpqqqqmmaapmmapmmamqZpmmaapqmqmqZppmmapmmapmmapqlpNpuqqqqmaZqmaZqmqaqmaZppaprNZpqmaZqmaZqmaZqmaZqmaZqmaZqmKUmqqmmapmmapmmapqqSpGmaZpqmaZqmaZqapqqaZpqapmmmaZqmqaqaZpqmqWkCB/YVooS+ddd1mW1qmqaZpmmapmnabJqmaZqmaaZpmpqmqpqmaapqs6mqqqqqqqqqpmmapmmaqmqapmmaqmqaaZqmpmmaaZqmppmmaZqmpmmaaZqmaZqmaZqmaZqmaZqmaWqaqmqaaZqmaZqmaWqaaZqmaZqmpqmqpmmapmmaaZqmaWqapmmaaZqmaWqappmmaZqmpmmapqmqr7TZTNM0TdM0TdM0TdM0Nc1ms9k8lyRVVVVN0zRNM03TNE1NM03TNE3TtNk0zTRN0zRN02ZTVdM0TdM0TdPUNE3TNE3TNFXVNNM0TdM0TdM0TdM0TVVVVVXVNNM0TdM0TU3TNE3TNNM0TVWVJE0zTU3TNE3TNFVVVUnSNNM0TdM0TU3TNNM0TU1TVVU1TdPUNE0zTdPUNE1TVU3TNNM0TdPUNFW12TRN01TVZpMk0zRN0zRN0zRNTdM0TdM00zRNz2020zRN0zRN01RVTdM00zRNTdM0TTNN09Q0TTNN01RVm03TTNM0VVVVVVVVVVWSbDabTVVN0zRNU9NUVZJM0zRN0zRN0zQ1TdNsNlXVNKfT6XQ6NU3TNE3TTNM0TVPTVFVVVVVVVVXTTNM0TdM0TdM0TdM0Jclm0zRNM03f/xe+3zQlyYvk0e19JaVkzuncNs89YCD8T+dJSm7fpgjGYAzW8lxEOI5DwUjJszld16W15na73W7vX49u70tpLQ2X/yVjvPaaiHD7Nuw7+07v9C5ee80YQynFa6+9Zs7pui61Vrfb7XZ7/3t0e/85Dl+W0HClRIScs1KKiHD7BtZiLSKIYC2BgbKWiDDndJ6nbdvcbrfb7YPj0e39JYLXXiPCV0pzanN6enqybZucs5yztZbb11EKpTCGwEBJSdTqPE9zTtu2ud1ut9sHz6Pb+8da5MxaXpcS28a2+bLWmqenJ7VW+77LOTuOw+3NAmMtJYLenedpziml5Ha73W4fXI9u7w8RjOFNzpPz9LW01lzXZc5pjCHnbIzhRkQYKSkpUavzPLXWpJTcbrfb7YPv0e29txalsJY3SMk3Y9s213WZczqOQ87ZGMPLKCLs+66UQq2u69Jak1Jyu91utxfHo9t7K4IxiPAGvXNdpOSbtW2b67qc52mtJedsjOFlEBH2fVdKkVJyXZfWmtvtdru9mB7d3jtrkTNreYNt40d+xLcrpeQ8T+d5igg5Z2MML6KIUEpRSpFScl2X1prb7Xa7vdge3d4bY1CKN9k2zpNt851KKZlzOs9TRMg5G2N4ERzHoZSilGLbNtd1aa253W6328vh0e3dE0EEY9C716VESszJeXq7pZTMOZ3n6bmcszGGD6LjOJRSjDE8e/bMdV1aa2632+32cnl0e3dEsBY507s3uS5q9U5KKWmtOc/TczlnYwwfBMdxKKUYY3j27JnrutRa3W632+3l9Oj2zotgDPbdG6RE71yXd1NKSWvNeZ6eyzkbY3i/iQjHcSilGGN49uyZ67rUWt1ut9vt5fbo9s6JYAxy5ji8QUrUSmveKyklrTXneXru4eHBGMN7LSIcx6GUYoyhtea6LrVWt9vtdrs99+j2zohg3+ndm9TKasW8jgAAIABJREFUddGa94OUktaa67o89/DwYIzh3RYRjuNQSjHGMOd0XZdt29xut9vt9pUevUT+xb/4F/7SX/pLfuzHfsxrr73m85//vLfdWqzFvrOWN5mTOb0fpZS01lzX5bmHhwdjDO+0iHAch1KKMYY5p+u6bNvmdrvdbrev5dFL4q/8lb/ij/2xP+Zf/at/5b/8l//ir//1v+4P/IE/4Bd/8Re9bY6DfacU1vK6WjlPnp6o1ftdSklrzXVdnnt4eDDGEBHeThFhjKGUYoxhzum6Ltu2ud1ut9vtrTx6B3zuc5/z6quv+oN/8A/6j//xP3qvffrTn/Z3/+7f9cf/+B/3Uz/1U/7m3/ybPvWpT/niF7/oz//5P+87EkEEObPvRHhdrfROa2ybD5qUktaa67o8l3M2xhARvhMRYYyhlCIizDld12XbNrfb7Xa7fTMevQM+9rGP+XN/7s/5z//5Pyul+KN/9I96L/2dv/N3fOhDH/Jn/+yf9WU/+IM/6NmzZz7zmc/49//+3/u2rEUp5EyE16XEttEarZGSD7KUktaa67o8l3M2xhARvhURYYyhlCIizDnNOW3b5na73W63b8Wjd8if+BN/ws/8zM/46Z/+af/1v/5Xv/k3/2b/6T/9J++Ff/bP/pnf83t+j1deecVX+i2/5bd47jOf+YxvyVqUQilEeIOUqJXzJCUvkpSS1prrujyXczbGEBHeSkQYYyiliAhzTnNO27a53W632+3b8egd9tGPftRP/dRP+ct/+S/73b/7d/viF7/o3fSFL3zBf//v/92v//W/3lf77b/9t3vu537u53zT9p1SWMub9M6ctOZFllLSWnNdl+dyzsYYIsJXighjDKUUEWHOac5p2za32+12u30nHr1L/sgf+SP+wT/4Bz7+8Y97N/3sz/6s537dr/t1vtp3f/d3e+5LX/qSb+g4yJnj8CYpMSetsW1eFikl7Ud+xNU7xyHnbIxhrWWMoZQiIsw5zTlt2+Z2u91ut7fDo3fRb/ttv83f+Bt/w1/9q3/Vu+VXf/VXfSO/+qu/6utay/99Xew7Ed5g2zhProtavXT2nVKk3rUI53k6jkMpRe9da82c07Ztbrfb7fbu+Imf+AmvvvqqV1991f/+sY/5xOc/z3F40Tx6B3zuc5/ziU98ws/+7M/6whe+4Cv98A//sF/5lV/x3/7bf/Nu+A2/4Tf4ev7H//gfnnvllVe8lR/40pe8wbZxnpwn2+alFeG5wMC+77Ztc12X3rt935VSRITb7Xa7vTt+9Ed/1P/zT/6J/+cv/kX/1y/8gr/2S7/EvrOWF8mjd8CHPvQhP/dzP+cP/+E/7Id+6If8zt/5O33iE5/wb//tv/WFL3xBa81xHN4NKSXP/cqv/Iqv9ou/+Iue+8hHPuLrSsnrUqJ3zpNt89KIIIIIXylSMlBSErU6z9OcU0pJa83T05Nt2+SclVJEhNvtdru9gyIohX1n373IHr0Dvud7vscP/MAP+OxnP+tTn/qUj33sY37hF37BH/pDf8gP/dAP+fjHP+7v/b2/593wyiuv+I2/8Tf63Oc+56v9u3/37zz3W3/rb/V1peR/y5nr4rpozUtnDHImZ45DRBhjKGuJWp3nac4ppeSrtdY8PT3Ztk3OWSlFRLjdbrfb2yiCMSiFtVjLl33mu7+bWr1oHr0DPvzhD/v9v//3+97v/V6vvvqqn/zJn/Qv/+W/9NnPftanPvUpH/vYx3zpS1/ybvl9v+/3+exnPysifKV/+A//oQ996EM+/vGPeyv/4ZVXSMlLI4IIIvya4/BcYLz2mlKKiHCepzmnlJJvpLXm6enJtm1yzkopIsLtdrvdvgPHQSnkTO9EeIOU/MRHPsKcbJsXyaN3yI/92I/5at/7vd/r1Vdf9ZM/+ZP++T//594tn/zkJ33P93yPT37yk37mZ35GRPjxH/9xP/3TP+1P/sk/6cMf/rDbV4ggZ3LmOAQGSkoiJed5mnNKKflWtdY8PT3Ztk3OWSlFRLjdbrfbt+A4eHhg31nLm6TEeXJdPvPhD3sRPXoJfPSjH/W3/tbf8twnP/lJv/f3/l5//+//fX/6T/9pf+pP/Sm3/+k42HdyZt89FxivvaakJGp1nqc5p5SS71RrzdPTk23blFLknK213G632+3riGAtHh7Yd2+SErVyXVwX2+ZF9ugl8Tt+x+/wT//pP/WP//E/9rf/9t/2r//1v/Zn/syf8dI7DsZg3zkOIkSEkZKSEtvmPE9zTiklb7fWmuu61Frt+y7nbK3ldrvdbv+f42AM9p1SvElK1MqczElKXgaPXjI/+IM/6Hf9rt/lu77ru9z+p9deo3fPBQZKStTqPE+tNSkl77TWmuu61Frt+y7nbK3ldrvdXkoR7Ds5s+/0zlreICXm5DyZk23zMnl0e+kFBkpK9O48T601KSXvttaa67rUWu37LufsOA632+32wotgLdYiZ46DCG+QEr0zJ+dJraTkZfTo9tKKCCMlJSV6d56n1pqUkvdaa811XWqtxhhyzo7jcLvdbi+cCCIYg1IoxZtsG9vGnLRGraTkZfbo9uKK4Dg4DiJ8WUQYYyilkJLrurTWpJS837TWXNdlzmmMIefsOA632+32gRbBGOw7Y5Azx+F1KbFtbBtzMifnyba5/S+Pbi+2fWffee01EWGMoZTiueu6tNZ8EGzb5rouc05jDDlnYwy32+32gbIW+07O9M5xcBzepDXOk/OkVlJye6NHtxdeYD8OpRTPXdelteaDaNs213U5z9NaS87ZGMPtdru9b0VwHOw7Y3Ac3iQlemdOrota3d7ao9sLK7CnpKQk1eq6Lq01L4KUkvM8nedprSXnbIzhdrvd3nMRRDAGOZMz+85xsJbXbRu10jvXRWvUSkpu39ij2wfbcZAzORPhuYhQSlFKkWp1XZfWmhdRSsl5ns7zFBFyzsYYbrfb7V0VQQTHwRjkTO9EeJNto1ZaY05ac/vWPbp9sP38zxNBhOO115RSlFJs2+a6Lq01L4OUkjmn8zxFhJyzMYbb7XZ7x0QQQSmUQs7sO8fhTWqld+ZkTuZk29y+fY9uH2iBAwXjODx79sx1XVprXkYpJXNO53l6LudsjOF2u92+YxFEEMG+Uwo5sxYR3iQl5mRO5qQ1aiUlt+/co9sHUkQ4jkM5DiMlz+Z0XZdaqxspJa0153l67uHhwRjD7Xa7fcuOg1LYd3ImZ46DCF9TrVwX10Wt1Or29nt0+0CJCGMMpRRjDHNO13Wptbq9WUpJa811XZ57eHgwxhARbrfb7U0iiCCCtXh4YN9Zi7W8QUqkREpsG09PPD0xJym5vbMe3T4QIsIYQylFRJhzuq7Ltm1u31hKSWvNdV2eyznb911EuN1uL7EIjoN9pxRKIWdyZgxfV0pcF9fFdXGebu+uR7f3jzHYd8bwZRFhjKGUIiLMOc05bdvm9q1LKWmtua5LSknOWc7ZWsvtdnsJRLAW+86+s+/sO8fBWkR4XUrUSq30zpycJ09PXJfbe+vR7f1jLY6D4xARxhhKKZ47z9Oc07Ztbt+5lJLWmqenJ7VW+77LOTuOw+0lFUEEEazFWt4ggggi3D6gIiiFUjgOjoO1vEFKpERKpMSczElr1Mq2ub0/PLq9rwT2CKUUz53nqbUmpeT2zmitua5La80YQ87ZGMPtBRBBBMfBvrPvlEIp7DulkDM5kzM5kzOlUAoPDzw88PBAzuRMzuTMwwMPD5TCvlMKpVAK+84YHAfHwXGwlts7KILjYN/Zd8Zg3ymFnMnZr4nwNW0b20ZrXBfXRWtu71+Pbu8Lay0FJSWpd9d1aa1JKbm9O2qtrutynqe1lpyzMYbbB0AEEUQQQc7kTM7kzL5zHBwHa7EWx8FaRBDhWxLhdWtxHKzFWqzFcdA7+86+s++UQimUQimUwr4zBmMwBsfh10QQQYTbV4ngOBiDUsiZhwdyZt85Do6D3jkO1iKCCG+QErUyJ9fFeXKe1Or2wfDo9p6JCMdxKKXY9922ba7r0lpze++klJzn6TxPESHnbIzh9j4UwRjkTM7kTClEEOF9Zy3WYi3W4jjond7pnTEohZzJmZwphVLYd8ZgDMZgDI7DC28M9p2HBx4eyJl9p3fWIsLXlRIpkRLbRko8PfH0xHUxJ7WSktsHz6Pbuy4ijDGUUowxPHv2zHVdWmtu7x8pJXNO53l67uHhwRhDRLi9hyIohVLImd69QYS3lBIpkRLbxraxbdRKrVwX58l5cp6cJ+dJ7/ROrdRK7/RO78zJeZKS120btfqWRLCWN1iLtTgOeqd3eqd39p2cyZlS2HdyJmdKYd/Zd8ZgDI6D4/BrIogggghvmwjWYi3WYi3W4jg4DsZgDPadUiiFUsiZhwceHljL69biOHxTUqJWemdOWuO6uC7O0+3F8uj29luLfefhgYcHjsNzEWGMoZQiIsw5Xdel1ur2/pVS0lpzXZfncs5KKdZabu+i46AUSmEt1vImKZEStbJtbBu9Mydzcp5cF9fFdXGenCfnyZzMSUpsG9vGtrFtbBut0RpzMiet0RqtUSvbxnXx9MTTE+fJnDw98fTEnPROrdTKtrFtpOQ7EkEEa3EcRBDBWhwHx0Hv9M6+s+88PJAzOZMzOfPwwMMDOfPwwMMDDw/kzMMDDw+MQSk8PPDwwMMDDw/kTM7sO6VQCqVQCqVQCvvOvtM7vXMcrMVarEWE10V4S7UyJ73TO+fJ0xPXxZy0Rq3U6vbienR7+6xFzpTCcfiy+PmfN8ZQShERzvM057Rtm9sHR0pJa83T05Nt2+z7LudsjOH2DlqLMdh31iLC19Ua18WcnCfnSWvUSq1sm/dMrbTGnMzJeXKeXBdPT1wX18V1cV1cF9fFnPTOtrFt1Mq2kRIpkZK3VYQ3iPC63lnLm0QQwXEQ4W11njw98fTEdXFdzEmttEZrbJvby+fR7e3x8EApRPiyhYJyHJ67rsucU0rJ7YOttea6LnNOx3HIORtjuL0DXnuN3n1dKbFtnCe1+sBKiZRIiZRIiZSoldY4T86TOTlProvr4rqYkznpnd6plVqplW3znkuJlEiJ8+Q8qZVamZPz5Dx5euLpiVp9TSmRktvtuUe3b10EEUT4aoHj/2UPfoC1quvEj7+fExiBk2vEOrU7/b6ndfyoM1YWoan4nOOwUIkaZu4yjt5zTLouG5k0XjWdPfckbjWxWWIx5nXPc5GL079rF8X8Q3vOTXP4Ixdbk/iIeo5jWayYLSUF4X1+v6f5aYCAWqk8935eLyAEYucIurspy5IkSTAjTxAElGVJnudUVYXv+6RpSlVVmL9QGEKtBo0GL+IcdHdDWUJZQp5DEDBqRRFEESQJJAlkGWQZZBnkOTSb0GxCswllCWUJZQnNJuQ55DnkOWQZZBnkOZQllCWUJZQllCVkGWQZZBnkOeQ55DnkOeQ55DmUJZQllCU0m9BsQllCWUJZQhBAEECWQZZBFEEQQBBgzCvhYV65qgLfB9+HRoOWKghIgRDoDQKSPKcsS5IkwYx8zjmyLCPPc1p83yeOY6qqwvwZigKKghdxDoIAkgSSBJzDvELOgXPgHH8UBBAEEAQQRRBFEATgHDgHzoFz4BxEEUQRRBEEAQQBBAEEAQQBBAE4B86BcxjzavIwf5Hq8ceJ45iwqqiiiCzPyfOcIAgwo49zjiRJKMsS5xxhGOL7PmmaYl6BNOVFggCiCPIcoghjzOjmYV6xCmg4R+wcYaOBc46yLMmyjCAIMMY5R5IklGVJlmUURYHv+6RpinkJVQVVxW6cg44OSBKMMabFw7xsVVWRpilhHJMC9SShLEuSJMGYfQmCgDzPyfOcllqtRpqmVFWF2UNRQBxDVfEC5yBJIIowxpjneZiX9Ic//IE0TQnDkKqqyLKMsiyJoghjXi7nHEmSUJYlLb7v4/s+aZpi/r/eXigKdhMEEEUYY/ajqqAooCigqhgNPMxL+tnPfkZLnudkWUYQBBjz53LOkSQJzWaTJEkoigLf90nTFLMXWYYx5mUIQwhD6O2lpaoqGo0GTz/9NCORh3lJvu+TJAnOOYz5a4qiiDzPyfOcllqtRhzHNBoNjDHmz1FVFWmaEoYhaZoyduxYRiIPY8zrzjlHkiSUZYlzjjRN8X2fNE0Z9YoCY8xLcI5GEBADYVFQVRVZllGWJW9+85sZiTyMMQcM5xxJklCWJXme01Kr1UjTlKqqGPGcwxjz8lVVRZqm+L5PWlW47m7KsiTLMoIgYCTzMMYckJxzJElCWZa0hGGI7/ukacqI1dEBzrGbqsIYs7uiKIjjmDAMqaqKLMsoy5IkSRgtPIwxBzTnHEmSUJYleZ5TVRW1Wo00TSmKghHFOYgidtPbC1WFMSNaVUFVQVWxL1VVkaYpvu8TxzHOOcqyJMsygiBgtPEwxrQN5xxZllGWJS1xHOP7PmmaMmIkCTjHC4oCfB+KAmNGNN8H34c05XlVVdFoNIjjmDAMqaqKLMsoy5IkSRjNPEaJoaEhBgYGGBgYYGBggIGBAQYGBhgYGGDLli0Y006ccyRJQlmW5HlOS61WI45jGo0GbS/PIQjYTZpCo4ExI0JVQZpCmkJVsaeqqkjTlDAMSdMU5xxlWZJlGUEQYMBjlPja175GV1cXXV1ddHV10dXVRVdXF11dXVRVhTHtyjlHkiSUZYlzjjRN8X2fNE2pqoq25Bx0dLCbooA0haLAmLYVxxCGEIbQ3Q3d3VBV4BxVFNFwjrDRIAxDqqoiyzLKsiRJEszuPEaJNWvWcNJJJ9HX10dfXx99fX309fXR19fH0UcfjTHtzjlHkiSUZUme57T4vo/v+6RpStsJAogidlNVEMfQaGBM2ygKCEMIQygKKAqoKloqoBgcJI5jwqJgMAjoSBLKsiTLMoIgwOydxyjw5JNPsmPHDk4++WQmT57M5MmTmTx5MpMnT2by5MmMHz8eY0YS5xxJktBsNsnznKqqqNVqhGFIo9GgLTgHWQZlyW6qCuIYigJjDkhVBWkKaQpFwR8VBRQFf+QcFZBGEaFzxI0GzjnKsiTLMqIowrw0j1HgJz/5CS3OOYwZbZxzZFlGWZYEQUBvby++75OmKUVRcMBzDsoSnGM3YQi+D40GxryuqgqKAooCqgqqCrq7obsbqgqcA+eogNQ5QucInQPnyLKMsixJkgTzyniMAj/96U9p2bBhA9OnT+foo4/mhBNO4Etf+hLbtm3DmNHAOUeSJOR5Tp7ntMRxjO/7pGlKVVUcsJyDPIcoYjdVBXEMYQhFgTGvmzCEMITeXnZVPf44jaIgdI7QOSrnSJKEsixJkoQgCDB/Ho9RYNOmTbR861vf4tRTT+XSSy/FOUdPTw/nn38+w8PDvBQRQUQQERYtWoQx7cw5R5IklGVJnue0+L6P7/ukaUpVVRxwnIMsg+5uCAJwjhcUBYQh+D4UBca8nirnaHR3EzpH2GgwODhIR0cHZVmSZRlBEPBqWrRoESKCiCAijFQeo8Db3vY2zjzzTG699VYuuugiOjo6WLZsGbNnz2b9+vUsW7aMl6KqqCqqyrx58zBmpHDOkSQJzWaTPM9p8X0f3/dJ05SqqjigJAnkOWQZL1JVEIaQphjzV1EUUBRQVeyTc1Td3TSCgLjRIAxDBquKjiShLEuyLCOKIl4r8+bNQ1VRVVSVkcpjhLj//vvp7Oyks7OTzs5OOjs7Wbx4MS1XXHEFn//85zn44IPZ1ac+9SlaVq1ahTEGnHMkSUKz2STPc1p838f3fdI0paoqDhhBAGUJWQZRBM7xgu5uqNXA9yFNMeZlqyqoKkhTSFOIYwhDCEP2VFUVjUaDOI4JGw16gXqSUJYlWZYRRRHm1eMxQvzqV79i7dq1rF27lrVr17J27VoeffRR9uctb3kLBx10ENu3b8cYszvnHEmS0Gw2yfOcFt/38X2fNE0pioLXnXMQRZBlkGW8SFVBdzeEIaQpVBXGvEhRQKMBjQbEMfg+dHdDdzdUFbuqqopGo0EYhoRhyODgIPV6nbIsyfOcKIowrw2PEWL69OkMDQ0xNDTE0NAQQ0NDLFy4kM2bN3PppZeydOlS9rRt2zZ27NjB+PHjMcbsm3OOJEloNpvkeU5LHMf4vk+aphRFwesuCKAsIct4kaKA7m4IQwhDKAqM+aM4hjCEOIY4hqJgN93dVN3dpEAYhoRhyODgIB0dHZRlSZZlRFGEee15jHCTJk3izjvv5MYbb2T79u3sqq+vj5ZTTjkFY8zL45wjSRLKsiTPc1rSNMX3fcIwJE1TXjfOQRRBswllCc6xm6qCooAwBN+HRgMzwlUVVBU0GtBoQFGwX1FEFUUUQUAaRYRFQdhoUAUBSZJQliVZlhFFEeb15THCeZ7HRRddxJNPPsknPvEJ1qxZw2OPPcbixYtZuHAhU6ZM4YwzzsAY88o550iShDzPyfOcIAgoioJarYbv+6RpSlEUvC6cg7KEPIc850WqCuIYajWo1aAooKowI0BVQaMBjQbEMfg+xDHEMaQpu6nXIYqogoBGFBFXFX6jQVxV4BxJklCWJVmWEQQB5sDhMQrEccxnP/tZHnroIc4991w+9KEPsWjRIj72sY9x/fXXY4z5yznnSJKEPM9pNptkWUZLHMf4vk+apqRpymsuCCAIoCyhuxucY6/CEHwf4hjSFNIU0yaKAhoNaDT4I9+HOIY4hqJgb6qqoigK0scfJ6wqwqpiEKh3dFCWJWVZkiQJQRBgDkweo0RHRwdr1qxh+fLl3HTTTTz44IMsWLCA8ePHY4z56wuCgCRJKMuSPM9pKYqCWq2G7/ukaUpRFLxmnIMkgbKEZhO6u8E5XqTRgO5u6O6GWg3SFBoNKArMAaq3F+IY4pgXCQKIIogiqu5uGs4RxzG+7xPHMVVVkSQJZVmSZRlRFOGcwxz4PEYRz/MQEaZMmcIb3vAGjDGvDeccSZKQ5znNZpM8z2lJ05RarYbv+6RpSlEUvGaSBPIcyhKyDKIInONFurshjiEMwffB96EooKqgqjCvsjSFOIY05WXr7obubqrubhpBQAzUGg3CRoNBoF6v02w2KcuSLMsIggDTfjyMMeY15pwjSRLyPKcsS7IsoyWOY3zfJwxD0jSlKApeVc6BcxBFkGWQ55DnEEUQRRAE7KaqoKqgqsD3wffB9yEMIU2hKDCvUFVBVUFVsVdFAY0GNBrsU5JAnlNlGY1Gg7iqCIuCsNFgsKqo1+vkeU5ZlmRZRhRFmPbnYYwxryPnHEEQkCQJZVmS5zkdHR20pGlKrVbD933SNKUoCl5VzkEQQJZBlkGeQ5ZBFEEQgHPgHLupKigK6O6GMATfB9+HMIQ4hqKAqmLUqyooCigKqCpe0NsLvg++D1XFy1VVFVVV0Wg0iNOUWhgSpimDg4PU63WSJKEsS7IsI4oigiDAjCwexhhzAHHOEUURSZKQ5zllWZJlGS1pmlKr1fB9nzRNSdOUoih4VUURZBnkOZQllCVEEXR3QxCAc+ymqqCqoCig0YAwBN+HWg1qNSgKKAooCqgqRoyqgkYDGg2IY4hjaDR4QVFAGEIYQlHwsuU5NJtUeU6j0SCOY8IwJAxDwjBkcHCQer1OnueUZUmWZURRRBAEmJHNwxhjDmDOOYIgIEkS8jyn2WyS5znPi+OYWq2G7/ukaUqaphRFwasuSSDPIc8hzyHPIcsgCMA59itNIQwhDHlBVUEYQhhCmkKaQppCmkKjQVuIY4hjaDSg0YDBQV5SvQ7d3dDdDc7RUlUVRVHQaDQIw5BarUYYhvT29uKcI0kSyrKkLEuyLCOKIoIgwIwuHsYY02accyRJQpIklGVJWZZkWUZLVVWEYUitVsP3fdI0JU1TiqLgVeEcBAEEAUQR5DmUJTSbkGWQZdDdDVEEUcR+FQUUBTQa0N0N3d3Q3Q1xDFXFbsIQajWo1cD3odHgj+IYwhB8H3wffB98H4qCP6oqCEMIQ2g0eM0EAWQZZBkEAS1VVVE5R+P//B/iqiIMQ2q1GmEYkqYpg4ODdHR0kOc5ZVmS5zlJkhAEAcZ4GGNMm3POEQQBSZKQZRnNZpOyLMmyjOelaUqtVsP3fcIwJE1T0jSlKApeNVEEUQRJAlkGWQZBAEkCWQZJwgucA+fAOV6xquIFRQFFAVUFVQVVBVXFbooCigIef5y/GucgyyDLIMugLCHLaKmqigpoAA0gTlPCMMT3fcIwZHBwkJaOjg7yPKcsS/I8J8syoigiCAKM2ZOHMcaMQM45giAgSRKSJCHPc5rNJnme09HRQUtVVaRpSq1Ww/d9wjAkTVPSNKUoCoqi4FURBBBFEEXspiyhLCHPoSyhLCHPIc/BOXbT0QFRBEEAQQDO8UfOgXPgHAQBBAEEAS9wDpwD5/hrq4KAwjkaQJymxHFMGIb4vk8YhvT29jI4OEi9XidJEprNJmVZkmUZWZYRRRFBEGDMy+FhjDGjiHOOKIpIkoQsy8jznGazSZ7nJEnC89I0JY5jarUavu/j+z5xHJOmKWma0mg0KIqCV4Vz4Bw4B0EAQcCLRBFkGeQ55DkEAX+U51CWUJaQ55DnkOcQBLygLKEsIUl4uaqqoqoqiqKg0WiQpilxHBOGIb7vU6vVCMOQNE0ZHBzEOUe9XidJEprNJmVZkuc5WZYRRRFBEGDMX8LDGGMMzjmCICBJEpIkIc9zyrKk2WyS5zlZllGv13leb28vaZpSq9Wo1Wr4vo/v+4RhSBzHpGlKmqY0Gg2KoqAoCqqqoqoqDgRVVVFVFUVRUBQFjUaDRqNBmqbEcUwcx4RhiO/71Go1wjAkDEPSNGVwcJCqqqjX6yRJQpZlNJtNyrIkz3OyLCNJEqIoIggCjHk1eBhjjNkv5xxBEBBFEUmSkCQJeZ6T5znNZpNms0me5+R5TpIk1Ot1njc4OEiapqRpShiGhGFIrVajVqvh+z6+7+P7PmEYEoYhYRgShiFxHBOWWRwYAAAgAElEQVTHMXEcE8cxcRwTxzFxHBPHMXEcE8cxcRwTxzFxHBPHMXEcE8cxYRgShiFhGBKGIb7v4/s+tVqNWq1GGIaEYUgcx6RpyuDgIIODg7TU63Xq9TpJkpBlGc1mk7IsKcuSPM/Jsowsy4iiiCAICIIAY15rHsYYY/5izjmccwRBQBRFJElCkiRkWUae5+R5TlmWlGVJs9mk2WyS5zl5npPnOUmSkCQJSZKQJAn1ep16vU69Xqder1Ov16nX69Trder1OvV6nXq9Tr1ep16vU6/Xqdfr1Ot16vU6SZKQJAlJkpAkCXmek+c5zWaTZrNJWZaUZUlZluR5TpZlZFlGkiREUUQURQRBQBAEGHMg8jDGGPO6cM7hnMM5RxAEBEFAEAQEQUAURURRRBRFRFFEFEVEUUQURURRRBRFRFFEFEVEUUQURURRRBRFRFFEEAQEQUAQBARBgHMO5xzGjBQexhhjjDFtxsMYY4wxps14GGOMMca0GQ9jjDHGmDbjYYwxxhjTZjyMMcYYY9qMhzHGGGNMm/EwxhhjjGkzHsYYY4wxbcbDGGOMMabNeBhjjDHGtBkPY4wxxpg242GMMcYY02Y8jDHGGGPajIcxxhhjTJvxMMYYY4xpMx7GGGOMMW3GwxhjjDGmzXgYY4wxxrQZD2OMMcaYNuNhjDHGGNNmPEaQzZs3M3/+fJ577jn2ZfXq1Vx55ZVccskl9Pb2snXrVowxxhjTXjxGiN/97ndcfPHFrFixguHhYfbmc5/7HOeddx4//vGP+fWvf80Xv/hFTjvtNH7xi19gjDHGmPbhMQJs3ryZKIpYt24d+zI4OEhfXx/nn38+t956KzfccAPLly9n27ZtdHV1YYwxxpj24dHment7OfXUU3nsscc48sgj2ZelS5cybtw45s+fz/MOP/xwOjo6WLNmDY888gjGGGOMaQ8ebe6rX/0qJ5xwArfddhvHHHMM+3LfffcxdepUxo4dy66OOeYYWtasWYMxxhhj2oNHm/vOd77Dtddey2GHHca+/Pa3v2Xnzp38zd/8DXs69thjadmwYQPGGGOMaQ8ebe6d73wnL+Whhx6i5aCDDmJPb3rTm2j5wx/+gDHGGGPag8co8Nxzz/FSnnvuOfZHRBARRIRFixZhjDHGHIgWLVqEiCAiiAgjlccB7v7776ezs5POzk46Ozvp7Oxk8eLFvBKTJk1iX4aHh2kZO3Ys+6OqqCqqyrx58zDGGGMORPPmzUNVUVVUlZHK4wD3q1/9irVr17J27VrWrl3L2rVrefTRR3klnHO0PPvss+zpF7/4BS0TJ07EGGOMMe3B4wA3ffp0hoaGGBoaYmhoiKGhIRYuXMgrMXbsWP72b/+WJ554gj09/PDDtLzrXe/CGGOMMe3BY5T44Ac/yLp166iqil19+9vfZty4cZx00kkYY4wxpj14jBIXXHABEyZM4IILLuCee+6hqioWLFjAD3/4Qy688ELGjx+PMcYYY9qDxyhx2GGH0dPTQ8sFF1zAjBkzuPnmm5k7dy7/8i//gjHGGGPah8cIsmDBAlSVsWPHsjfvfe97WblyJStWrGDJkiX893//NxdddBHGGGOMaS8eo9Dhhx/Occcdxxve8AaMMcYY0348jDHGGGPajIcxxhhjTJvxMMYYY4xpMx7GGGOMMW3GwxhjjDGmzXgYY4wxxrQZD2OMMcaYNuNhjDHGGNNmPIwxxhhj2oyHMcYYY0yb8TDGGGOMaTMexhhjjDFtxsMYY4wxps14GGOMMca0GQ9jjDHGmDbjYYwxxhjTZjyMMcYYY9qMhzHGGGNMm/EwxhhjjGkzHsYYY4wxbcbDGGOMMabNeBhjjDHGtBkPY4wxxpg242GMMcYY02Y8jDHGGGPajIcxxhhjTJvxMMYYY4xpMx7GGGOMMW3GwxhjjDGmzXgYY4wxxrQZD2OMMcaYNuNhjDHGGNNmPIwxxhhj2ozHCLJ582bmz5/Pc889x94MDQ0xMDDAwMAAAwMDDAwMMDAwwMDAAFu2bMEYY4wx7cFjhPjd737HxRdfzIoVKxgeHmZvvva1r9HV1UVXVxddXV10dXXR1dVFV1cXVVVhjDHGmPbgMQJs3ryZKIpYt24d+7NmzRpOOukk+vr66Ovro6+vj76+Pvr6+jj66KMxB4bf/va33H777Wzbto0/xwMPPMADDzzAgWR4eJidO3fycuzcuZOdO3dijDFm3zzaXG9vL6eeeiqPPfYYRx55JPvy5JNPsmPHDk4++WQmT57M5MmTmTx5MpMnT2by5MmMHz8e89I6Ojqo1WqsXLmSV8u//uu/cvXVVzN+/Hj+HM888wzHH388Gzdu5EBx+umn86EPfYh92bx5M3PmzGH8+PGMHTuWsWPH8g//8A98+ctfxhhjzIt5tLmvfvWrnHDCCdx2220cc8wx7MtPfvITWpxzmAPXHXfcwZIlS7j22mv5c4VhyLRp0+jo6OBAMH/+fFasWMG+PPXUU7z3ve+lp6eHU045hcWLF9Pd3c3YsWP5zGc+w8c//nGMMcbszqPNfec73+Haa6/lsMMOY39++tOf0rJhwwamT5/O0UcfzQknnMCXvvQltm3bhnn9DQ8P8+lPf5pTTz2V973vffwlFixYwJo1a7j55pt5vWzdupWzzjqLa665hv256qqrePLJJ/nc5z7HbbfdxoUXXkiSJNx///0cc8wx/Od//ierV6/GGGPMn3i0uXe+8528HJs2baLlW9/6FqeeeiqXXnopzjl6eno4//zzGR4eZrQbHh5m27ZtbNu2jeHhYV6OHTt2sG3bNl6Obdu2sW3bNvbl5ptvRlX59Kc/zb4MDw+zbds2tm3bxvDwMPvynve8hxNOOIE0TXk9fPvb30ZE+O53v