Analytical and Numerical Solutions of Generalized Dispersion Equations for One-Dimensional Damped Plasma Oscillation

Analytical and numerical solutions of dispersion equations describing one-dimensional unsteady-state propagation of perturbation of electric field are derived within the framework of generalized Boltzmann physical kinetics. The solution in the Landau form is defined as a decaying harmonic wave in plasma of electrons with Maxwellian distribution and quiescent ions. The analytical solution of the problem is represented in terms of the Lambert $W$ function. Numerical solutions of the problem are found in a wide range of variation of determining parameters.