Quadrupole moment of a localized langmuir perturbation in a electron plasma

The aim of the paper is to investigate the structure of the electric field (EF) of a localized Langmuir disturbance in an electron plasma. Three-dimensional problem is solved (the one-dimensional case has been considered earlier). Equations for the electron distribution function and Poisson equation serve as the initial equations for the solution of the problem. It is shown that a static EF of a quadrupole character arises around the three-dimensional localized Langmuir disturbance at a distance much greater than the disturbance dimensions. The long-range field is caused by HF-pressure which is proportional to the square of the EF amplitude and distorts the distribution function of electrons which pass through the disturbance region. The disappearance of HF-pressure compensation is a principally new circumstance in contrast to the one-dimensional problem; HF-pressure acting on electrons is compensated by means of a space charge field. At the same time the power law of EF decrease is preserved