A semi-Lagrangian relativistic Vlasov–Maxwell solver is used to describe the non-linear momentum transfer between electron beams, which is driven by spontaneous fluctuations in the oblique filamentation instability (a type of Weibel mode) in two-dimensional plasmas. For counter-streaming plasmas, these filamentation instabilities may strengthen the generation of a fine structure of the distribution function in phase space. Properties of such counter-streaming beams are investigated using full-kinetic simulations and a Hamiltonian reduction technique based on the invariance of the transverse canonical momentum, the so-called multi-stream model. In the regime where , being the wavevector and de the electron skin depth, a momentum transfer takes place when a mesoscale current filamentation mode couples with microscopic phase-space fluctuations. This regime is characterized by the appearance of filamentation modes with large wavenumbers and large amplitude fluctuations, which induce variations of the L2-norm of the plasma in link with the self-organization of counter-streaming electron beams. We also discuss some theoretical aspects of information theory that highlight the role of the (reversible) entropy production in momentum transfer, thus by clarifying the connections between (microscopic) fluctuations of the distribution function and the fundamental aspects of the filamentation in Vlasov theory. The momentum transfer between beams is quantitatively analyzed by means of both theoretical estimations and numerical experiments.
Fast nonlinear scattering of runaway electron beams through resonant interactions with plasma waves