Coupling Impedance of SIS18 and SIS100 beampipe CERN-GSI-Webmeeting
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1 Coupling Impedance of SIS18 and SIS100 beampipe CERN-GSI-Webmeeting 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 1
2 Contents Motivation / Overview / Definitions Analytical calculation - Helmholtz Eq. & relativistic motion - Wire measurements - Wall current - Impedance results Lumped element circuit Numerical calculation - Method & results - SIS18 - SIS100 Conclusion and outlook 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 2
3 Motivation by SIS18 and SIS100 Stainless steel elliptical pipe SIS18 SIS100 Fast ramped synchrotron magnets Eddy currents in the pipe wall create heat and field errors Wall thickness 0.3 mm < skindepth at revolution frequency EM-Fields at low frequency can escape the pipe Objects outside the pipe might affect the impedance / the beam stability 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 3
4 The coupling impedance spectrum in SIS18 and SIS100 Dominating devices 1 MHz 50 MHz 1 GHz f Beampipe (wall current) MA Cavities (Broadband) Kicker, loading network (PFN) Ferrite Cavities (Narrowband) Kicker, Ferrite yoke Kicker Waveguide cutoff of beampipe (structural dependence) Rough estimates! Imaginary part dominated by SPACE CHARGE! Pics. taken from SIS100 design spec. 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 4
5 Definition of coupling impedances Rigid beam assumption or single charge uniformly moving Finite integration length due to infinite pipe length Focus on real part of resistive wall impedance! Current dipole moment Panofski-Wenzel relation Dipolar beam current Proof of equivalence: See e.g. R. Gluckstern, CERN Accelerator School, October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 5
6 Helmholtz wave equation Combination of Faraday s law and Ampere s law in FD: Cylindrical geometry: m: Azimuthal mode number m=0 dominates longitudinal impedance m=1 dominates transverse impedance Radius of the beam Displacement of the beam 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 6
7 Source terms for Helmholtz equation Beam is modeled as charged disc traveling with velocity v Transverse coordinates Magnitude independent of beam velocity!!! Harmonic z-dependence provides: In metal or vacuum: Axial model equation 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 7
8 Source Fields Coulomb field in moving frame x Observation point Lorentz transformation to lab-frame y v z Source Fields 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 8 TEM Mode!
9 Fields of a moving charge of 1 As as observed in the lab frame Distance: TD FD 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 9
10 Measuring coupling impedance using one or two wires TEM Mode as in coax-line Measurement of forward transmission (S 21 ) by Network Analyzer For electrically short Device Under Test (DUT) waves propagate only in radial direction Approximation by an entirely 2D model The radial model 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 10
11 Bench measurements and the radial model: Charge and current decoupled Resistive wall coupling impedance only due to current Solved by Hankel-functions Sommerfeld radiation condition on the outside Can be obtained from the axial model equation Connection of both models is unphysical! See H. Hahn, PRSTAB, October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 11
12 Comparison of axial and radial model; Magneto-Quasi-Static approximation Radial propagation constant in vacuum Removed due to the choice of modified Bessel functions Radial propagation constant within the metal wall Nonrelativistic motion has to be excluded! Both models show same behaviour in MQS case! 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 12
13 Comparison of axial and radial model; Inner surface impedance Wall coupling impedance (excluding direct space charge): Constant in front of hom. solution inside the pipe, decelerating field Behaviour of the space beyond an arbitrary cylindrical surface Within the metal wall: Agreement between both models in the MQS case Only difference between the two models is outside surface impedance! 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 13
14 Outside surface impedance Skin effect Open BC: Closed BC: Lengthy expressions Frequency with depends on: Evanescent wave Radially propagating wave (Sommerfeld condition!) Boundary radius h 2 (weak dependence, closed boundary only!) Relativistic velocity (strong dependence, axial model only!) 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 14
15 Longitudinal Impedance Result Plateau: Ohmic resistance At high frequency: Skin effect At low frequency: Bypass due to outside surface impedance suppressed outside longitudinal electric field 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 15
16 Wall current and shielding effectiveness Axial model Radial model PEC pipe: (surface current) 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 16 For comparison: FCC Class B shielding requirement
17 Transverse Impedance Proportional to v! ReWall: Implementation of Axial Model by N.Mounet, CERN Radial model Axial model Monopole Dipole 2 components Current in transmission line 3 components Current loop 3 components TEM+TM01 6 components TEM+TM11+TE11 Hybrid mode! 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 17
18 Simplified Lumped Element Circuit according to the radial model (1) Radius of boundary 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 18
