Producing suprathermal tails in the stationary velocity distribution

Abstract

We revisit effective scenarios for the origin of heavy tails in stationary velocity distributions. A first analysis combines localization with diffusive acceleration. That gets realized in space plasmas to find the so-called kappa-distributions having powerlaw decay at high speeds. There, localization at high energy already takes place for the reversible dynamics, but becomes effective by an active diffusion in velocity space. A model for vibrating granular gases and giving rise to stretched exponential tails is also briefly discussed, where negative friction is the energizer. In all cases, the resulting nonMaxwellian velocity distributions are frenetically caused by the dependence on the speed of kinetic parameters.Dedicated to the memory of Christian Van den Broeck.

Frenesy: Time-symmetric dynamical activity in nonequilibria

“…Similar considerations can be made in a more general set-up where the escape rates gradually decrease as the energy gets larger. In fact, in exactly that same way we get a general scenario for the origin of suprathermal tails in nonequilibrium velocity distributions ν( v), [29].…”

“…That is what really happens in space plasmas where those kappa-distributions (7) have indeed been observed and are well established, [30]. There, the γ(v) is derived from Coulomb scattering and the B(v) gets its dependence from the diffusive acceleration of electrons or ions in time-dependent electromagnetic fields in a turbulent plasma; see [29].…”

Active velocity processes with suprathermal stationary distributions and long-time tails

“…The fact that an effective diffusivity that depends inversely on the speed can produce suprathermal velocity distribution functions was already discussed, e.g. in [8,38], in the context of highly-energetic space plasmas. A general formulation based on a Fokker-Planck equation was e.g.…”

“…Mathematically rigorous work for the more general case can be found in [23][24][25]. The main physical mechanism goes back to the phenomenon of Taylor dispersion [16,[32][33][34], from where the general concept of stochastic or turbulent acceleration arises [35][36][37][38].…”

KAPPA: A Package for the Synthesis of Optically Thin Spectra for the Non-Maxwellian κ-distributions. II. Major Update to Compatibility with CHIANTI Version 10

“…Consequently, the solar corona above about 1.05 R ⊙ is expected to be non-Maxwellian (Scudder & Karimabadi 2013;Scudder 2019). Particle acceleration resulting in high-energy tails can also occur via multiple processes, including turbulence (where the inverse proportionality of turbulent diffusion coefficient to velocity leads directly to κ-distributions, see Hasegawa et al 1985;Laming & Lepri 2007;Bian et al 2014;Demaerel et al 2020), magnetic reconnection (e.g., Gontikakis et al 2013;Ripperda et al 2017;Threlfall et al 2018;Arnold et al 2021;Oka et al 2022), wave-particle interactions (Vocks et al 2008(Vocks et al , 2016, or steep gradients of temperature and density, such as in the transition region (e.g., Roussel-Dupré 1980;Ljepojevic & MacNeice 1988;Dzifčáková et al 2017). Furthermore, physical correlations between particles specifically lead to κ-distributions (see Livadiotis & McComas 2022, and references therein).…”