Universal power-law distribution functions in an electromagnetic kinetic plasma: implications for the inverted temperature profile in the solar corona

There is ample evidence for non-thermal power-law distribution functions in space and astrophysical plasmas in the collisionless/kinetic regime, with a preference for the v ^-5 velocity (v) distribution and E ^-2 energy (E) distribution in the solar wind. I will present a novel self-consistent theory for particle acceleration in weakly collisional plasmas, based on the perturbed Vlasov-Maxwell equations, that yields a quasilinear transport equation for the combined relaxation of the electron and ion distribution functions. I will show how a weakly collisional plasma tends to relax to a v ^-5 distribution function (E ^-2 energy distribution) for both species, if it is subject to white noise-like electromagnetic turbulence on super-Debye scales, independent of the detailed power spectrum. Stronger Debye shielding of slower particles reduces their effective charge and suppresses their acceleration relative to the unshielded faster particles in a near-universal manner, leading to this power-law tail. I will discuss how the presence of such a power-law distribution function in the collisionless solar corona can potentially solve the coronal heating problem. Large-scale electromagnetic (e.g., Alfvenic) turbulence can trigger the ~v ^-5 suprathermal tail at the coronal base. This allows gravity to let the high velocity particles escape (velocity filtration), inverting the temperature profile and heating the plasma to a million degrees K in the corona.