Damping of plasma-electron oscillations and waves in low-collision electron-ion plasmas

Previously developed methods for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is applied to low-collision electron-ion plasma.[l] Taking into account Coulomb collisions in the limit m_e « m_i, |V_i|_mean « |V_e|_mean and T_em_e «T_im_i results in the expression for longitudinal high-frequency plasma-electron oscillation wave decrement essentially depending on oscillation frequency (ω) This expression is quite different from the one used for low-frequency plasma sound waves, which can be derived using expansion in asymptotically divergent series in δ/ω₀, kv_i/ω₀ where δ is imaginary part of the frequency ω = ω +iδ and does not reduce to a simple expression with some effective collision frequency δ ∼ v_ei.