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.matrixElement .verticalEllipsis,.textElement .verticalEllipsis,.rtcDataTipElement .matrixElement .verticalEllipsis,.rtcDataTipElement .textElement .verticalEllipsis { margin-left: 35px; /* base64 encoded version of images-liveeditor/VEllipsis.png */ width: 12px; height: 30px; background-repeat: no-repeat; background-image: url("data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAZCAYAAAAIcL+IAAAALklEQVR42mP4//8/AzGYgWyFMECMwv8QddRS+P//KyimlmcGUOFoOI6GI/UVAgDnd8Dd4+NCwgAAAABJRU5ErkJggg==");}</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>Pill-box cavity with beam pipe (Section 6.4.2)</span></h1><div class = 'S0'><span>Volker Ziemann, 211124, CC-BY-SA-4.0</span></div><div class = 'S0'><span style=' font-weight: bold;'>Important:</span><span> this example requires the PDE toolbox!</span></div><div class = 'S0'><span>In this example we calculate the eigenfrequencies of a pill-box cavity with a beam pipe connected to its center. This will perturb the eigenmodes and eigenfrequencies of a pure cavity. We therefore use the PDE toolbox to find the TM eigenmodes and note that the system is still rotationally symmetric such that we can use a 2D model to find the rotationally symmetric modes.</span></div><div class = 'S0'><span>We first define the beam pipe radius </span><span style=' font-family: monospace;'>rr</span><span>, the cavity radius </span><span style=' font-family: monospace;'>R</span><span>, and the the cavity length </span><span style=' font-family: monospace;'>L</span><span> to specify the cavity dimensions.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >clear; </span></span></div></div><div class="inlineWrapper outputs"><div class = 'S3'><span style="white-space: pre"><span >rr=</span></span><span>0.01</span><span style="white-space: pre"><span > </span><span style="color: rgb(2, 128, 9);">% Slider for the beam pipe radius</span></span></div><div class = 'S4'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>rr = 0.0100</div></div></div><div class="inlineWrapper outputs"><div class = 'S5'><span style="white-space: pre"><span >R=</span></span><span>0.23</span><span style="white-space: pre"><span > </span><span style="color: rgb(2, 128, 9);">% Slider for the cavity radius</span></span></div><div class = 'S4'><div class='variableElement' style='font-family: Menlo, Monaco, Consolas, "Courier New", monospace; font-size: 12px; '>R = 0.2300</div></div></div><div class="inlineWrapper"><div class = 'S6'><span style="white-space: pre"><span >L=0.3; </span><span style="color: rgb(2, 128, 9);">% Cavity length</span></span></div></div></div><div class = 'S7'><span>Now we use these parameters to define the cavity and the beam pipe as three polygons </span><span style=' font-family: monospace;'>Cav, Pl,</span><span> and </span><span style=' font-family: monospace;'>Pr,</span><span> assemble them in </span><span style=' font-family: monospace;'>gd</span><span>, define names </span><span style=' font-family: monospace;'>ns</span><span> and specify the relation </span><span style=' font-family: monospace;'>sf</span><span> among the regions, before we construct the geometry </span><span style=' font-family: monospace;'>g</span><span> and create the model for one parameter </span><span style=' font-family: monospace;'>u = </span><span texencoding="E_z" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="16" height="20" /></span><span>. Then we add the geometry </span><span style=' font-family: monospace;'>g</span><span> to it and inspect the model to note the </span><span style=' font-family: monospace;'>EdgeLabels</span><span> and the </span><span style=' font-family: monospace;'>SubDomainLabels.