The Influence of Ion-Acoustic Solitons on the Energy Distribution Functions of Cold Ions in a Two-Component Plasma

Within the framework of a one-dimensional two-component MHD model of plasma with hot electrons and cold ions, an analytical expression is obtained that describes the ion energy distribution functions, perturbed by ion-acoustic solitons. The calculations used both averaging over an ensemble of ions and time-averaging for a single ion. It is shown that ion-acoustic solitons strongly influence the ion distribution function, deviating it from the initial equilibrium state. After the passage of the soliton, the distribution function returns to its original state. Using the Korteweg-de Vries equation, an explicit formula for describing the perturbed distribution function is obtained, which can be applied in practice. A practically important situation of propagation of a large ensemble of solitons of different amplitudes is considered. The cases of small and large time resolution in measuring distribution functions are modeled in detail. The obtained theoretical results are compared with known experimental data.