Kinetic Entropy-Based Measures of Distribution Function Non-Maxwellianity: Theory and Simulations

Identifying energy dissipation in weakly collisional/collisionless plasmas during fundamental plasma processes, such as magnetic reconnection, turbulence, and shocks, is crucial in many astrophysical, heliospheric, and planetary studies. A non-Maxwellianity measure, quantifying how "non-Maxwellian" a plasma is, gives a measure of the importance of non-equilibrium kinetic effects [e.g., ε in Greco et al, Phys. Rev. E, 86(6), 066405 (2012) and enstrophy in Servidio et al., Phys. Rev. Lett., 119(20), 205101 (2017)], and therefore is one of many candidates to identify where dissipation is likely to occur. In this study, we investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas. First, we assess the properties of a measure previously employed by Kaufmann and Paterson [J. Geophys. Res., 114, A00D04 (2009)]. By examining analytical expressions for three common non-Maxwellian plasma distribution functions, we show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits. We elucidate the reason for the divergence and introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. As an example, we use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for many applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.