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >Cav=[2;4; -L/2;L/2;L/2;-L/2; 0.0;0.0;R;R]; </span><span style="color: rgb(2, 128, 9);">% cavity</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >Pl=[2;4; -0.4;-L/2;-L/2;-0.4; 0.0;0.0;rr;rr]; </span><span style="color: rgb(2, 128, 9);">% pipe left</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >Pr=[2;4; L/2;0.4;0.4;L/2; 0.0;0.0;rr;rr]; </span><span style="color: rgb(2, 128, 9);">% pipe right</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >gd=[Cav,Pl,Pr]; </span><span style="color: rgb(2, 128, 9);">% assemble geometry</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >ns=char(</span><span style="color: rgb(170, 4, 249);">'Cavity'</span><span >,</span><span style="color: rgb(170, 4, 249);">'Pl'</span><span >,</span><span style="color: rgb(170, 4, 249);">'Pr'</span><span >)'; </span><span style="color: rgb(2, 128, 9);">% names of the regions </span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >sf=</span><span style="color: rgb(170, 4, 249);">'Cavity+Pl+Pr'</span><span >; </span><span style="color: rgb(2, 128, 9);">% geometry relations</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >g=decsg(gd,sf,ns); </span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >model=createpde(1);</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >geometryFromEdges(model,g);</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S3'><span style="white-space: pre"><span >pdegplot(model,</span><span style="color: rgb(170, 4, 249);">'EdgeLabels'</span><span >,</span><span style="color: rgb(170, 4, 249);">'on'</span><span >,</span><span style="color: rgb(170, 4, 249);">'SubDomainLabels'</span><span >,</span><span style="color: rgb(170, 4, 249);">'on'</span><span >); axis </span><span style="color: rgb(170, 4, 249);">tight</span></span></div><div class = 'S4'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="B55BE3C8" data-scroll-top="null" data-scroll-left="null" data-testid="output_2" style="width: 1327px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" style="width: 560px;"></div></div></div></div></div><div class = 'S7'><span>Since the longitudinal electric field </span><span style=' font-family: monospace;'>u = </span><span texencoding="E_z" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="16" height="20" /></span><span> must vanish on the boundaries where it is parallel to the boundaries E1, E9, E10 and on the exit from the beam pipe E2 and E3, we select Dirichlet boundary conditions. On the verical walls E5 and E12 the electric field is given by the derivative of the longitudinal field </span><span texencoding="E_z" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="16" height="20" /></span><span>, which implies the use of von-Neumann boundary conditions. Moreover, we also use von-Neumann conditions on the symmetry axis E6, E7, and E8. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >applyBoundaryCondition(model,</span><span style="color: rgb(170, 4, 249);">'Edge'</span><span >,[1,2,3,9,10],</span><span style="color: rgb(170, 4, 249);">'u'</span><span >,0); </span><span style="color: rgb(2, 128, 9);">% Dirichlet</span></span></div></div><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >applyBoundaryCondition(model,</span><span style="color: rgb(170, 4, 249);">'Edge'</span><span >,[6,7,8,5,12],</span><span style="color: rgb(170, 4, 249);">'q'</span><span >,0,</span><span style="color: rgb(170, 4, 249);">'g'</span><span >,0); </span><span style="color: rgb(2, 128, 9);">% Neumann</span></span></div></div></div><div class = 'S7'><span>The rotational symmetry requires to use the Laplace operator in cylindrical coordinates, which has to be brought into Matlab's generic form to specify a partial differential equation in divergence form, which is discussed further in Section 6.4.2. In the code this is accomplished by using functions </span><span style=' font-family: monospace;'>cfun()</span><span> and </span><span style=' font-family: monospace;'>dfun()</span><span> when specifying the material properties.