Solution of the k-space diffusion equation for the problem of a Langmuir plasmons motion in an inhomogeneous turbulent plasma

Abstract

This article considers the interaction of Langmuir plasmons with areas of nonsteady density inhomogeneity in the longwave approximation in ion-acoustic weak turbulence plasma. The interaction process is described by the kinetic equation for the distribution function of the plasmons at the wave numbers obtained on the basis of Liouville’s theorem. According to the basic equation, the evolution of the distribution function represents the sequential processes of spherical symmetrization, diffusion over ion-acoustic turbulence and “runaway” along the decreasing density profile under the action of regular in homogeneity. The article focuses on finding the exact self-similar solutions of the initial-boundary value problems to the diffusion and “runaway” equations. It is found that in the interaction of Langmuir plasmons with ion-acoustic turbulennce, there occurs the pumping of the ion-acoustic oscillation energy as well as relatively short Langmuir wave energy into the long wave part of the Langmuir wave spectrum.