Kinetic theory of ion acoustic waves in a plasma with collisional electrons

An analytical theory of ion acoustic waves in Maxwellian plasmas and in plasmas with an externally applied temperature gradient has been developed. The emphasis is upon the effects of electron-electron and electron-ion collisions on ion acoustic wave damping and on the effective electron heat conductivity associated with the waves. The asymptotic limits of weakly and strongly collisional electrons are studied analytically and then a numerical solution is compared to Fokker-Planck simulations and fitted by simple algebraic expressions. The limit of large Z has also been investigated and the condition of validity for the Lorentzian plasma approximation has been found. It is also shown that the heat flux driven ion acoustic instability exists over a wide range of parameters with a smooth transition from the collisionless to the collisional limit. Accounting for ion-ion collisions leads to the separation of the instability region in two domains. The long wavelength part dominates in plasmas with a relatively high ion temperature.