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >cfun=@(location,state)-location.y;</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >dfun=@(location,state)-location.y;</span></span></div></div><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >specifyCoefficients(model,</span><span style="color: rgb(170, 4, 249);">'m'</span><span >,0,</span><span style="color: rgb(170, 4, 249);">'d'</span><span >,dfun,</span><span style="color: rgb(170, 4, 249);">'c'</span><span >,cfun,</span><span style="color: rgb(170, 4, 249);">'a'</span><span >,0,</span><span style="color: rgb(170, 4, 249);">'f'</span><span >,0);</span></span></div></div></div><div class = 'S7'><span>At this point we can mesh the geometry... </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >generateMesh(model,</span><span style="color: rgb(170, 4, 249);">'Hmax'</span><span >,0.01);</span></span></div></div><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span style="color: rgb(2, 128, 9);">%figure; pdemesh(model); axis tight</span></span></div></div></div><div class = 'S7'><span>...and solve the eigenvalue system with </span><span style=' font-family: monospace;'>solvepdeeig()</span><span>, which returns the structure </span><span style=' font-family: monospace;'>result</span><span> that contains the </span><span style=' font-family: monospace;'>Eigenvalues</span><span> and the </span><span style=' font-family: monospace;'>Eigenvectors</span><span> as members.</span></div><div class="CodeBlock"><div class="inlineWrapper outputs"><div class = 'S10'><span style="white-space: pre"><span >result=solvepdeeig(model,[1,800]); </span></span></div><div class = 'S4'><div class="inlineElement eoOutputWrapper embeddedOutputsTextElement" uid="0563F585" data-scroll-top="null" data-scroll-left="null" data-width="1297" data-height="143" data-hashorizontaloverflow="false" data-testid="output_3" style="max-height: 261px; width: 1327px; 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;"> Basis= 10, Time= 0.09, New conv eig= 0
Basis= 12, Time= 0.11, New conv eig= 0
Basis= 14, Time= 0.12, New conv eig= 2
Basis= 16, Time= 0.12, New conv eig= 3
Basis= 18, Time= 0.13, New conv eig= 3
Basis= 20, Time= 0.13, New conv eig= 4
Basis= 22, Time= 0.14, New conv eig= 5
End of sweep: Basis= 22, Time= 0.14, New conv eig= 5
Basis= 15, Time= 0.17, New conv eig= 0
End of sweep: Basis= 15, Time= 0.17, New conv eig= 0</div></div></div></div><div class="inlineWrapper"><div class = 'S11'><span style="white-space: pre"><span >k2=result.Eigenvalues; </span></span></div></div><div class="inlineWrapper"><div class = 'S9'><span style="white-space: pre"><span >Ez=result.Eigenvectors;</span></span></div></div></div><div class = 'S7'><span>From the eigenvectors, which are </span><span texencoding="k^2=\omega^2/c^2" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="68" height="20" /></span><span> we derive the frequencies of the eigenmodes in GHz.</span></div><div class="CodeBlock"><div class="inlineWrapper outputs"><div class = 'S10'><span style="white-space: pre"><span >freq_GHz=sqrt(k2')*3e8/(2*pi*1e9) </span></span></div><div class = 'S4'><div class="inlineElement eoOutputWrapper embeddedOutputsVariableMatrixElement" uid="4DDA2A32" data-scroll-top="null" data-scroll-left="null" data-width="1297" data-testid="output_4" style="width: 1327px; 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: 1297px; 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;">freq_GHz = </span><span class="veVariableValueSummary veMetaSummary" style="white-space: normal; font-style: normal; color: rgb(179, 179, 179); font-size: 12px;">1×5</span></div></div><div class="valueContainer" data-layout="{"columnWidth":72,"totalColumns":"5","totalRows":"1","charsPerColumn":10}" style="white-space: nowrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableValue" style="width: 362px; white-space: pre; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"> 0.5138 0.7271 1.1253 1.1655 1.2768
