Generalized Plasma Dispersion Function: One-Solve-All Treatment, Visualizations, and Application to Landau Damping

Abstract

A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $\delta$, flat top, triangular, $\kappa$ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion $\gamma \propto \partial f_0/\partial v$ is only a rough approximation when discussing the distribution function effects on Landau damping, this approach provides a useful tool for rigorous calculations of the linear wave and instability properties of plasma for general distribution functions. The results are also verified via a linear initial value simulation approach. Intuitive visualizations of the generalized plasma dispersion function are also provided.

Accepted by Physics of Plasmas, 9 pages, 14 figures, see arXiv "Other formats" link for supplementary material

References in corpus (3)

• Generalized Plasma Dispersion Function: One-Solve-All Treatment, Visualizations, and Application to Landau Damping
• The incomplete plasma dispersion function: properties and application to waves in bounded plasmas
• Constant residual electrostatic electron plasma mode in Vlasov-Ampere system

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• Landau Damping for Non-Maxwellian Distribution Functions