Paper Info
Title
Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm
Abstract
The pseudo-spectral analytical time-domain (PSATD) particle-in-cell (PIC) algorithm solves the vacuum Maxwell@?s equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and particle beam simulations. It is, however, not free of the usual numerical instabilities, including the numerical Cherenkov instability, when applied to relativistic beam simulations. This paper derives and solves the numerical dispersion relation for the PSATD algorithm and compares the results with corresponding behavior of the more conventional pseudo-spectral time-domain (PSTD) and finite difference time-domain (FDTD) algorithms. In general, PSATD offers superior stability properties over a reasonable range of time steps. More importantly, one version of the PSATD algorithm, when combined with digital filtering, is almost completely free of the numerical Cherenkov instability for time steps (scaled to the speed of light) comparable to or smaller than the axial cell size.
Year
DOI
Venue
2014
10.1016/j.jcp.2013.10.053
J. Comput. Physics
Keywords
Field
DocType
psatd algorithm,usual numerical instability,beam simulation,pseudo-spectral analytical time-domain pic,conventional pseudo-spectral time-domain,time step,numerical cherenkov instability,numerical dispersion relation,finite difference time-domain,numerical stability analysis,particle beam simulation,pseudo-spectral analytical time-domain,numerical stability,particle in cell
Time domain,Mathematical optimization,Mathematical analysis,Finite difference,Instability,Algorithm,Cherenkov radiation,Finite-difference time-domain method,Mathematical model,Maxwell's equations,Numerical stability,Physics
Journal
Volume
ISSN
Citations 
258,
0021-9991
6
PageRank 
References 
Authors
0.93
4
3
Name
Order
Citations
PageRank
Brendan B. Godfrey1495.87
Jean-Luc Vay27310.83
Irving Haber3212.42