Two Modes of the Self-Similar Evolution of Charged Plasma

Abstract

Two self-similar modes of evolution of charged particles’ high-current beam are described analytically. The situation being considered falls within the field of nonneutral plasma electrodynamics. The process is considered in terms of the nonlinear 1D evolution of the charge density w(x, t) in the channel of a longdistance transmission line with nonlinearly distributed resistance R, capacitance C, and inductance L: R = R(w), C = C(w), and L = 0. It is shown that initially the front of w(x, t) accelerates and then slows down. The description of the process in the channel is based on the charge conservation law. An idealized “kinematic” approach is used according to which an equation in two unknowns (charge density and current density in the channel) can be reduced to an equation in one unknown w(x, t). A strongly nonlinear wave process is studied. A discontinuous solution w(x, t) is constructed with a zero boundary condition at infinity. Such a model description can apply only for revealing the main qualitative features of a complex process. Analytical expressions for the variation in the evolution of the front velocity and perturbed area length are derived. An interrelation between the nonlinearity parameter of the process and the amount of charge in the interelectrode gap is suggested based on the experimental data for the evolution of streamers.