Eigenvalue Solution For The Ion-Collisional Effects On The Fast And Slow Ion Acoustic Waves In Multi-Ion Species Plasmas

The fast and slow waves in multi-ion species collisionless plasmas have been widely studied, but the collision effect on ion acoustic waves is a difficult problem. In this paper, plasmas with azimuthal symmetry velocity distribution in different collisional regimes are studied by eigenvalue solution of the linearized Fokker-Planck equation. The frequency, damping rate and distribution function from the solutions are consistent with the analytical result in collisionless limit. For the fast wave, the damping rate agrees well with the prediction of both fluid theory in collision limit and kinetic theory in collisionless limit. But for the slow wave, the frequency and damping rate predicted by fluid theory are not accurate. In two-ion species plasmas, the light and heavy ion density perturbation phases of two-ion species are the same for the fast wave, but opposite for the slow wave. Polytropic index of C5H12 plasmas is also calculated, which is simply affected by mean-free paths of ions for the fast wave, but affected by multiple factors, such as mean-free paths, heat transfer and the opposite phases for the slow wave.