</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 = 'S0'><span>Since we are interested in the accelerating mode around 500 MHz, we choose to inspect the lowest-frequency mode=1 and first use </span><span style=' font-family: monospace;'>meshToPet()</span><span> to obtain information about the points </span><span style=' font-family: monospace;'>p</span><span>, edges </span><span style=' font-family: monospace;'>e</span><span>, and triagnles </span><span style=' font-family: monospace;'>t</span><span> of the mesh, such that we can use </span><span style=' font-family: monospace;'>pdeInterpolant()</span><span> to prepare a interpolant structure </span><span style=' font-family: monospace;'>F</span><span> that allows us to find the field at points that are not on grid points. We use it to find the field </span><span style=' font-family: monospace;'>Ez0</span><span> in the center of the cavity and then use that to normalize u = </span><span texencoding="E_z" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="16" height="20" /></span><span> to its maximum value at the center and display it with equipotential lines superimposed. We observe that the equipotential lines at large radius are almost parallel to the z-axis, which is what we would also observe in the analytical solution from Section 5.1. At smaller radii, however, we find the equipotential lines successively more distorted at smaller radii. </span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >mode=1; </span><span style="color: rgb(2, 128, 9);">% mode to view and analyze</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >[p,e,t]=meshToPet(model.Mesh);</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >F=pdeInterpolant(p,t,Ez(:,mode)); </span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >Ez0=evaluate(F,0,0);</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >figure; pdeplot(model,</span><span style="color: rgb(170, 4, 249);">'xydata'</span><span >,Ez(:,mode)/Ez0,</span><span style="color: rgb(170, 4, 249);">'contour'</span><span >,</span><span style="color: rgb(170, 4, 249);">'on'</span><span >); </span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'z [m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'r [m]'</span><span >); axis </span><span style="color: rgb(170, 4, 249);">tight</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S3'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'E_z(r,z)/E_z(0,0)'</span><span >)</span></span></div><div class = 'S4'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="C21980C0" data-scroll-top="null" data-scroll-left="null" data-testid="output_5" style="width: 1327px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" style="width: 560px;"></div></div></div></div></div><div class = 'S0'><span>In the next figure we use the interpolant </span><span style=' font-family: monospace;'>F</span><span> to evaluate </span><span texencoding="E_z" style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAoCAYAAACfKfiZAAACjklEQVRYR+3XO4jUVxQG8N9GwURBRYxvMAZBRSvRwlSKxEICCmoR1ARtRIuAXYJIROOjMQo+sIsgSsRCCwtFBAUV0mglCCEpIoqPxMKEqAgqX7gLy5/Z+c/szmQt9lQzc88957vnfOcxPYZYeobYv2EAwxF47yOwB8uxpM1qeYLJrdxpNQLnsLYYvIpNiJO3+BBjMBdfYDsuYWUnAVzGimLwK5xqYvw0fsfOTgJ4gGnlxVPxuInx3biNC50CMBu/FmN3sLDG8Ne4goedArANx4qxA/iugeFwKXxoW1oh4XmsLpaX4VrFywKswt62vVM7C0biL4zFP5iA1xVHyfV+/NINAJ/hZjGcvH5ZQI/CFGwt0ZmEN90AsAvf1xg+g/UDcZ47dRzI6xOFSHJ9t9wZj0W4iM1I7Q9ImgEYV/I/opTU9AYeAmgpng7Ie00EwvxUQORkab9VP+HF5wN1XpeC44Vk0UuOk+uqpCqedQtAul+6YGQG0o7rJOX6vE6p73l/HJhVBkp0f+sDpJntjN+zhRMtY+gPwBacKFZ+KkxvZjR9ISM4nNjXsvcmJEx3S3uNpMwCoj/5BD9jMfL5fh/F7AgB11de4V7vD40iMLMoZNGIHMUh/IGPMBEfY34hZ+bDB+X1vTtD7o0uBK0C+AZHGgFIvedgXXHSTiSju6HSkLIdBWh48S/Cq0T1cCskbNd5I/1E8GU5SNQyN36oju26VtwJIElbdogsuNVJWjsLBgsgac1ueBB/NzLW7Qh8W9r4o/5e0k0AeXl2hB/x4v8GsBHZJcL8TMyU6p+FC9dxq1kfGGzecz+1n4YzBzswD2vK/4l8v9FtANVHfFoWm+yNvSv+fzrd5EBLkRwGMByBd457Zymtc8y8AAAAAElFTkSuQmCC" width="16" height="20" /></span><span> at z=0 along the radial direction and compare this to the analytical result from Equation 5.21 </span><span texencoding="E_z\propto J_0(2.405 