Nonlinear evolution of a cold non-relativistic electron-ion plasma with an arbitrary initial density profile: A phase mixing perspective

TL;DR

This paper derives a third-order perturbative evolution equation for cold non-relativistic electron-ion plasmas with arbitrary initial density profiles, providing insights into phase mixing dynamics and validating results with fluid simulations.

Contribution

It introduces a novel third-order perturbative framework for analyzing nonlinear plasma evolution with arbitrary density profiles, extending previous models.

Findings

Reproduces known phase mixing times for homogeneous and periodic inhomogeneous plasmas.

Provides insights into finite-size plasma inhomogeneity effects.

Validates theoretical predictions with fluid simulation results.

Abstract

Using a perturbative approach, an evolution equation for the space charge density, correct up to the third order, is deduced for arbitrary initial density profiles of the electron and ion fluids in a cold nonrelativistic plasma. The evolution equation is solved to reproduce known results pertaining to the phase mixing time in the immobile ion limit as well as in the case of mobile ions, for a homogeneous plasma as well as for a plasma with a periodic inhomogeneity. The case of non-periodic plasma inhomogeneity, as in a finite-size plasma, is also discussed and some insights are given which are well supported by fluid simulation observations.