On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

Journal Article · Tue Sep 15 00:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2015.05.037· OSTI ID:22465656

Zeng, Y.; Yi, S. A.; Albright, B. J. ^[1]

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1. Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

• OSTI ID: 22465656
• Journal Information: Journal of Computational Physics, Vol. 297; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DEPOSITION
DIRECT CURRENT
DISPERSION RELATIONS
DISTRIBUTION FUNCTIONS
ELECTRIC CHARGES
LASER-PRODUCED PLASMA
MAXWELL EQUATIONS
NUMERICAL SOLUTION
PARTICLE BEAMS
PLASMA DRIFT
PLASMA INSTABILITY
PLASMA SIMULATION
RELATIVISTIC PLASMA
RELATIVISTIC RANGE