A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution

Abstract

A numerical method for studying one-dimensional electron plasma evolution under typical interplanetary conditions is presented. The method uses the Fourier-Fourier transform approach to a plasma model which is a generalization of the electrostatic Vlasov-Poisson system of equations. Conservation laws which are modified to include the plasma model generalization and also the boundary effects of nonperiodic solutions are given. A new conservation law for entropy in the transformed space is introduced. These conservation laws are used to check the accuracy of the numerical solutions. A discretization error analysis is given. Two numerical instabilities and the methods used for their suppression are discussed. Several solution examples are presented. Two of these are comparisons with earlier independent results; the comparison is favorable. A third example is also discussed which uses an interplanetary observation of a bump-on-tail unstable velocity distribution as initial data. It is shown that in interplanetary plasma conditions the bump-on-tail instability leads to significant excitation of plasma oscillations at the Bohm-Gross frequency and its second harmonic. An explanation of the second harmonic excitation in terms of wave-wave coupling during the growth phase of the instability is given.