This theoretical analysis shows that the Fokker–Planck equation can be applied to obtain identical wavelength-dependent (k2) damping as previously derived from the much more complicated Liouville equation approach. It is also noted that electron (ω ~ ωp) and ion (ω ~ Ωp) oscillations are only slightly damped by Coulomb collisions. The k2 dependent damping is difficult to observe for electron oscillations but perhaps not for ion oscillations (where it is the only Coulomb damping) if Landau damping effects do not obscure the observation and if the electron temperature is not too high compared with the ion temperature. The electron and ion oscillations are effectively free (the ratio of specific heats γ multiplying the temperature is effectively 3). The low-frequency sound oscillations [Formula: see text] are isothermal for electrons (γ = 1) and can be adiabatic (γ = 5/3) or free (γ = 3) for ions as the ion–ion collision frequency is much more or less than ω.
Growth rate and gain of stimulated Brillouin scattering considering nonlinear Landau damping due to particle trapping