19 Simplified Lumped Element Circuit according to the radial model (2) Independent of boundary! E x does not contribute to resistive wall impedance B y is independent of the velocity! Nassibian and Sacherer, Methods for measuring transverse coupling impedances in circular accelerators L. Vos, The transverse impedance of a cylidrical pipe with arbitrary surface impedance 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 19
20 Numerical calculations with CST EMS according to the radial model Power loss calculation with CST EM STUDIO MQS Frequency-Domain T. Kroyer, Simulation of the low frequency collimator impedance CERN, Tech.Rep., 2008 Radial model: Agreement Axial model: Disagreement due to outside surface impedance ReWall: Implementation of Axial Model by N.Mounet, CERN In agreement with radial model 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 20
21 Results for the SIS18 synchrotron, transverse coasting beam instability measurement Courtesy of V. Kornilov H Revolution frequency V Lowest f sees highest imp!!! Transverse Impedance provides coherent force coherent instability 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 21
22 Numerical LF transverse impedance model for SIS18 and measurement Obtained by V. kornilov from measured transverse coasting beam instability rise time Drift sections contribute negligibly small! No other impedance sources at LF! Cannot be calculated by analytical model for circular pipe! (equivalent radius frequency dependent) 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 22
23 Results for the SIS18 synchrotron, numerical transverse impedance Obtained by V. kornilov from measured transverse coasting beam instability rise time Rel. difference between numerical simulation and measurement: Vertical +56% Horizontal: -35% Reason for higher measured vertical impedance: closed orbit deviation Reason for lower measured value: unknown (under investigation) 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 23
24 Transverse impedance of different proposed setups for SIS100 pipe Longitudinal E-field at 100kHz (strongly clamped) 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 24
25 Transverse impedance of different proposed setups for SIS100 pipe (2) Lowest relevant frequency (spec.) Outside equipment contributes only below f g! 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 25
26 Transverse impedance of different proposed setups for SIS100 pipe (3) Lowest relevant frequency (spec.) Outside equipment contributes only below f g! 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 26
27 Relative increase of transverse impedance for displaced excitation in elliptical pipe SIS100 dipole chamber exemplary chosen 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 27
28 Summary and conclusion Longitudinal impedance of circular pipe obtained analytically for arbitrary velocity (axial model) Fields in ultrarelativistic limit behave like TEM mode Motivates wire measurements and numerical method (radial model) Difference between radial and axial model for long.imp. in the ultrarelativistic limit Only due to outside surface impedance No difference between both for the transverse impedance Demonstrated by lumped element circuit Pipe provides good shielding for frequencies higher than f g Onset of wall current Numerical method has been applied to SIS18 and SIS100 beampipes In a certain tolerance range, agreement between simulation and SIS18 transverse coasting beam instability measurements Closed orbit deviation increases impedance significantly 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 28
29 Outlook More measurement points and error range of coasting beam instability growthrates in order to verify LF impedance model of SIS18 Numerical method according to radial model can be used for calculation of real part of coupling impedance for devices with Source fields as excitation terms in numerical field simulation codes (FIT, FEM) in frequency domain will be implemented This allows also higher frequencies & 3D structures (Kicker, ) Cross-check of material data for ferrites (stripline method) In the near future, we will measure the SIS100-kicker impedance at GSI using the wire/coil technique Currently acquiring money to buy a NWA and LCR-meter or combined device Can you recommend a particular device??? 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 29
30 Thank you very much for your kind attention Any questions? 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 30
31 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 31
32 Field matching with MATHEMATICA Generalized multilayer structure N layers, 2N-2 constants to determine N-1 surfaces with 2 continuity conditions each Conditions are formalized by matrices Consecutive multiplications lead to 2 by 2 system for decelerating field A and outside field F Coefficients very lengthy and complicated expressions 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 32
33 Beam induced heat load in SIS100 cryo-dipoles Bunches periodically traverse Fourier series decomposition of longitudinal bunch shape Only high frequencies (>1/T=hf 0 =2.55MHz) contribute Challenge: Skindepth has to be resolved h: number of bunches in the ring Fourier coefficient Total Power at flat top: 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 33 Fourier harmonic
34 Longitudinal impedance of different proposed SIS100 pipes 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 34
35 Monopolar longitudinal E-field 23 October 2011 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder Uwe Niedermayer 35
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