8t5553H/nz3u9/ljW98I1dccQW7Ovjgg7n44otpueOOOzDGGPMnHqPE2972Ns4880xuvfVWLrroIjo6Oli2bBmzZ89m/fr1LFu2jP0REUQEEWHRokWMJOvWrWPmzJmMGzeOCRMmMGHCBMaNG8eZZ57Jz3/+c/Zm8+bNzJw5kze+8Y1MmDCBSZMmcdVVV7GnnTt3csUVV/CWt7yFCRMmMGHCBMaPH8/cuXN5+umn2dXXv/513vrWtzJt2jT2tG7dOmbOnMm4ceOYMGECEyZMYNy4cZx55pn8/Oc/Z2/OPfdcVJWVK1fyUr785S8zZ84c5syZw5w5c5gzZw5z5sxhzpw5zJkzhzlz5jBnzhx27tzJy3HzzTczfvx4BgYG6O3tZX8WL15Mb28vnuexpzFjxtCyY8cOjDHm5Vi0aBEigoggIoxUHge4+++/n87OTjo7O+ns7KSzs5PFixfzSl1xxRV8/vOf5+CDD2ZXn/rUp2hZtWoV+6OqqCqqyrx58xgpHnjgAU488URWr17NJZdcwtKlS1m0aBHHHnsst9xyC6eddhp709nZySOPPMLixYu5/vrr+bu/+zv+7d/+jTlz5rCrrq4u/v3f/52TTz6ZJUuWsGTJEqZNm8bixYs5/fTTed7jjz/Offfdx/Tp09nTAw88wIknnsjq1au55JJLWLp0KYsWLeLYY4/llltu4bTTTmNvgiCgpa+vj5fy/e9/n56eHnp6eujp6aGnp4eenh56enro6emhp6eHnp4ehoeHeTmuuOIKNm3axOmnn85LOf300/mnf/on9mbJkiW0TJ06FWOMeTnmzZuHqqKqqCojlccB7le/+hVr165l7dq1rF27lrVr1/Loo4/y1/KWt7yFgw46iO3btzMadXd3s337dvr7+7n66qs555xz+OQnP8nq1asREdavX8/mzZvZ0zve8Q7WrFnDhRdeyCc+8QlWrVrFu9/9bnp6eli3bh3Pu+666zj++OP53ve+x7nnnsu5557L8uXLCYKA1atXs2HDBlruvfdeWj7wgQ+wp+7ubrZv305/fz9XX30155xzDp/85CdZvXo1IsL69evZvHkzezryyCN505vexF133cVLueWWW9iyZQtbtmxhy5YtbNmyhS1btrBlyxa2bNnCli1b2LJlCwcddBAvx/ve9z48z+MvkWUZK1eu5N3vfjcf/OAHMcYY8yceB7jp06czNDTE0NAQQ0NDDA0NsXDhQl6JzZs3c+mll7J06VL2tG3bNnbs2MH48eMZjebOncvSpUuZOnUqezr22GNp2bBhA3u6/PLLefOb38zzxo0bx+WXX05LX18fu3rkkUfYuHEju1qxYgU7duzg6KOPpqUoClqcc+xp7ty5LF26lKlTp7KnY489lpYNGzawN8cddxxPPvkkO3bsYH8OPvhgJk6cyMSJE5k4cSITJ05k4sSJTJw4kYkTJzJx4kQmTpzIa2X58uV0dnZy6KGH0t/fjzHGmN15jAKTJk3izjvv5MYbb2T79u3sqq+vj5ZTTjmF0Wj69Omcc845DA8Ps3r1ar73ve+xcOFCzj77bL7//e/T8txzz7Gn6dOns6dTTjmFlkceeYTnzZ07ly1btnDUUUfx3ve+l66uLvI8Z9y4cXiex/OeeeYZWiZMmMCepk+fzjnnnMPw8DCrV6/me9/7HgsXLuTss8/m+9//Pi3PPfccezNx4kRa1q1bR7u48cYbOeOMMzjkkEO48847eec734kxxpjdeYwCnudx0UUX8eSTT/KJT3yCNWvW8Nhjj7F48WIWLlzIlClTOOOMMxiNnnnmGTo7Oxk3bhzHH388s2bN4rLLLuPxxx/n0EMPZV8OPfRQ9nTIIYfQsnPnTp73la98hf/4j/9ARFi/fj1f+tKXOOWUUzjssMP44he/yPOGh4dpGTNmDHt65pln6OzsZNy4cRx//PHMmjWLyy67jMcff5xDDz2U/Rk7diwtzz77LPvzj//4j9RqNWq1GrVajVqtRq1Wo1arUavVqNVq1Go1duzYwavp05/+NBdccAF///d/zz333MP73/9+jDHGvJjHKBHHMZ/97Gd56KGHOPfcc/nQhz7EokWL+NjHPsb111/PaHX22WfzjW98g6lTp7Js2TJWrVrF73//e1avXs3xxx/PvuzcuZM9Pfvss7SMGTOGXc2fP5+NGzeiqvT09HDaaafxzDPPcNlll3HTTTfR4nkeLTt37mRPZ599Nt/4xjeYOnUqy5YtY9WqVfz+979n9erVHH/88ezPc889R8vYsWPZn5NOOolZs2Yxa9YsZs2axaxZs5g1axazZs1i1qxZzJo1i1mzZuF5Hq+GnTt3cvrpp/PVr36VKVOmMDQ0xJFHHokxxpi98xhBFixYgKoyduxY9qajo4M1a9awfPlybrrpJh588EEWLFjA+PHjGY0efvhhVq5cyVFHHcUPfvADZs+ezXHHHceYMWNo+eUvf8m+/Nd//Rd7yvOclsMPP5yWzZs3881vfpM8z2k54ogj+PjHP87y5cu58cYbabnjjjtoOfTQQ2l59tln2dXDDz/MypUrOeqoo/jBD37A7NmzOe644xgzZgwtv/zlL9mfrVu30vKBD3yA/UmShP7+fvr7++nv76e/v5/+/n76+/vp7++nv7+f/v5+xowZw6vhIx/5CLfeeiunnXYag4ODTJo0CWOMMfvmMcp4noeIMGXKFN7whjcwmj399NO0HHLIIezpRz/6EUVR0DI8PMyerrvuOna1c+dOFixYQMt5551Hy//+7//yz//8z3zmM59hT+PGjaPl0EMPpeXkk0+m5Wc/+xm7evrpp2k55JBD2NOPfvQjiqKgZXh4mL259957eetb38pBBx3Egerqq69mxYoVnHrqqSxfvpxx48ZhjDFm/zzMqHXcccfhnGPVqlXMnz+fu+66i7vuuoskSZgxYwZvf/vbadmxYwd7Wr9+PR/+8IdZvnw5/f39nHjiiaxfv56LLrqI97znPbQcccQRfPSjH2X9+vWEYUh/fz+333471113HZ/61Kd405vexNy5c2k57rjjaBkcHGRXxx13HM45Vq1axfz587nrrru46667SJKEGTNm8Pa3v52WHTt2sKdHHnmEZ599lmnTpnGgevrpp7nqqqtoefrpp5k5cyYzZ85k5syZzJw5k5kzZzJz5kyuvfZajDHG/ImHGbU8z2NgYAAR4ZprrmHGjBnMmDGDJUuWcMMNN3D99dfTcu+997Kn2267DVXljDPO4KMf/SgPPvggCxYs4Ctf+Qq7ajQanH/++dxzzz189KMf5dRTT2XevHm87W1v48477+Too4+m5YgjjuDd7343K1euZFee5zEwMICIcM011zBjxgxmzJjBkiVLuOGGG7j++utpuffee9nTypUraTn33HM5UN1zzz1s376dllWrVrFixQpWrFjBihUrWLFiBStWrGDFihU8+OCDGGOM+RMPM6q9613vYuPGjagqd999N5s2baIsS2bPns3MmTNpNpt84Qtf4Hm9vb00m03e//738+ijj7J+/Xp++MMfsnXrVq644gr2dPDBB3PjjTfy+9//nnvvvZe7776b//mf/+GBBx5g6tSp7OrCCy9ky5YtrFy5kl29613vYuPGjagqd999N5s2baIsS2bPns3MmTNpNpt84QtfYE99fX284x3v4MMf/jCvt2azyd13382ePvKRj9BsNmk2mzSbTZrNJs1mk2azSbPZpNls0mw2ueGGGzDGGPMnHsb8P0cccQTTpk3j8MMP55V4z3vew9SpUxkzZgz7M2bMGE488USmTZvGpEmT2JsLLriAd7zjHXz9619nb4444gimTZvG4YcfzkvZuHEj9957L5dccgnGGGNGHg9jDhBjxozhC1/4ArfccgsbN27kL3HVVVdx1FFHMXfuXIwxxow8HsYcQGbPns2MGTP47Gc/y5/rJz/5CcuWLeOGG27A8zyMMcaMPB7GHGDuuOMO+vv7+XPleU6z2eTEE0/EtIdFixZh2seiRYsw5vXmYcwIc91112Hay3XXXYdpH9dddx3GvN48jDHGGGPajIcxxhhjTJvxMC9pypQpiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogIIoKIICKICCKCiCAiiAgigoggIogII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</div></div></div></div></div><div