r/R_{cav})" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="129" height="20" /></span><span>, where 2.405 is the first zero of </span><span texencoding="J_0(x)" style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEQAAAAoCAYAAABHJVyTAAAFcklEQVRoQ+2ZZcgtVRSGn6tii4Vit2Jho2JhJ2IHJhYWdne3CLbYCioY2CJ2i9jdYKEitv6wlQfWwP7GmTl7zpnLvT9m/bv37L322u+s9a537W8cvY1BYFyPx1gEekBKGdED0gPSTBITU4YsDFwA7AT81AG3bQJsCBwK/Jnrb2IBZDHgFmAr4OPc4DPW7QZsHn7/ylhPG0BOA9YBVoYx+14CrgKuzDmwYs0cwBPAjsCLQ/po2nYyMC8gOAOtDSCFs9uAreMfjwDrDTylfoHnPwPcD5w5gp+mrZMAzwE3ApcNOmMYQB4F1g7H2wICNKztAxwFLAr8PqyTjH0rAQ8DSwKfNa1vC4jrvwNmBKzJmYGfMwKqWjJtBGdKXzSkjzbbngQ+BXbpEpDlATlD84A120RUWnsAcD4wa0ddZVAoOwPXAAsCn9ctbpshxwGnh7NjgLMHRdHw+2vA19EaR3CTvXUm4Bvg+Ka42wLyNLBahLAM8Hp2OGMXzh3lcixwVqaP6YGNgRWBSYEjgd+SvWqOLYA7gQdrfL4J/AKs0kWGGNC3wGTAV8CcwL+ZlykvM31l/fWD7Aa52QhYC/gDODoASQn9sCg//bwKLFfj8Ppo79OEr/8ta5Mhttqio1wH7D7oFg2/nxNfWHX6UUs/tnr1kEJuB2ANYJto2wL3LvB8jU8J/CRgaeCNqjVtALka2COcbAfc2vIi6fLbQz1OVUr7HJf7A5dEllq2V4Qu+idj814hIFWvd48KyBdRJn8DswA/ZARQt0RNYAlYfm1tqYS7ngX2Bt7OdGJG3QTsGiU7dMkoaCQkTdW3amYAdcu8yLLA1EP4UXn+CEwHnBvCLtfNlsAdwL6RWUMDcjhwXuw+IWm9qcMpoj6XCPE2O3AE8FZFtKNkiO4KHlHuKwVyrbMMSeX6CsDLpQj8ag8AsrckZ/fZFJB3LI13SusLDplyCMku7zkMek7bWargkM2Ae4blEC/5PTB5jOYLVTgqOpDKVQVbmKXhjFLMPsX/m21mnb7ajvsHBgfYWn8FZgDktRw7BTgxZppK3il3GS9vqqet0C9doHlqlEX5cKdVL21w6ZB2BqD48r3jvWST88QNMSn7lXNt8cg6BdiXgJnpOPFKpgO1z/aRyZWPRikgOvdrzQeYWqa7dimwXwxzTqXlL2rrVP0pxS2n1AoSU0ypPQpbIPyU/7/pXmaopWvr/yAEmG33oGQ4FGgvXWdqFMcFy7jSUkDmiWnQhTeHopMoPwFmi+c9FWHZHJbMKIlS5ZmaBz8W7xDqh9QkW0dx5Xid+Rj1YZSsg5nlaGZpFwKWT8Ejdg4/1kM1zhwiBcNS9alyICCCY2u1S5iCloDzgilv8LbaqlF/deApQKJUMaZma9XXfUGy6W+Ca0kZaJVfOULyNrUd222XZlRhxuPjkgSuFDB7VKF1ZtZfDPjhHfIGAuKCuaKl+gpmn7c7yOhOtfb+KnNQkjyV9c4XqRUiymFLWZ2a/s0Qp0/Lsmy+l3hJL3BtTXuV2yRyy8TSaSLXF0LANY4cbaR7Hah2CtPaVN2gtMjWaJrXzT6W0SGAZOngNr7M0r0rXuYcTGutC0AkVbNHUvWpLjX7vYE4VNnyyub5AqaGGeVtpemOjgeWnjPP5YMQ7wIQz7g3mNu2mz73W9OCIZcIWJXZ5i1L/x4zPl7d7W4+de45CAx/7wqQQhLLJ+no7UUdBCXqJlskpmen6PdzAs9cI1+ooxSOWeKtK0DUMLY/R/B1I1hbsJnjS9bjGReQi2ylgtvVX+4k8oNLWdsYSleAeIiTq++t6hJV5PzxPJhK+QxcJuySLgGZsDfp6PQekBKQPSA9IM211WdInyF9hrTqP/8BGsEOOKsBIdMAAAAASUVORK5CYII=" width="34" height="20" /></span><span>. The figure shows good agreement between the two curves, because the center of the cavity is far away from the beam pipe entry points.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >y=0:0.01:R; x=0*L*ones(1,length(y)); </span><span style="color: rgb(2, 128, 9);">% define line</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >Ez=evaluate(F,x,y)/Ez0; </span><span style="color: rgb(2, 128, 9);">% Ez on that line</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >Ez_analytic=besselj(0,2.405*y/R); </span><span style="color: rgb(2, 128, 9);">% eq. 5.21</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >figure; plot(y,Ez,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,y,Ez_analytic,</span><span style="color: rgb(170, 4, 249);">'r*'</span><span >); </span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'r [m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'E_z(r,0)/E_z(0,0)'</span><span >); xlim([0,R]); ylim([0,1.08]);</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'E_z(r,0) along radial line in the center'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S3'><span style="white-space: pre"><span >legend(</span><span style="color: rgb(170, 4, 249);">'Numerical'</span><span >,</span><span style="color: rgb(170, 4, 249);">'J_0(2.405*r/R)'</span><span >)</span></span></div><div class = 'S4'><div class="inlineElement eoOutputWrapper embeddedOutputsFigure" uid="17A77766" data-scroll-top="null" data-scroll-left="null" data-testid="output_6" style="width: 1327px;"><div class="figureElement"><img class="figureImage figureContainingNode" 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" style="width: 560px;"></div></div></div></div></div><div class = 'S0'><span>Finally, we calculate the accelerating field </span><span