The Maxwellian plus water-bag model: application to the propagation of longitudinal electron waves in a plasma with Maxwellian and mono-energetic supra-thermal electrons

Abstract

This paper is a theoretical and experimental study of the propagation of longitudinal electron waves in a collisionless, homogeneuos, isotropic plasma, composed of Maxwellian and supra-thermal electrons. Assuming the supra-thermal electrons are mono-energetic, the velocity distribution function is chosen as a Maxwellian plus water-bag distribution; then, using the method of residues (inverse Fourier–Laplace transform), the behaviour of the electric field is found to be in good agreement with experimental results obtained for a plasma of Maxwellian and quasi-mono-energetic electrons. The plasma parameters can be deduced from the theoretical dispersion curves matching the experimental points; they are found to agree well with those measured by electrostatic probes. Experimental values of damping and excitation coefficients are also compared with the theoretical. The results suggest that a longitudinal electron wave propagation experiment may be used as a powerful diagnostic tool to examine non-Maxwellian plasmas.

Propagation of electronic longitudinal modes in a truncated maxwellian plasma

“…The classical way to solve such a problem is well known: define the electric field in Fourier-Laplace space and calculate the inverse Fourier-Laplace transform; this transform has been mainly calculated by the method of residues, so this involves the study of the analyticity of the dispersion function before the search for these roots. The important result of this theoretical study is similar to that obtained with the Maxwellian plus water-bag model (Treguier & Henry 1975), that is, the behaviour of the electric field is well represented by two independently propagating modes, which are the new non-dispersive mode (introduced by the truncation) and a mode which approximates to the classical Landau mode (due to the Maxwellian part of the distribution function).…”

“…The experimental results have been obtained in a homogeneous isotropic hot diffusion plasma of xenon. The experimental system and the general characteristics of the plasma have been described previously (Henry & Treguier 1972;Treguier & Henry 1975).…”