Collisional damping of electrostatic ion waves

Starting from the linearized Fokker-Planck-Poisson system for an unbounded plasma in a homogeneous magnetic field, the general electrostatic dispersion relation is derived taking collisions into account as a perturbation. The velocity integrations in the collisional term of the dispersion relation are performed exactly for any kind of electrostatic wave in a Maxwellian background plasma. A simple asymptotic method is developed to approximate the resultant expressions n i the hot-ion limit (ion Larmor radius much larger than wave-length). As an application, collisional damping rates γ c are calculated for ion Bernstein waves and lower-hybrid waves. The resulting formulas are discussed, especially with regard to the possibility of heating thermonuclear plasmas by parametric excitation of ion Bernstein or lower-hybrid wave turbulence. It is shown, in particular, that ion Bernstein waves are extremely sensitive to ion-ion collisions: γ c ≫ ν ii ;, where ν ii is the ion-ion collision frequency. As a consequence, collisional damping rates are comparable, in this case, to parametric growth rates calculated from Vlasov's equation.