texencoding="E_z" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="16" height="20" /></span><span> that the beam 'sees', which is along the center line at r=0. We also calculate </span><span texencoding="E_z" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="16" height="20" /></span><span> at half the cavity radius </span><span texencoding="R/2" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="28" height="19" /></span><span>. For comparison we note that the analytic solution from Equation 5.21 for </span><span texencoding="p=k_zL=0" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="77" height="20" /></span><span> is constant along the z-axis. Here, on the other hand, we see a significant distortion. Especially at </span><span texencoding="r=0" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="35.5" height="18" /></span><span> the field decreases towards the cavity ends at </span><span texencoding="z=\pm L/2" style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAAmCAYAAADpyZQRAAAFjklEQVR4Xu2adagtRRzHP88OsLAbCwxU7MZE7BYTxMIOjD9UUBRUVFRsfSoGtihiInaLjSgGBhYqioiJzee+2cO56+7ZObt7z7v33PnBg8c9O9+Z+X1nfjlTSDLpNDBl0u04bZhE+iQ8BIn0RPok1MD43vIMwBvAgcBrbS013fS2NDk2OFsC9wELAT+3NUUivS1Njg3OjcBMwL5twifS62lzNeAUYGNgkRzEM8D9wAX1oDuj5gC+AfYAHinAkrvDgO2AVYE5gbeBJ4HzgN/K5k+kN2NmGeCjLoiTWiA7g9sHuBBYDPg7t0zN/V3h0BXt4GNgR+Cdoh8T6c1IX6lLsd8CiwN/NoPsjH4YeA84vgBPS7I+cBHwJjAboPU5Cpg3fG8AuG7RehLpzRjaC7gtQFwPHNQMrjPam/wlsA7weg5Tc38JsDbwRe63BYAXgWXD3/cGbs+vKZHejKUrg18VxQNwRzO4zujjgEMBLUle7gWmAg+VzKWPfyD8Zlyhyxklk5X0V4MW1mpIkv5cv/4vsCDwXUO8bLg5+d3AOTm8mQHNvqlcmRjQ/QQj1dZbgP0S6dM0kPldlVhXuoM4D5Hmtg1ZMcQJSwOfFQBasPmnYqLvgfmAs4FTY0l34psqgI8GXmpjl9MBow3STZc070qhcmvuS6wNgE1rjp81pGvedDGejiX9ROD8HpNeARwZuShxjCqbiiffvLUNaYP0e4BdwmI2A55qYWES9SlwJnBdTTwjdi+jkb+X939S5tMfDEGJG+su/2nCTgd2Bv6KXJRphYFJU1l4HJE+I6AJnRv4JZjSP5puMNxMfbZ7/bEm3mXhQur3H48l3YNgxGdVp1sWBW4Np/uHmgsaL8Oa3nRz5BfCZrwg27e0sWuBuYA9a+ItAbwL3AwcUYYRG72b/Fv4PwZ4v+aCBjnMwsTqDScsNY/B2p0R8I8NeXPD6UYKLF8D+4cybh08izbibNurSBRL+g3hlj9aZyXTYYzRtBWqMrGJofRyUR7uVUoAngM2DL/pNz0gTcXbfTmgRa1T1Ts5NGY2qXINMaQLZvH+0qa7Gkfjm5h3za/+3INjRUyT2oZ4Sw3izIr6ld1D8Ge0bjm4p1SRbnVHf3V4FVCP34ctejeItSqmGGEfHKEbrY418bIIf37gq9BAeTkCr/uTLcKF3CqUbiuH9yJds3Uu4CmqY26yyYctetcEZ0FSbOn1MUCLma+jZzoypTVeWqGSsdEfmM9b898G+KRkrIfNDKzDYRnpVnOM1G3ea8qGTZqY9w+B5YJClgQ+r1COTQ8vz1I9vvN2Wy8/qw9FrxmaPTv0CK5nD7i2WU0tR6SIdH3VncBpIfzvYx0T5tO6pHsTs+zl1/BwodemdwvEaB2KWqSOXT5gepDsg8fIyuGxhIfprYIB8jpPcMsf5N1zEem27TQ3vsAwb8xahzGLmSjf1CXdrtUJXZu0nuEttQ36eyjWWLCxeqiVzPJ3I+pnS5Rj9W1zYKNI5XlIfJ1jASdG1giPKzvf5kk/BLgmh+QJvbjrb1Z89E36kokqvkpRdGExYplVn7tTiXXshWE07ZOqsiaJnToLYVdHLMQD5ZOo2IzhldCTHwXdTbr/N1d8AtB8WFs3iLNtqJJsxhsU6OMtfuhTkjTTgLm++vbWDqzKWZWyWWu366N5OiA07j1pvt3qvv3Ntt7+6LGuyLW14qtCH37XtgBjcKpIzzD0N1sHn2VDwH/jWaoqcjFr71WRixlf9c0soezqE6ss768a08rvsaS3MlkCGaUB27IWdzTtbXTootWbSI9WVesf2rY2yPMxxkAlkT5QdXcmMyC2o2aq9vygl5BIH7TGp823XqiXt/Wurq9dJNL7UtdwfJxIHw4e+9pFIr0vdQ3Hx4n04eCxr138BzlH7yeeOp/jAAAAAElFTkSuQmCC" width="62.5" height="19" /></span><span> and even 'leaks' somewhat into the beam pipe. The fields </span><span texencoding="E_z" style="vertical-align:-6px"><img src="data:image/png;base64,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" width="16" height="20" /></span><span> at </span><span texencoding="R/2" style="vertical-align:-5px"><img src="data:image/png;base64,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" width="28" height="19" /></span><span>, shown as the red line, is not constant either, but much less distorted.</span></div><div class="CodeBlock"><div class="inlineWrapper"><div class = 'S2'><span style="white-space: pre"><span >x=-0.4:0.01:0.4; y=0*ones(1,length(x)); </span><span style="color: rgb(2, 128, 9);">% line in center of cavity</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >Ez1=evaluate(F,x,y)/Ez0; </span><span style="color: rgb(2, 128, 9);">% Ez on center line</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >y=0.5*R*ones(1,length(x)); </span><span style="color: rgb(2, 128, 9);">% line at R/2</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >Ez2=evaluate(F,x,y)/Ez0; </span><span style="color: rgb(2, 128, 9);">% Ez at R/2</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >figure; plot(x,Ez1,</span><span style="color: rgb(170, 4, 249);">'k'</span><span >,x,Ez2,</span><span style="color: rgb(170, 4, 249);">'r-.'