Estimation of Effective Viscosity to Quantify Collisional Behavior in Collisionless Plasma

While dissipation in collisional plasma is defined in terms of viscosity and resistivity, the exact functional form of dissipation, i.e., the so-called dissipation function in nearly collisionless plasma, is unknown. Nevertheless, previous studies have suggested that there exists viscous-like energy conversion in collisionless plasma with scaling characteristics analogous to collisional plasma, and in particular that the average dissipation is proportional to the square of the rate of strain as in hydrodynamics. In this study, using 2.5D kinetic particle-in-cell (PIC) simulation of collisionless plasma turbulence, we provide an estimate of effective viscosity at each scale, obtained via a scale-filtering approach. We then compare the turbulent dynamics of the PIC simulation with that from MHD and two-fluid simulations in which the viscosity is equal to the effective viscosity estimate obtained from the PIC simulation. We find that the global behavior in these MHD and two-fluid simulations has a striking similarity to that in their kinetic/PIC counterpart. In addition, we explore the scale dependence of the effective viscosity and discuss implications of this approach for space plasmas.