Nonlinear structures in a nonequilibrium plasma: impact of small fluctuations

In many plasma environments, e.g., in the solar wind, collisions between particles are rare, challenging therefore the assumption of strict equilibrium. In this paper, we propose to model such nonequilibrium plasmas as a collection of small subsystems that remain infinitely close to equilibrium. This allows us to describe their statistical properties using superstatistics, i.e., a superposition of statistics. Focusing on the three universality classes of superstatistics that have strong empirical evidence (Gamma, inverse-Gamma, and log-normal superstatistics), we study systematically the effect of small thermal fluctuations on the nonlinear structures occurring in plasmas. We focus on the typical scenario of ion acoustic waves in the presence of nonequilibrium electrons and analyze various nonlinear structures governed by the Korteweg-De Vries (KdV) equation and the nonlinear Schrodinger equation. We examine the impact of fluctuations on solitons, rogue waves, and the phenomenon of modulational instability. Our findings demonstrate the universal influence of thermal fluctuations on these structures. Interestingly, the results associated with the Cairns nonthermal distribution, widely addressed in the plasma physics literature, can be recovered by truncating our method to the leading order. Thus, the proposed approach may be regarded as an extension of the Cairns approach, with additional corrections accounting for the different underlying temperature dynamics.