Formation of Power-law Energy Spectra in Space Plasmas by Stochastic   Acceleration due to Whistler-Mode Waves
  A non-relativistic Fokker-Planck equation for the electron distribution function is formulated incorporating the effects of stochastic acceleration by whistler-mode waves and Coulomb collisions. The stationary solution $f$ to the equation, subject to a zero-flux boundary condition, is found to be a generalized Lorentzian (or kappa) distribution, which satisfies $f\propto v^{-2(\kappa+1)}$ for large velocity $v$, where $\kappa$ is the spectral index. The parameter $\kappa$ depends strongly on the relative wave intensity $R$. Taking into account the critical energy required for resonance of electrons with whistlers, we calculate a range of values of $R$ for each of a number of different space plasmas for which kappa distributions can be expected to be formed. This study is one of the first in the literature to provide a theoretical justification for the formation of generalized Lorentzian (or kappa) particle distribution functions in space plasmas. 
Chun-yu Ma, and Danny Summers