Calculation of Eigenfields for the European XFEL Cavities
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1 Calculation of Eigenfields for the European XFEL Cavities Wolfgang Ackermann, Erion Gjonaj, Wolfgang F. O. Müller, Thomas Weiland Institut Theorie Elektromagnetischer Felder, TU Darmstadt Status Meeting December 21, 2010 DESY, Hamburg December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 1
2 Overview Task - Calculation of fields for the European XFEL cavities in 3D considering coupling ports as well as non-ideal geometries - Coupling ports: Modeling of ports Include ports in the eigenvalue formulation Implementation for large scale applications - Non-ideal geometries Support flexible geometry description in 3D December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 2
3 Motivation Particle accelerators - Linear accelerator at DESY, Hamburg Cavity 1.3 GHz Cavity 3.9 GHz December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 3
4 Computational Model Superconducting resonator - Geometry 9-Cell Cavity Beam Tube Input Coupler Upstream Higher Order Mode Coupler Downstream Higher Order Mode Coupler December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 4
5 Computational Model Available grid structures Staircase -grid partially filled cells tetrahedral mesh December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 5
6 Computational Model Modeling using CST Studio Suite - 3d.tet: NodeID, X, Y, Z EdgeID, NodeID0, NodeID1 FaceID, EdgeID0, EdgeID1, EdgeID2 ElemID, FaceID0, FaceID1, FaceID2, FaceID3 ElemID, NodeID0, NodeID1, NodeID2, NodeID3 Object3D GroupID, #Elems <immediately followed by> ElemID List Object2D GroupID, #Faces <immediately followed by> FaceID List Object1D GroupID, #Edges <immediately followed by> EdgeID List Object0D GroupID, #Nodes <immediately followed by> NodeID List - bc3d.tet Obj3D_ID, MediaCode Obj2D_ID, BCCode Obj1D_ID, BCCode PEC, PMC and port boundary conditions can be extracted December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 6
7 Computational Model Modeling using CST Studio Suite modify point locations but maintain the topology - 3d.tet: NodeID, X, Y, Z EdgeID, NodeID0, NodeID1 FaceID, EdgeID0, EdgeID1, EdgeID2 ElemID, FaceID0, FaceID1, FaceID2, FaceID3 ElemID, NodeID0, NodeID1, NodeID2, NodeID3 Object3D GroupID, #Elems <immediately followed by> ElemID List Object2D GroupID, #Faces <immediately followed by> FaceID List Object1D GroupID, #Edges <immediately followed by> EdgeID List Object0D GroupID, #Nodes <immediately followed by> NodeID List CST 3d.tet Modify 3d.tet December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 7
8 Computational Model Modeling using CST Studio Suite - 3d.tet: standard points linear element curvilinear element only linear geometry transformation available December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 8
9 Computational Model Modeling using CST Studio Suite - 3d.tet: additional points linear element curvilinear element insert additional control points (at the surface) December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 9
10 Computational Model Modeling using CST Studio Suite - 3d.slim: control points linear element curvilinear element available in CST but not yet used here (ToDo) December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 10
11 Motivation Input coupler and coupler to extract unwanted modes Coaxial Line Beam Tube Antennas Coaxial Input Coupler Downstream Higher Order Mode Coupler December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 11
12 Motivation Input coupler and coupler to extract unwanted modes Coaxial Line Beam Tube in linear scale Antennas Coaxial Input Coupler Downstream Higher Order Mode Coupler f 0 = GHz December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 12
13 Motivation Input coupler and coupler to extract unwanted modes Coaxial Line Beam Tube in linear scale Antennas Coaxial Input Coupler Downstream Higher Order Mode Coupler f 0 = GHz December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 13
14 Motivation Problem definition - Accelerating field 9-Cell Cavity including couplers Determine the accelerating -mode with high precision December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 14
15 Computational Model Problem formulation - Fundamental equations Maxwell s equations - Boundary conditions Material relations December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 15
16 Motivation Wave propagation in the applied coaxial lines - Main coupler 60.0 mm 12.5 mm - HOM coupler 16.0 mm 3.4 mm Dispersion relation propagation damping TE 11 TE f 0 = 1.3 GHz TEM f 0 = 1.3 GHz TEM TE 11 TE December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 16
17 Computational Model Problem formulation - Local Ritz approach + boundary conditions continuous eigenvalue problem Galerkin vectorial function scalar coefficient global index number of DOFs discrete eigenvalue problem December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 17
18 vector scalar Pär Ingelström, A New Set of H(curl)-Conforming Hierarchical Basis Functions for Tetrahedral Meshes, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 1, JANUARY 2006 Computational Model Numerical formulation - Function definition FEM06: lowest order approximation (edge elements, Nedelec) December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 18
19 vector scalar Pär Ingelström, A New Set of H(curl)-Conforming Hierarchical Basis Functions for Tetrahedral Meshes, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 1, JANUARY 2006 Computational Model Numerical formulation - Function definition FEM12: higher order approximation December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 19
