Inhomogeneous Spatial Distribution of Electrons in a Compressed Gas Bubble of Submicron Size

Abstract

The inhomogeneous spatial distribution of the macroscopic amount of electrons (N <109) in a spherical potential well is considered. It is shown that the electron distribution has two spatial scales. The first scale is the Fermi length. By effect, we mean the existence of the second scale, which is related with the radius of the potential well and much larger than the first scale. Two systems are considered: a system of free electrons in a spherical well and electrons in a compressed gas bubble. Based on the analysis of the distribution function of a system of free semiclassical electrons, we demonstrate the cause of the appearance of the spatial heterogeneity. This result is confirmed by a numerical summation of exact solutions of the wave functions of electrons in an infinite potential well. It is shown that there is an analogous effect for the spatial distribution of electrons in compressed hydrogen gas bubble of submicron size (<0.1 μm). This system can be realized in the thermonuclear experiments. Numerical simulation of the electron distribution was carried out by the DFT method. The limiting factors of the effect are considered. The aim of problem considered in the article deals with the analysis of possible physical processes occurring in the thermonuclear experiments.