Numerical Stability of the Pseudo- Spectral EM PIC Algorithm* Brendan Godfrey, IREAP, U Maryland Jean-Luc Vay, Accelerator & Fusion Research, LBNL Irving.

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Presentation transcript:

Numerical Stability of the Pseudo- Spectral EM PIC Algorithm* Brendan Godfrey, IREAP, U Maryland Jean-Luc Vay, Accelerator & Fusion Research, LBNL Irving Haber, IREAP, U Maryland LBNL, 19 June 2013 *Research supported in part by US Dept of Energy

Pseudo-Spectral “Analytical” Time Domain (PSATD) Algorithm* Numerical Cherenkov instability largely eliminated for PSATD relativistic beam simulations Numerical stability software collection at – Contains this talk, some software; more to come Algebra omitted from this talk available at Details from *Introduced by I. Haber, et. al., Sixth Conf. Num. Sim. Plas. (1970) Expanded upon by J.-L. Vay, et. al., paper 1B-1, PPPS /19/20132

Generalized PSATD Algorithm 6/18/20133

2-D High-γ Dispersion Relation 6/18/20134

PSATD Normal Modes 6/18/2013 5

Full Dispersion Relation Growth Rates 6/19/

6/18/20137

8 Red=1 Purple=0

Linear Interpolation, No Filter, γ=130 6/18/20139

Cubic Interpolation, Filter, γ=130 6/18/ Numerical Cherenkov instability largely eliminated Option (c) residual growth a finite-γ effect

Option (c), Cubic Interpolation, Variable Width Sharp Filter, γ=130 6/18/201311

WARP Simulations Confirm Numerical Cherenkov Instability Suppression 6/18/ Numerical energy growth in 3 cm, γ=13 LPA segment FDTD-CK simulation results included for comparison

Analysis Also Valid at Low γ 6/18/ Performed to identify errors not visible at high γ Electrostatic numerical instability dominates at low γ Option (b) used

PSATD with Potentials (Use for Pushing Canonical Momenta) 6/18/201314

First Attempt Partly Successful 6/18/201315

Linear Interpolation, No Filter, γ=130 6/18/201316

Cubic Interpolation, Sharp Filter, γ=130 6/18/201317

New, but Weak, Instability Occurs 6/18/

Next Steps 6/18/201319

BACKUP 6/18/201320

Analytical Approximations Available 6/18/201321

6/18/201322

Cubic Interpolation, Filter, γ=130 6/18/201323