Speaker
Description
Non-equilibrium velocity distributions with enhanced suprathermal tails are ubiquitous in space plasmas and are commonly described using kappa-type distributions. However, multiple kappa formulations coexist in the literature, leading to ambiguity in the definition of temperature and thermodynamic parameters and complicating their physical interpretation.
In this work, we present a unified framework in which all kappa velocity distributions naturally emerge from superstatistics. By assuming that the inverse temperature fluctuates according to a gamma distribution, we derive a generalized non-equilibrium velocity distribution that recovers standard kappa forms as limiting cases and provides a direct physical interpretation of the kappa parameter in terms of temperature fluctuations. We further introduce a complementary, moment-based formulation that reproduces the same non-thermal features without invoking a temperature definition, thereby resolving long-standing ambiguities in out-of-equilibrium plasma modeling.
As an application of this framework, we explore its implications for velocity-space cascades in weakly collisional plasmas. Projecting the superstatistical distribution onto a Hermite basis, we derive analytical expressions for the Hermite coefficients and the associated velocity-space spectrum. The resulting spectrum exhibits power-law behavior at large Hermite indices, with amplitudes controlled by superstatistical parameters, while the spectral slope remains largely insensitive to them. This indicates that temperature intermittency alone cannot account for the velocity-space cascades observed in fully developed turbulence, pointing to the role of additional nonlinear phase-space dynamics.
Our results provide a coherent theoretical foundation for non-thermal velocity distributions and offer an analytical baseline for interpreting velocity-space spectra in spacecraft observations and kinetic simulations. This framework opens the door to future extensions incorporating nonlinear effects and to systematic comparisons with MMS and Solar Orbiter data, as well as hybrid-Vlasov and PIC models.
