Wake fields and impedances calculations with GdfidL, MMM and CST for - PowerPoint PPT Presentation

Wake fields and impedances calculations with GdfidL, MMM and CST for benchmarking purposes Oscar Frasciello 1 , M. Zobov 1 , N. Biancacci 2 1 INFN, Laboratori Nazionali di Frascati, Rome, Italy 2 CERN, Geneva, Switzerland Impedance meeting, CERN, February 2nd, 2015 Aknowledged people: W. Bruns, D. Alesini, A. Gallo

General outline Resistive insert benchmark I Analytical and Numerical Loss and Kick factors; II Computed transverse impedance; Simulation of S 11 measurement setup; TT2-111R ferrite loaded pillbox benchmark I Longitudinal; II Transverse Dipolar; Tsutsui model for TT2-111R ferrite loaded kicker benchmark I Longitudinal; II Transverse Dipolar; III Transverse Quadrupolar. Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Resistive insert GdfidL model Whole view One quarter view L=30 cm, a=5 mm, b=10 mm, σ =7 . 69 · 10 5 S/m The length is chosen in order to minimize z ends contributions Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Resistive insert For Azimuthally Symmetric Thick Resistive Walls Longitudinal Loss factor Transverse kick factor � 3 � � 2Z 0 ρ cL � 5 � Z 0 ρ k ⊥ = σ z Γ cL � k � = 2 Γ π 2 b 3 4 4 π b σ 3 / 2 4 Loss and Kick factors benchmark: GdfidL vs. Analytical formulas Some excess in Kicks may be due to the rough mesh Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Resistive insert Transverse impedance benchmark: GdfidL, CST, MMM Results are shown down to ∼ 10 MHz because this is the frequency range of interest up to now. We also got results down to fractions of MHz (not shown here) Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Simulation of S 11 measurement setup In our opinion it was a very useful method to arrange simple coaxial probe measurement simulations, in order to check for the numerically computed S-parameters to be fully in agreement with theoretical prediction. Measurement layout (From R. Boni et al. , Simulated measurement LNF-93/014) Analytical formulas � µ r S 11 = ∆ · tanh ( γ L ) − 1 γ = j ω √ εµ ; ∆ · tanh ( γ L )+ 1; ∆ = ε r Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Simulation of S 11 measurement setup µ experimental data (Courtesy of B. Salvant) & Data fits with n th order Lorentz function & GdfidL DUT model S 11 results comparison Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

TT2-111R ferrite loaded pillbox The simple pillbox geometry Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

TT2-111R ferrite loaded pillbox Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Tsutsui model for TT2-111R ferrite kicker Kicker model in CST and GdfidL Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Tsutsui model for TT2-111R ferrite kicker Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Conclusions We simulated several impedance standard test cases in order to benchmark analytical models and numerical codes. Apart for small discrepancies, all tests resulted in a quite good agreement between theory, MMM, CST and GdfidL computations For the resistive insert a good agreement was found between the loss and kick factors obtained analytically and in GdfidL simulations. There is a reasonable good agreement between MMM GdfidL and CST results. The oscillatory behaviour of the CST calculated impedance is believed to be removable using better windowing techniques in the wake Fourier transforms. TT2-111R measured magnetic permeability was implemented into GdfidL code, by means of a 3 rd order Lorentz function fit. S 11 from coaxial cable measurement simulation was benchmarked with analytical formula and FD code HFSS, while ferrite filled pillbox longitudinal impedance with a MMM code and CST PS; TT2-111R ferrite implementation was also tested benchmarking GdfidL with MMM and CST for a simple pillbox loaded with ferrite in its toroidal region. Very good agreement was found for both the longitudinal and dipolar transverse impedance We finally simulated a TT2-111R ferrite loaded Tsutsui model kicker with CST and GdfidL, benchmarking with analytical outcome. Here we exploited the distinguishing role of ε r . In all the tests above good results were found with GdfidL setting it to 1. Unless it is properly set to 12.5, the real value for that ferrite, no agreement can be reached for GdfidL computations with either theory or CST. Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

The end... Thanks for your kind attention Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST

Appendix: ε r contribution to Z � and Z ⊥ in Tsutsui models For axisymmetirc model: � µ ′′ Z � L ≃ ( 1 − j ) Z 0 r 2 ε ′ 2 π b r For rectangular model: ∞ E ( S ) xn sh + E ( S ) Z � yn ch L = j ∑ I 0 � k ( 1 + ε r µ r ) shch + kyn � kxn k ( µ r sh 2 tn − ε r ch 2 ct ) / ( ε r µ r − 1 ) − k kxn shch n = 0 � − 1 ∞ � k ( 1 + ε r µ r ) shch + kyn kxn k ( µ r sh 2 tn − ε r ch 2 ct ) Z X k 2 L = j Z 0 − k ⊥ ∑ xn k xn shch ( ε r µ r − 1 ) 2 a k n = 0 � − 1 ∞ � k ( 1 + ε r µ r ) shch + kyn kxn Z Y k ( µ r ch 2 tn − ε r sh 2 ct ) k 2 L = j Z 0 − k ⊥ xn ∑ k xn shch 2 a k ( ε r µ r − 1 ) n = 0 In all above formulae: sh = sinh ( k xn b ) ; ch = cosh ( k xn b ) ; tn = tan ( k yn ( b − d )) ; ct = cot ( k yn ( b − d )) ′ ′′ ε r = ε r − j ε r + σ j ωε 0 ′ ′′ µ r = µ r − j µ r Oscar Frasciello et al. Wake fields and impedances calculations with GdfidL, MMM and CST