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Title: Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm

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.
Authors:
 [1] ;  [2] ;  [1]
  1. University of Maryland, College Park, MD 20742 (United States)
  2. Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
Publication Date:
OSTI Identifier:
22230860
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 258; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; COMPARATIVE EVALUATIONS; DIGITAL FILTERS; DISPERSION RELATIONS; INSTABILITY; MATHEMATICAL MODELS; MAXWELL EQUATIONS; PARTICLE BEAMS; PARTICLES; PLASMA; RELATIVISTIC RANGE; SIMULATION; STABILITY; VELOCITY