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

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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.