Longitudinal electron waves for a plasma with a bi-Maxwellian velocity distribution

An original method for calculating and representing the excitation coefficients of longitudinal electron waves is applied to the case of a hot, collisionless, homogeneous and isotropie plasma with a bi-Maxwellian velocity distribution function. Using a Van Kampen treatment we introduce a ‘wave density’ distribution which is represented graphically. When hot electrons are added to a plasma of cool electrons the Landau mode is distorted and its damping increases with the hot/cold temperature ratio θ. The Landau mode separates into two modes for θ ≥ θ₀ where θ₀ increases as the hot/cold density ratio α decreases. We show that no wave seems to be able to propagate at frequencies below the plasma frequency. Using an abrupt cut-off in the hot electron distribution function, we recover the results for a Maxwellian plus water-bag distribution.