Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {\it in-situ} spacecraft observations and numerical simulations suggest a novel scenario for turbulence, characterized by a so-called phase space cascade -- the formation of fine structures, both in physical and velocity space. This new concept is here extended by directly taking into account the role of inter-particle collisions, modeled through the nonlinear Landau operator or the simplified Dougherty operator. The characteristic times, associated with inter-particle correlations, are derived in the above cases. The implications of introducing collisions on the phase space cascade are finally discussed.

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Keywords Plasma Physics
Pezzi, O, Valentini, F, Servidio, S, Camporeale, E, & Veltri, P. (2018). Fourier-Hermite decomposition of the collisional Vlasov-Maxwell system: Implications for the velocity-space cascade.