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 whistlermode 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 ∝ v for large velocity v, where κ is the spectral index. The parameter κ 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.