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.
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