Non-thermal particle acceleration in multi-species kinetic plasmas: universal power-law distribution functions and temperature inversion in the solar corona

TL;DR

This paper develops a self-consistent quasilinear theory linking non-thermal power-law particle distributions and temperature inversion in the solar corona, revealing universal behaviors driven by turbulence and Debye screening.

Contribution

It introduces a multi-species Fokker-Planck framework explaining the origin of universal power-law tails and temperature inversion in plasmas, especially the solar corona.

Findings

Universal $f(v) o v^{-5}$ tail for $eta o ext{large}$ spectra.

Tails resist Maxwellianization due to collision limitations.

Tails explain coronal temperature inversion and transition phenomena.

Abstract

Non-thermal power-law distribution functions are ubiquitous in astrophysical, space, and laboratory kinetic plasmas, but their origin remains unclear. A related puzzle is the temperature inversion of the solar corona. We show that these phenomena are deeply connected by developing a self-consistent quasilinear theory for electromagnetically driven, unmagnetized kinetic plasmas. The theory yields a multi-species Fokker-Planck equation with drive-induced diffusion from direct acceleration by broad-band turbulent or narrow-band wave-like fields, indirect acceleration by excited waves, and Balescu-Lenard diffusion/drag from Debye-scale fluctuations and Coulomb collisions. For a super-Debye turbulent electric-field spectrum, $|{\bf E}_{\bf k}|^2\propto k^{-\alpha}$, electrons and ions relax toward a universal $f(v)\propto v^{-5}$, or $N(E)\propto E^{-2}$, attractor, equivalent to the high-energy tail of a $\kappa=1.5$ distribution, when $\alpha\ge5$. This universality follows from Debye screening: large-scale fields accelerate unscreened fast particles but not screened slow ones. For shallower spectra, $\alpha<5$, the tail scales as $v^{-\alpha}$; incomplete relaxation and anisotropy also break universality. Anisotropic wave drives yield branch- and spectrum-dependent exponents. Because collisions cannot decelerate suprathermal particles, the tails resist Maxwellianization. In the solar atmosphere, such tails may be generated by chromospheric convection or nanoflares despite collisional and radiative losses. Direct wave heating energizes electrons through Landau-resonant interactions with whistler and electron-cyclotron waves, while ions may be accelerated by turbulent ambipolar fields. Resulting $\kappa\simeq1.5$--$3$ distributions produce an abrupt upper-chromosphere/lower-corona transition and velocity-filtration-driven inverted profiles, yielding coronal temperatures $\sim10^6\,{\rm K}$.