Formation of power‐law energy spectra in space plasmas by stochastic acceleration due to whistler‐mode waves

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Abstract
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 ∝ υ2(κ+1) for large velocity υ 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.
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