</span><span >); </span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >xlabel(</span><span style="color: rgb(170, 4, 249);">'z [m]'</span><span >); ylabel(</span><span style="color: rgb(170, 4, 249);">'E_z(*,z)/E_z(0,0)'</span><span >); ylim([0,1.08]);</span></span></div></div><div class="inlineWrapper"><div class = 'S8'><span style="white-space: pre"><span >title(</span><span style="color: rgb(170, 4, 249);">'E(*,z) at r=0 and r=R/2'</span><span >)</span></span></div></div><div class="inlineWrapper outputs"><div class = 'S3'><span style="white-space: pre"><span >legend(</span><span style="color: rgb(170, 4, 249);">'E_z at r=0'</span><span >,</span><span style="color: rgb(170, 4, 249);">'E_z at r=R/2'</span><span >)</span></span></div><div class = 'S4'><div 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" style="width: 560px;"></div></div></div></div></div><div class = 'S7'><span>And now it's time to play around with this model. First you may increase the beam pipe radius and second, you might want to change the radius </span><span style="font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: normal; color: rgb(0, 0, 0);">R</span><span> of the cavity to tune it to 500 MHz. In the present configuration it is a bit off-frequency.</span></div>
<br>
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##### SOURCE BEGIN #####
%%
% Companion software for "Volker Ziemann, _Hands-on Accelerator physics using
% MATLAB, CRCPress, 2019_" (https://www.crcpress.com/9781138589940)
%% Pill-box cavity with beam pipe (Section 6.4.2)
% Volker Ziemann, 211124, CC-BY-SA-4.0
%
% *Important:* this example requires the PDE toolbox!
%
% In this example we calculate the eigenfrequencies of a pill-box cavity with
% a beam pipe connected to its center. This will perturb the eigenmodes and eigenfrequencies
% of a pure cavity. We therefore use the PDE toolbox to find the TM eigenmodes
% and note that the system is still rotationally symmetric such that we can use
% a 2D model to find the rotationally symmetric modes.
%
% We first define the beam pipe radius |rr|, the cavity radius |R|, and the
% the cavity length |L| to specify the cavity dimensions.
clear;
rr=0.01 % Slider for the beam pipe radius
R=0.23 % Slider for the cavity radius
L=0.3; % Cavity length
%%
% Now we use these parameters to define the cavity and the beam pipe as three
% polygons |Cav, Pl,| and |Pr,| assemble them in |gd|, define names |ns| and specify
% the relation |sf| among the regions, before we construct the geometry |g| and
% create the model for one parameter |u =| $E_z$. Then we add the geometry |g|
% to it and inspect the model to note the |EdgeLabels| and the |SubDomainLabels.|
Cav=[2;4; -L/2;L/2;L/2;-L/2; 0.0;0.0;R;R]; % cavity
Pl=[2;4; -0.4;-L/2;-L/2;-0.4; 0.0;0.0;rr;rr]; % pipe left
Pr=[2;4; L/2;0.4;0.4;L/2; 0.0;0.0;rr;rr]; % pipe right
gd=[Cav,Pl,Pr]; % assemble geometry
ns=char('Cavity','Pl','Pr')'; % names of the regions
sf='Cavity+Pl+Pr'; % geometry relations
g=decsg(gd,sf,ns);
model=createpde(1);
geometryFromEdges(model,g);
pdegplot(model,'EdgeLabels','on','SubDomainLabels','on'); axis tight
%%
% Since the longitudinal electric field |u =| $E_z$ must vanish on the boundaries
% where it is parallel to the boundaries E1, E9, E10 and on the exit from the
% beam pipe E2 and E3, we select Dirichlet boundary conditions. On the verical
% walls E5 and E12 the electric field is given by the derivative of the longitudinal
% field $E_z$, which implies the use of von-Neumann boundary conditions. Moreover,
% we also use von-Neumann conditions on the symmetry axis E6, E7, and E8.
