Approximate Solutions of Quantum Equations for Electron Gas in Plasma

Abstract

We have obtained the solutions of linearized Shr{\"o}dinger equation for spherically and axially symmetrical electrons density oscillations in plasma in the approximation of the self-consistent field. It was shown that in the center or on the axis of symmetry of such a system the static density of electrons can enhance, which leads to the increasing of density and pressure of ion gas. We suggest that this mechanism could be realized in nature as rare phenomenon called the 'fireball' and could be used in carrying out the research concerning controlled fusion.