COMBI Improved Field Solver and Space Charge Adrien Florio 22nd - PowerPoint PPT Presentation

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion COMBI Improved Field Solver and Space Charge Adrien Florio 22nd February 2016 COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion New numerical solver § Aim: Lessen numerical noise for head-on simulations COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion Fixed Fast Multipole Method Fast Polar Poisson Solver F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion § Far-field and nearest-neighbours field decomposition § Efficient far-field computation based on multipole expansion COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion ρ p r q9 exp p ´ r 2 2 σ 2 q 0 . 4 0 . 2 E p r q 0 N “ 256 p “ 8 ´ 0 . 2 Analytic. ´ 0 . 4 ´ 4 ´ 2 0 2 4 r σ Errors 1 ¨ 10 ´ 4 0 . 5 ∆ 0 ´ 0 . 5 ´ 1 ´ 4 ´ 2 0 2 4 r σ COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion x “ r cos p θ q r P r 0 , r max s y “ r sin p θ q B r B r φ p r , θ q ` 1 r B r φ p r , θ q ` 1 r 2 B θ B θ φ p r , θ q “ ´ ρ Ó Fourier expansion r B r φ n p r q ´ n 2 B r B r φ n p r q ` 1 r 2 φ n p r q “ ´ ρ n COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion x “ cos p θ q f : r 0 , 1 s Ý Ñ r 0 , 8r u ÞÝ Ñ f p u q y “ sin p θ q B r B r φ p r , θ q ` 1 r B r φ p r , θ q ` 1 r 2 B θ B θ φ p r , θ q “ ´ ρ Ó Fourier expansion r B r φ n p r q ´ n 2 B r B r φ n p r q ` 1 r 2 φ n p r q “ ´ ρ n COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion x “ f p u q cos p θ q f : r 0 , 1 s Ý Ñ r 0 , 8r u ÞÝ Ñ f p u q y “ f p u q sin p θ q f 1 p u q 2 B u B u φ p u , θ q ` f 1 p u q 1 f p u q B u φ p u , θ q ´ ¯ ´ f 2 p u q 1 1 ` f 1 p u q ` B θ B θ φ p u , θ q “ ´ ρ p u , θ q f 1 p u q 2 f p u q 2 Ó Fourier expansion f 1 p u q 2 B u B u φ n p u q ` f 1 p u q 1 f p u q B u φ n p u q ´ ¯ n 2 ´ f 2 p u q 1 ´ f 1 p u q ` φ n p u q “ ´ ρ n p u q f 1 p u q 2 f p u q 2 COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion Finite difference scheme for u dependence. g p´ r , θ q “ g p r , θ ` π q 8 8 g n p´ r q e in θ “ ÿ ÿ p´ 1 q n g n p r q e in θ ´8 ´8 ñ g n p´ r q “ p´ 1 q n g n p r q ù COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion Finite difference scheme for u dependence. g p´ r , θ q “ g p r , θ ` π q 8 8 g n p´ r q e in θ “ ÿ ÿ p´ 1 q n g n p r q e in θ ´8 ´8 ñ φ n p u 0 q “ p´ 1 q n φ n p u 1 q ù COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion ρ p x , y q9 exp p´ x 2 x ´ y 2 y q with σ x σ y “ 5 2 σ 2 2 σ 2 0 . 1 E p x , 0 q 0 . 05 0 0 10 20 30 40 50 60 70 80 x σ x COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion ρ p x , y q9 exp p´ x 2 x ´ y 2 y q with σ x σ y “ 5 2 σ 2 2 σ 2 0 . 1 E p x , 0 q 0 . 05 0 0 1 2 3 4 5 x σ x COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion Conv. rates: FFT=1.95, F2M2=1.91, FPPS=1.96 FFT ´ 2 F2M2 log 10 p max p ∆ qq FPPS ´ 3 ´ 4 ´ 5 4 5 6 7 8 9 log 2 p N q COMBI Improved Field Solver and Space Charge

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion Timing 10 4 10 2 t r s s 10 0 10 ´ 2 10 ´ 4 0 200 400 600 800 1 , 000 N COMBI Improved Field Solver and Space Charge

COMBI Improved Field Solver and Space Charge Adrien Florio 22nd - PowerPoint PPT Presentation

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion COMBI Improved Field Solver and Space Charge Adrien Florio 22nd February 2016 COMBI Improved Field Solver and Space Charge F2M2 FPPS F2M2, FPPS

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Measurements and modeling of space charge assisted photoemission at PITZ M.Krasilnikov for the

Charge transport in disordered organic field-effect transistors Eduard Meijer Charge transport

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COMBI Improved Field Solver and Space Charge Adrien Florio 22nd - PowerPoint PPT Presentation

F2M2 FPPS F2M2, FPPS & FFT COMBI, FPPS & HFMM OpenMP FPPS Space Charge Conclusion COMBI Improved Field Solver and Space Charge Adrien Florio 22nd February 2016 COMBI Improved Field Solver and Space Charge F2M2 FPPS F2M2, FPPS

Ions Transport equations and El.Field Distortion from Space Charge in LAr Ionization Chambers

Hollow Bunches for Space Charge Mitigation Adrian Oeftiger Space Charge 2017, GSI, Germany

Outline Introduction to problem compressibleInterFoam solver Equations for electric field

1 AP Physics C E &amp; M Electric Charge &amp; Field 20151229 www.njctl.org 2 Electric

PIC Simulation of Space Charge Compensation by Electron Lens Eric G. Stern for the Space Charge

Electric Charge and Field the density of the negative charge is C greater on the bottom of the

1 GeV FFAG Space charge studies update 28/3/12 Suzie

Electric Charge and Atomic Structure Return to Table of Contents Slide 5 / 95 Electric Charge

CASA Seminar Self- -consistent Space Charge consistent Space Charge Self Distributions: Theory

Space Charge Effect at ProtoDUNE Michael Mooney BNL ProtoDUNE Measurements Meeting December 22

Particle in a static E-field Consider a charge particle q interacting with a E-field E =E x .

NPSOLVER A SAT Based Solver For Optimization Problems Norbert Manthey and Peter Steinke Trento,

Dispersion and space charge in circular accelerators Y. S. Yuan, O. Boine-Frankenheim, G.

Gmunu : Toward multigrid based Einstein field equations CHEONG, Chi-Kit field equations solver

Agent Coordination Mechanism s in the COMBI NED System s First Aid Case Patrick Storm s

Measurements and modeling of space charge assisted photoemission at PITZ M.Krasilnikov for the

Charge transport in disordered organic field-effect transistors Eduard Meijer Charge transport

Electric Charge and Field Multiple Choice Slide 2 / 34 1 An isolated conducting sphere is

Origin of Magnetic field A current (or moving charge) experience a magnetic force when it is in a

x 2 ( x 2) dx A. 0 B. 2 C. 4 D. E. Something else A point charge

Space Charge Efgects in LArTPCs Michael Mooney Colorado State University Workshop on

e.m. field of charge in rectilinear motion I Start with Maxwells equations Lets work

SUBTOPIC Charge units Electric field Electric force &amp; Coulombs Law

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