Eigenvalue solution for the ion-collisional effects on ion-acoustic and entropy waves

Abstract

The linearized ion Fokker–Planck equation is solved as an eigenvalue problem under the condition of collisionless electrons in the quasineutral limit (φ=0) for ionization-temperature ratios, ZTe/Ti=2, 4, and 8 for entropy waves and ionization-temperature ratios, ZTe/Ti=4, 8, 16, 32, 48, 64, and 80 for ion-acoustic waves. The perturbed ion distribution function for the ion-acoustic and entropy waves is formed from a Legendre polynomial expansion of eigenvectors and can be used to calculate collisionally dependent macroscopic quantities in the plasma such as gamma (Γ=Cp/Cv), the ratio of specific heats, and the ion thermal conductivity (κi).