applyBoundaryCondition(model,'Edge',[1,2,3,9,10],'u',0); % Dirichlet
applyBoundaryCondition(model,'Edge',[6,7,8,5,12],'q',0,'g',0); % Neumann
%%
% The rotational symmetry requires to use the Laplace operator in cylindrical
% coordinates, which has to be brought into Matlab's generic form to specify a
% partial differential equation in divergence form, which is discussed further
% in Section 6.4.2. In the code this is accomplished by using functions |cfun()|
% and |dfun()| when specifying the material properties.
cfun=@(location,state)-location.y;
dfun=@(location,state)-location.y;
specifyCoefficients(model,'m',0,'d',dfun,'c',cfun,'a',0,'f',0);
%%
% At this point we can mesh the geometry...
generateMesh(model,'Hmax',0.01);
%figure; pdemesh(model); axis tight
%%
% ...and solve the eigenvalue system with |solvepdeeig()|, which returns the
% structure |result| that contains the |Eigenvalues| and the |Eigenvectors| as
% members.
result=solvepdeeig(model,[1,800]);
k2=result.Eigenvalues;
Ez=result.Eigenvectors;
%%
% From the eigenvectors, which are $k^2=\omega^2/c^2$ we derive the frequencies
% of the eigenmodes in GHz.
freq_GHz=sqrt(k2')*3e8/(2*pi*1e9)
%%
% Since we are interested in the accelerating mode around 500 MHz, we choose
% to inspect the lowest-frequency mode=1 and first use |meshToPet()| to obtain
% information about the points |p|, edges |e|, and triagnles |t| of the mesh,
% such that we can use |pdeInterpolant()| to prepare a interpolant structure |F|
% that allows us to find the field at points that are not on grid points. We
% use it to find the field |Ez0| in the center of the cavity and then use that
% to normalize u = $E_z$ to its maximum value at the center and display it with
% equipotential lines superimposed. We observe that the equipotential lines at
% large radius are almost parallel to the z-axis, which is what we would also
% observe in the analytical solution from Section 5.1. At smaller radii, however,
% we find the equipotential lines successively more distorted at smaller radii.
mode=1; % mode to view and analyze
[p,e,t]=meshToPet(model.Mesh);
F=pdeInterpolant(p,t,Ez(:,mode));
Ez0=evaluate(F,0,0);
figure; pdeplot(model,'xydata',Ez(:,mode)/Ez0,'contour','on');
xlabel('z [m]'); ylabel('r [m]'); axis tight
title('E_z(r,z)/E_z(0,0)')
%%
% In the next figure we use the interpolant |F| to evaluate $E_z$ at z=0 along
% the radial direction and compare this to the analytical result from Equation
% 5.21 $E_z\propto J_0(2.405 r/R_{cav})$, where 2.405 is the first zero of $J_0(x)$.
% The figure shows good agreement between the two curves, because the center of
% the cavity is far away from the beam pipe entry points.
y=0:0.01:R; x=0*L*ones(1,length(y)); % define line
Ez=evaluate(F,x,y)/Ez0; % Ez on that line
Ez_analytic=besselj(0,2.405*y/R); % eq. 5.21
figure; plot(y,Ez,'k',y,Ez_analytic,'r*');
xlabel('r [m]'); ylabel('E_z(r,0)/E_z(0,0)'); xlim([0,R]); ylim([0,1.08]);
title('E_z(r,0) along radial line in the center')
legend('Numerical','J_0(2.405*r/R)')
%%
% Finally, we calculate the accelerating field $E_z$ that the beam 'sees', which
% is along the center line at r=0. We also calculate $E_z$ at half the cavity
% radius $R/2$. For comparison we note that the analytic solution from Equation
% 5.21 for $p=k_zL=0$ is constant along the z-axis. Here, on the other hand, we
% see a significant distortion. Especially at $r=0$ the field decreases towards
% the cavity ends at $z=\pm L/2$ and even 'leaks' somewhat into the beam pipe.
% The fields $E_z$ at $R/2$, shown as the red line, is not constant either, but
% much less distorted.
x=-0.4:0.01:0.4; y=0*ones(1,length(x)); % line in center of cavity
Ez1=evaluate(F,x,y)/Ez0; % Ez on center line
y=0.5*R*ones(1,length(x)); % line at R/2
Ez2=evaluate(F,x,y)/Ez0; % Ez at R/2
figure; plot(x,Ez1,'k',x,Ez2,'r-.');
xlabel('z [m]'); ylabel('E_z(*,z)/E_z(0,0)'); ylim([0,1.08]);
title('E(*,z) at r=0 and r=R/2')
legend('E_z at r=0','E_z at r=R/2')
%%
% And now it's time to play around with this model. First you may increase the
% beam pipe radius and second, you might want to change the radius $R$ of the
% cavity to tune it to 500 MHz. In the present configuration it is a bit off-frequency.
##### SOURCE END #####
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