Collaborative Webmeeting November 24th, 2010 Geneve / Darmstadt Calculation of Beam Coupling Impedance for ferrite loaded kickers: Studies for the SIS-100 kicker system Lukas Hänichen Collaborative Webmeeting November 24th, 2010 Geneve / Darmstadt 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 1 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Coupling Impedance calculation Hysteresis losses Thermal loading Outline Introduction Core tasks Coupling Impedance calculation Hysteresis losses Thermal loading Conclusive Remarks 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 2 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Introduction: Kicker principle Provide transverse kick to extract particle beam from synchrotron ring Multiple units in a single vessel Ferrite block Coil Pulse former (PFN) Support structures Strong beam coupling also in idle state PFN 0.8 m 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 3 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Core tasks Coupling Impedance calculation Ferrite modeling of hysteresis Sensitivity on ferrite data Beam induced hysteresis losses Beam current spectrum Heat energy Thermal loading Heat distribution Nonlinearity 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 4 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Coupling Impedance calculation (1) : Ferrite hysteresis Material datasheet provides complex permeability as a function of frequency Complex permeability maintains a linear dependency “Tilted ellipse” approximates hysteresis loop 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 5 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Coupling Impedance calculation (2) : Obtaining reliable data for ferrite Different for every frequency Typically provided by manufacturer datasheet or Bench measurements Tolerances 10 … 30 % ??? 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 6 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Coupling Impedance calculation (3) : Sensitivity analysis High computational accuracy is of no use when material parameters have high uncertainty  influence has to be studied Recomputing for altered material data is costly Use perturbation approach with reference solution instead Calculate tolerances from reference solution reference case perturbed case Using a suitable expansion for Matrix A yields 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 7 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Hysteresis losses : For a given beam current spectrum the total heat power is given by In progress: impedance calculation including recent changes applying reference bunch scenarios studying influence / effectiveness of geometry and eddy current traps 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 8 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Thermal loading (1) : Total absorbed power Non-linear coupled problem since Heat energy is not equally distributed (FOURIER heat equation) Common approximation: assuming a constant average q to calculate the temperature increase This “0D” Model predicts a linear temperature increase 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 9 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Thermal loading (2) : Alternate approaches A more accurate approach would be to use the local losses from EM simulation Assumptions can be made for the temperature dependence in the longitudinal direction 1D Model: Temperature gradient for wall cross-section of ferrite 2D Model: Temperature gradient for kicker cross-section 3D Model Coupled Simulation 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 10 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Conclusive remarks Everything strongly depends on the material data Studies are required how much tolerances reflect on the results Electromagnetic-Thermal Coupled problem Still in progress : Achieve higher computational headroom for more more complicated structures Calculation for full SIS-100 kicker geometry Questions, Remarks, Discussion welcome… thank you ! 9. Dezember 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Dipl.-Ing. Lukas Hänichen | 11 9. Dezember 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland