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

Fourier-Hermite decomposition of the collisional Vlasov-Maxwell system: implications for the velocity space cascade