Abstract
The Arbitrary Linear Plasma Solver (ALPS) is a parallelised numerical code that solves the dispersion relation in a hot (even relativistic) magnetised plasma with an arbitrary number of particle species with arbitrary gyrotropic equilibrium distribution functions for any direction of wave propagation with respect to the background field. ALPS reads the background momentum distributions as tables of values on a$(p_{\bot },p_{\Vert })$grid, where$p_{\bot }$and$p_{\Vert }$are the momentum coordinates in the directions perpendicular and parallel to the background magnetic field, respectively. We present the mathematical and numerical approach used by ALPS and introduce our algorithms for the handling of poles and the analytic continuation for the Landau contour integral. We then show test calculations of dispersion relations for a selection of stable and unstable configurations in Maxwellian, bi-Maxwellian,$\unicode[STIX]{x1D705}$-distributed and Jüttner-distributed plasmas. These tests demonstrate that ALPS derives reliable plasma dispersion relations. ALPS will make it possible to determine the properties of waves and instabilities in the non-equilibrium plasmas that are frequently found in space, laboratory experiments and numerical simulations.
Highlights
The vast majority of the visible matter in the universe is in the plasma state
We present the mathematical and numerical approach used by Arbitrary Linear Plasma Solver (ALPS) and introduce our algorithms for the handling of poles and the analytic continuation for the Landau contour integral
We present our numerical code ALPS (Arbitrary Linear Plasma Solver), which solves the full hot-plasma dispersion relation in a plasma consisting of an arbitrary number of particle species with arbitrary background distribution functions f0j and with arbitrary directions of wave propagation with respect to the uniform background magnetic field
Summary
The vast majority of the visible matter in the universe is in the plasma state. The solar wind is an example of such an astrophysical plasma. Verscharen and others from thermodynamic equilibrium if the relaxation due to particle collisions occurs on time scales that are larger than the characteristic time scales of the collective plasma behaviour Such a collisionless plasma is characterised by non-Maxwellian features in its velocity distribution functions. The behaviour of plasma waves and instabilities is typically studied with the help of numerical codes that solve the hot-plasma dispersion relation These codes (like WHAMP, PLUME or NHDS) use a shifted bi-Maxwellian background distribution function as the zeroth-order description for the plasma state (Roennmark 1982; Quataert 1998; Klein et al 2012; Verscharen & Chandran 2018). The appendices describe how ALPS solutions depend on the resolution of the background distributions, discuss the Levenberg–Marquardt-fit routine used in our hybrid analytic continuation method and describe our strategy for numerically refining coarse-grained distribution functions obtained from spacecraft measurements
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