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A numerical study of Landau damping with PETSc-PIC

Daniel S. Finn, Matthew G. Knepley, Joseph V. Pusztay and Mark F. Adams

Vol. 18 (2023), No. 1, 135–152
Abstract

We present a study of the standard plasma physics test, Landau damping, using the particle-in-cell (PIC) algorithm. The Landau damping phenomenon consists of the damping of small oscillations in plasmas without collisions. In the PIC method, a hybrid discretization is constructed with a grid of finitely supported basis functions to represent the electric, magnetic and/or gravitational fields, and a distribution of delta functions to represent the particle field. Approximations to the dispersion relation are found to be inadequate in accurately calculating values for the electric field frequency and damping rate when parameters of the physical system, such as the plasma frequency or thermal velocity, are varied. We present a full derivation and numerical solution for the dispersion relation, and verify the PETSC-PIC numerical solutions to the Vlasov–Poisson system for a large range of wavenumbers and charge densities.

Keywords
simulation, particle-in-cell, PETSc, plasma, Landau damping
Mathematical Subject Classification
Primary: 35Q83, 65-04, 65Y05, 68-04, 82D10
Milestones
Received: 20 February 2023
Revised: 1 November 2023
Accepted: 12 November 2023
Published: 21 December 2023
Authors
Daniel S. Finn
Department of Computer Science and Engineering
University at Buffalo
Buffalo, NY
United States
Matthew G. Knepley
Department of Computer Science and Engineering
University at Buffalo
Buffalo, NY
United States
Joseph V. Pusztay
Department of Computer Science and Engineering
University at Buffalo
Buffalo, NY
United States
Mark F. Adams
Scalable Solvers Group
Lawrence Berkeley National Laboratory
Berkeley, CA
United States