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On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability
Open accessAbstract
Abstract 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.
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“Another set of works 26,116,156-160 studied numerically ECR discharges with a grid extraction system. They used the aforementioned simplified approach, where the MW fields were calculated from Eqs. (10) and (11), but without taking into account the plasma contribution, i.e., with j = 0.”
From Plasma propulsion modeling with particle-based algorithms (2023) · cites this paper as [156]
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“Ref. 156 considered the electron extraction in such a device and concluded that the electric field at the orifice edges played an important role.”
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Cites
Rigorous charge conservation for local electromagnetic field solvers
Villasenor, J., & Buneman, O. (1992) · Computer Physics Communications · doi:10.1016/0010-4655(92)90169-y · Cited by 438
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Cited by
Plasma propulsion modeling with particle-based algorithms
Taccogna, F., Cichocki, F., Eremin, D., Fubiani, G., & Garrigues, L. (2023) · Journal of Applied Physics · doi:10.1063/5.0153862 · Cited by 29
Metadata
- Authors
- Meyers, M. D., Huang, C.-K., Zeng, Y., Yi, S. A., & Albright, B. J.
- Affiliations
- Los Alamos National Laboratory (US)
- Corresponding author
- Huang, C.-K.
- Venue
- Journal of Computational Physics
- Publisher
- Elsevier BV
- Published
- 2015-09
- Volume
- 297
- Pages
- 565-583
- ISSN
- 0021-9991 (ISSN-L)
- OpenAlex
- W1587338275
- Cited by
- 13
- References
- 1
- Citations by year
- 2023: 3 · 2022: 2 · 2021: 1 · 2020: 2 · 2019: 1 · 2017: 1 · 2016: 3
- FWCI
- 0.64
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (am, 276 d)
- Locations
- Journal of Computational Physics (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (ACI-1339893, 20130744ECR, DE-NA0001833)
- Laboratory Directed Research and Development (ACI-1339893, 20130744ECR, DE-NA0001833)
- U.S. Department of Energy (ACI-1339893, 20130744ECR, DE-NA0001833)
- Los Alamos National Laboratory (ACI-1339893, 20130744ECR, DE-NA0001833)
- University of California, Los Angeles (ACI-1339893, 20130744ECR, DE-NA0001833)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Electromagnetic Simulation and Numerical Methods
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle accelerators and beam dynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Keywords
- particle-in-cell simulation, numerical dispersion relation, leapfrog scheme, charge conservation, relativistic particle beams, electrostatic modes, eigenmode analysis, growth rate (instability)
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- Meyers, M. D., Huang, C.-K., Zeng, Y., Yi, S. A., & Albright, B. J. (2015). On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability. Journal of Computational Physics. https://doi.org/10.1016/j.jcp.2015.05.037
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
