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

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, $|{\bf E}_{\bf k}|^2\propto k^{-α}$, 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 $κ=1.5$ distribution, when $α\ge5$. This universality follows from Debye screening: large-scale fields accelerate unscreened fast particles but not screened slow ones. For shallower spectra, $α