class="inlineElement eoOutputWrapper embeddedOutputsTextElement" uid="DD230BE9" data-scroll-top="null" data-scroll-left="null" data-width="1334" data-height="18" data-hashorizontaloverflow="false" data-testid="output_1" style="max-height: 261px; width: 1364px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="textElement" style="white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Elapsed time is 43.871730 seconds.</div></div></div></div></div><div class = 'S0'><span>Once the simulation is complete, we plot the </span><span style=' font-family: monospace;'>data</span><span>. the first plot shows the evolution of the magnitude of the field and the second plot shows its phase, whereas the third plot shows the gain per single pass through the undulator. Finally the last plot shows the increase in momentum spread of the electrons. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >figure</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >rep=1:Nrep;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >subplot(4,1,1); plot(rep,data(:,1),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,</span><span style="color: rgb(170, 4, 249);">'LineWidth'</span><span >,2); ylabel(</span><span style="color: rgb(170, 4, 249);">'abs(a)'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >subplot(4,1,2); plot(rep,data(:,2),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,</span><span style="color: rgb(170, 4, 249);">'LineWidth'</span><span >,2); ylabel(</span><span style="color: rgb(170, 4, 249);">'\phi [deg]'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >subplot(4,1,3); plot(rep,data(:,3),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,</span><span style="color: rgb(170, 4, 249);">'LineWidth'</span><span >,2); ylabel(</span><span style="color: rgb(170, 4, 249);">'Gain'</span><span >);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >ylim([0,0.2]);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >subplot(4,1,4); plot(rep,data(:,4),</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,</span><span style="color: rgb(170, 4, 249);">'LineWidth'</span><span >,2); ylabel(</span><span style="color: rgb(170, 4, 249);">'\sigma/\sigma_0'</span><span >);</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S6'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'Repetition'</span><span >);</span></span></div><div class = 'S7'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="3A695B13" data-scroll-top="null" data-scroll-left="null" data-testid="output_2" style="width: 1364px;"><div class="figureElement" style="cursor: default;"><div class="figureContainingNode" style="width: 560px; max-width: 100%; display: inline-block;"><div class="GraphicsView" data-dojo-attach-point="graphicsViewNode,backgroundColorNode" id="uniqName_333_55" widgetid="uniqName_333_55" style="width: 100%; height: auto;"><div class="ImageView" id="uniqName_333_59" widgetid="uniqName_333_59" style="width: 100%; height: auto;">
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">
