Beam–plasma instability and fast particles: the Lynden-Bell approach
Résumé
Beam–plasma instability, i.e., the response of plasma bulk to the injection of supra-thermal
charged-particle beams, can be appropriately characterized by a long-range interaction system.
This physical system hosts a number of very interesting phenomena and, in particular, the
emergence of long-lived quasi-stationary states. We characterize the self-consistent
distribution functions of such out-of-equilibrium states by means of the Lynden-Bell theory.
The prediction of this theory, based on the statistical mechanics of the Vlasov equation, are
checked against the outcomes of numerical simulations of the discrete system. Moreover, a
phenomenological study of the effective resonance band for the system response is also
addressed. A threshold value is found in the initial spread of beam-particle momenta. This
threshold allows discrimination between the resonant and non-resonant regimes. The analysis
of the thermalization of a few percent of the beam population characterized by large initial
momenta (with respect to the main part of the beam itself) is also performed and it confirms
and deepens our understanding of the physical meaning of the mentioned threshold.