Time-asymptotic wave propagation in collisionless plasmas

作     者：Carlo Lancellotti J. J. Dorning 

作者机构：Engineering Physics Program University of Virginia Charlottesville Virginia 22903-2442 USA 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2003年第68卷第2期

页      面：026406-026406页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

主　　题：Plasma waves 

摘      要：We report the results of a new, systematic study of nonlinear longitudinal wave propagation in a collisionless plasma. Based on the decomposition of the electric field E into a transient part T and a time-asymptotic part A, we show that A is given by a finite superposition of wave modes, whose frequencies obey a Vlasov dispersion relation, and whose amplitudes satisfy a set of nonlinear algebraic equations. These time-asymptotic mode amplitudes are calculated explicitly, based on approximate solutions for the particle distribution functions obtained by linearizing only the term that contains T in the Vlasov equation for each particle species, and then integrating the resulting equation along the nonlinear characteristics associated with A, which are obtained via Hamiltonian perturbation theory. For “linearly stable initial Vlasov equilibria, we obtain a critical initial amplitude (or threshold), separating the initial conditions that produce Landau damping to zero (A≡0) from those that lead to nonzero multiple-traveling-wave time-asymptotic states via nonlinear particle trapping (A≢0). These theoretical results have important implications about the stability of spatially uniform plasma equilibria, and they also explain why large-scale numerical simulations in some cases lead to zero-field final states whereas in others they yield nonzero multiple-traveling-wave final states.