</div></div></div></div></div></div></div></div><div class = 'S5'><span>Now feel free to play with the parameters to your heart's content!</span></div><h2 class = 'S8'><span>Appendix</span></h2><div class = 'S0'><span>The function </span><span style=' font-family: monospace;'>pendulumtracker2_phase()</span><span> integrates the equations of motion for a mathematical pendulum in terms of Jacobi elliptic functions. It is very similar to the one used in Chapter 5 (see those examples), exept this one takes the phase of the ponderomotive force </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">ϕ</span><span> into account.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">function </span><span >xout=pendulumtracker2_phase(x,omega,phi,dt)</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >x(1)=x(1)-pi/2+phi; </span><span style="color: rgb(2, 128, 9);">% adjust to new phase</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >k2=(0.5*x(2)/omega)^2+sin(0.5*x(1))^2; k=sqrt(k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >(x(1)>pi) x(1)=x(1)-2*pi; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >(x(1)<-pi) x(1)=x(1)+2*pi; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >s=1; </span><span style="color: rgb(14, 0, 255);">if </span><span >(x(1)<0) s=-s; x(1)=-x(1); </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >s1=1; </span><span style="color: rgb(14, 0, 255);">if </span><span >(x(2)<0) s1=-s1; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >(k>1) </span><span style="color: rgb(2, 128, 9);">% outside separatrix; check this part next</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(2, 128, 9);">% disp('outside')</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > kelf=ellipke(1/k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > trev=2*kelf/(k*omega);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > t0=mod(dt,trev);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > tmp=s1*k*omega*t0+s*elliptic12(0.5*x(1),1/k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > [sn,cn,dn]=ellipj(tmp,1/k2); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(14, 0, 255);">if </span><span >(abs(tmp) > kelf) sn=-sn; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xout(1)=2*asin(sn);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xout(2)=2*s1*omega*k*dn;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">else</span><span > </span><span style="color: rgb(2, 128, 9);">% inside separatrix</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > </span><span style="color: rgb(2, 128, 9);">%disp('inside')</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > trev=4*ellipke(k2)/omega;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > t0=mod(dt,trev);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > z0=asin(min(1,sin(0.5*x(1))/k));</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > tmp=s1*omega*t0+s*elliptic12(z0,k2);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > [sn,cn,dn]=ellipj(tmp,k2); </span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xout(1)=2*asin(k*sn);</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span > xout(2)=2*s1*omega*k*cn;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >x(1)=x(1)+pi/2-phi; </span><span style="color: rgb(2, 128, 9);">% adjust phase back</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span >xout(1)=xout(1)+pi/2-phi;</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >(xout(1)>3*pi/2) xout(1)=xout(1)-2*pi; </span><span style="color: rgb(14, 0, 255);">end</span><span > </span><span style="color: rgb(2, 128, 9);">% cast in range</span></span></div></div><div class="inlineWrapper"><div class = 'S3'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">if </span><span >(xout(1)<-pi/2) xout(1)=xout(1)+2*pi; </span><span style="color: rgb(14, 0, 255);">end</span></span></div></div><div class="inlineWrapper"><div class = 'S4'><span style="white-space: pre"><span style="color: rgb(14, 0, 255);">end</span></span></div></div></div><div class = 'S5'><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)
%% Free-electron laser oscillator (Section 10.4)
% Volker Ziemann, 211114, CC-BY-SA-4.0
%
% *Important:* requires the elliptic package from <https://github.com/moiseevigor/elliptic
% https://github.com/moiseevigor/elliptic> located in a subdirectory below the
% present one (for the fast evaluation of elliptic functions).
