Half Spectral, an Another General Method for Linear Plasma Simulation

TL;DR

The paper introduces a hybrid spectral method that combines eigenvalue and initial value approaches for linear plasma simulations, transforming PDEs into simpler ODEs by replacing spatial derivatives with spectral terms, simplifying complex plasma wave problems.

Contribution

It proposes a novel hybrid spectral method for linear plasma simulation that reduces PDEs to ODEs by spectral transformation of spatial derivatives, potentially simplifying plasma wave modeling.

Findings

Effective for MHD and plasma waves

Reduces computational complexity

Simplifies plasma wave simulations

Abstract

There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time derivative dt term (and other term if have, e.g., kinetic dv term), but transform the linear spatial derivatives dx term to ik, which then can reduce the computational dimensions. For example, most (fluid and kinetic) normal mode problems can be reduced from treating cumbersome PDEs to treating simple ODEs. Examples for MHD waves, cold plasma waves and kinetic Landau damping are given, which show to be extremely simple or even may be the simplest method for simulating them. [I don't know whether this idea is new, but it seems very interesting and useful. So, I choose making it public.]