20 vector scalar Pär Ingelström, A New Set of H(curl)-Conforming Hierarchical Basis Functions for Tetrahedral Meshes, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 1, JANUARY 2006 Computational Model Numerical formulation - Function definition FEM20: higher order approximation December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 20
21 Computational Model Numerical formulation - Implementation contribution of element-matrices ready availabe December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 21
22 Computational Model Eigenvalue formulation - Fundamental equation - Matrix properties Notation: A - stiffness matrix B - mass matrix C - damping matrix - Fundamental properties for proper chosen scalar and vector basis functions static or dynamic December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 22
23 Computational Model Fundamental properties - Number of eigenvalues Matrix B nonsingular: matrix polynomial is regular 2n finite eigenvalues Notation: A - stiffness matrix B - mass matrix C - damping matrix - Orthogonality relation If the vectors and are no longer B-orthogonal: December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 23
24 Computational Model Fundamental properties - Orthogonality relation - Scalar product 1) 2) 3) currently not available December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 24
25 Computational Model Eigenvalue formulation - Fundamental equation A, B, C: real symmetric conjugate complex eigenvalues Notation: A - stiffness matrix B - mass matrix C - damping matrix - Companion notation real asymmetric matrices real symmetric matrices December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 25
26 Computational Model Eigenvalue solution - Fundamental equation - Subspace projection method Notation: A - stiffness matrix B - mass matrix C - damping matrix - Companion notation for the projected system December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 26
27 Numerical Examples Problem definition - Geometry TESLA 3 rd harmonic 9-cell cavity including couplers December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 27
28 Numerical Examples Problem definition - Geometry 9-Cell Cavity including couplers ParMeTiS, VTK and CST - Studio Suite Distribution on 64 nodes - Task Search for the - mode field distribution December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 28
29 Numerical Examples Efficient solution of large problems - Domain composition cavity model domain #2 domain #1 parallel computing December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 29
30 Numerical Examples Fields along the axis of an accelerator cavity 9-Cell Cavity including couplers E z Longitudinal electric field strength z December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 30
31 Field component, Ex Ez0 Numerical Examples Simulation results reduced linear hierarchical set of basis functions cells reduced quadratic full linear Longitudinal coordinate, z m December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 31
32 Field component, Ex Ez0 Numerical Examples Simulation results reduced linear hierarchical set of basis functions cells reduced quadratic full linear Longitudinal coordinate, z m December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 32
33 Numerical Examples Transversal grid information - Cut plane plots Equator Iris unsymmetric mesh generation December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 33
34 Numerical Examples Symmetric mesh generation CST Microwave Studio TESLA 9 cell cavity Beam tube Higher order mode coupler (HOM) Idea: 1) Meshing performed only on ¼ of the model 2) Copy mesh to assemble the full information Coaxial coupler HOM December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 34
35 Numerical Examples Transversal grid information - Cut plane plots Equator Iris symmetric mesh generation December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 35
36 Numerical Examples Simulation results - Transverse mesh properties arbitrary distribution of tetrahedra tetrahedra faces aligned along coordinate faces symmetric distribution of tetrahedra December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 36
37 Field component, Ex Ez0 Numerical Examples Simulation results reduced quadratic set of basis functions cells cells cells Longitudinal coordinate, z m December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 37
38 Numerical Examples Simulation results Symmetric mesh: cells DOFs c 0 B y c 0 B x c 0 B z (no contribution) Symmetric mesh: cells DOFs December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 38
39 Numerical Examples Simulation results F y F x z z c 0 B x E y c 0 B y E x Contributions to the force for a particle moving with speed of light along the axis December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 39
40 Computational Model Eigenvalue distribution 0 f/mhz f/mhz target frequency search direction desired mode December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 40
41 Motivation Superconducting Resonator 9-Cell Cavity Beam Tube Input Coupler Upstream Higher Order Mode Coupler Downstream Higher Order Mode Coupler December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 41
42 f 0 = GHz f 0 = GHz Numerical Examples in linear scale December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 42
43 f 0 = GHz f 0 = GHz Numerical Examples in linear scale December 21, 2010 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Wolfgang Ackermann 43
44
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