%
% Like the example for the SASE FEL |SaseFreeElectronLaser.mlx| is this simulation
% based on numericall integrating Equation 10.32. The main difference is that
% here we operate at low current jcurr and assume that the laser field is recirculated
% by mirrors and meet a fresh electron bunch on the next iteration.
%
% First we define the |mirror_losses| to be 0.01, the initial complex field
% |a| of the laser and the scaled current |jcurr|, which represents the peak current
% of the electron distribution. Moreover, we define the initial distribution of
% electrons in the ponderomotive field and the number N of electrons used in the
% simulation. From Equation 10.32 we see that the magnnitude of a, which is a0
% describes the oscillation frequency $\Omega_s$ in the ponderomotive field.
clear all; close all; tic
addpath ./elliptic % needed for elliptic12
mirror_losses=0.01; % 0.01=1% extracted
a0=1e-8; phi=0; a=a0*exp(i*phi); % initial amplitude and phase of laser
jcurr=1; % scaled current from Equation 10.32
x0=[pi/2,2.6]; dx=[2*pi,0.1]; % center and spread of distribution
N=1000; % number of particles
Omegas=sqrt(a0); % synchrotron frequency
%%
% Next we need to define some parameters needed for annotating the plots. Since
% the increase of the field during one pass through the undulator does not grows
% significantly we decide to split the simulation within on pass through the unduator
% into |nstep=5| steps, rather than 100, as in the SASE suimulation. |Nrep|, on
% th other hand, specifies the number of round-trips of the laser caused by the
% mirrors. On each of these trips the laser interacts with a fresh electron bunch
% that is provided by an accelerator.
axis_scale=[-pi/2,3*pi/2,-17,17];
ypos=0.95*axis_scale(3)+0.05*axis_scale(4); % where to place text
zeta=-pi/2:0.01:3*pi/2;
nstep=5; dt=1/nstep; tau=(1:nstep)/nstep; % steps along the undulator
Nrep=100; % iterations = round-trips of the laser
%%
% Now we start iterating and first generate a fresh electron distribution that
% we display as a cloud of green dots.
data=zeros(Nrep,4);
for rep=1:Nrep % iteration over round-trips
hold off
a00=abs(a); % needed to caluclate the gain in this iteration
x1(:,1)=x0(1)+(rand(N,1)-0.5)*dx(1); % initial distribution
x1(:,2)=x0(2)+(rand(N,1)-0.5)*dx(2);
plot(x1(:,1),x1(:,2),'g.')
if (rep==1) dx0=dx(2); rms0=std(x1(:,2)); end
%%
% In the following loop over nstep iterations we follow the electron distribution
% as it passes through the undulator. In each step we update the electron coordinates
% and calculate the bunching factor |bf| that we subsequently use to update the
% field |a| before plotting the new electron coordinates as red dots.
hold on; % draw new image
for m=1:nstep % one pass through the undulator
Omegas=sqrt(abs(a)); phi=phase(a); % needed for electron dynamics
parfor k=1:N % update electron phase space
x1(k,:)=pendulumtracker2_phase(x1(k,:),Omegas,phi,dt);
end
bf=sum(exp(-i*x1(:,1)))/size(x1,1); % bunching factor <exp(-i*zeta)>
a=a-jcurr*bf*dt; % update laser field, Eq. 10.32
end
plot(x1(:,1),x1(:,2),'r.'); rms1=std(x1(:,2));
%%
% Now we reduce the field as a consequence of the mirror losses, plot separatrix
% and annotate the plot.
a=a*(1-mirror_losses);
title(['Iteration ',num2str(rep),' of ',num2str(Nrep)])
separatrix=2*Omegas*cos(0.5*(zeta-pi/2+phi));
plot(zeta,separatrix,'k',zeta,-separatrix,'k');
set(gca,'xtick',[-pi/2,0,pi/2,pi,3*pi/2],'fontsize',14, ...
'xticklabels',{'-\pi/2','0','\pi/2','\pi','3\pi/2'})
axis(axis_scale); xlabel('\zeta'); ylabel('\nu')
text(-pi/4,ypos,['abs(a) = ',num2str(abs(a),3),' '],'fontsize',16)
%%
% Before the next iteration, we save a number of interesting parameters for
% later plots to the array |data|.
data(rep,1)=abs(a);
data(rep,2)=phase(a)*180/pi;
data(rep,3)=(abs(a)-a00)/a00;
data(rep,4)=rms1/rms0;
pause(0.001);
if (mod(rep,100)==0) toc; end
end
%%
% Once the simulation is complete, we plot the |data|. the first plot shows
% the evolution of the magnitude of the field and the second plot shows its phase,
% whereas the third plot shows the gain per single pass through the undulator.
% Finally the last plot shows the increase in momentum spread of the electrons.
figure
rep=1:Nrep;
subplot(4,1,1); plot(rep,data(:,1),'k','LineWidth',2); ylabel('abs(a)');
subplot(4,1,2); plot(rep,data(:,2),'k','LineWidth',2); ylabel('\phi [deg]');
subplot(4,1,3); plot(rep,data(:,3),'k','LineWidth',2); ylabel('Gain');
ylim([0,0.2]);
subplot(4,1,4); plot(rep,data(:,4),'k','LineWidth',2); ylabel('\sigma/\sigma_0');
xlabel('Repetition');
%%
% Now feel free to play with the parameters to your heart's content!
%% Appendix
% The function |pendulumtracker2_phase()| integrates the equations of motion
% for a mathematical pendulum in terms of Jacobi elliptic functions. It is very
% similar to the one used in Chapter 5 (see those examples), exept this one takes
% the phase of the ponderomotive force $\phi$ into account.
function xout=pendulumtracker2_phase(x,omega,phi,dt)
x(1)=x(1)-pi/2+phi; % adjust to new phase
k2=(0.5*x(2)/omega)^2+sin(0.5*x(1))^2; k=sqrt(k2);
if (x(1)>pi) x(1)=x(1)-2*pi; end
if (x(1)<-pi) x(1)=x(1)+2*pi; end
s=1; if (x(1)<0) s=-s; x(1)=-x(1); end
s1=1; if (x(2)<0) s1=-s1; end
if (k>1) % outside separatrix; check this part next
% disp('outside')
kelf=ellipke(1/k2);
trev=2*kelf/(k*omega);
t0=mod(dt,trev);
tmp=s1*k*omega*t0+s*elliptic12(0.5*x(1),1/k2);
[sn,cn,dn]=ellipj(tmp,1/k2);
if (abs(tmp) > kelf) sn=-sn; end
xout(1)=2*asin(sn);
xout(2)=2*s1*omega*k*dn;
else % inside separatrix
%disp('inside')
trev=4*ellipke(k2)/omega;
t0=mod(dt,trev);
z0=asin(min(1,sin(0.5*x(1))/k));
tmp=s1*omega*t0+s*elliptic12(z0,k2);
[sn,cn,dn]=ellipj(tmp,k2);
xout(1)=2*asin(k*sn);
xout(2)=2*s1*omega*k*cn;
end
x(1)=x(1)+pi/2-phi; % adjust phase back
xout(1)=xout(1)+pi/2-phi;
if (xout(1)>3*pi/2) xout(1)=xout(1)-2*pi; end % cast in range
if (xout(1)<-pi/2) xout(1)=xout(1)+2*pi; end
end
%%
%
%
%
##### SOURCE END #####
-->
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