A new approach to the description of plasma Langmuir waves

After finding an exact solution to the Vlasov–Boltzmann kinetic equation (i.e., finding distribution functions for plasma particles), we consider the description of Landau damping using Poisson's equation, since with the complete distribution function, there is no need to split the kinetic equation into equilibrium and perturbed parts for the subsequent implementation of the pole bypass in the integrand expression. The found distribution function depends, in addition to velocity, on the coordinates and can be used to analytically consider different cases and configurations of the spatial confinement of the plasma. General distribution function for electrons is discussed. We consider the behavior of Langmuir waves, also at the nonlinear stage.