Modelling nonlinear electrostatic oscillations in plasmas

Abstract

The nonlinear 1-D plasma electrostatic oscillation is formulated in an analytic framework that allows closed-form analytic solutions along the characteristics, and solved numerically in configuration space. Additionally, a novel iterative analytical form for the finite-amplitude oscillation solution is derived, which compares favourably with the other two techniques. A fresh insight into the evolution of the oscillation is gained, including defining the least achievable density in the nonlinear oscillation as half of the equilibrium value, and relating the associated maximum density achievable in terms of that minimum.