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Formation of Power-law Energy Spectra in Space Plasmas by Stochastic Acceleration due to Whistler-Mode Waves

Chun-yu Ma·Danny Summers
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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 $f\propto v^{-2(κ+1)}$ 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.

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BibTeXRIS

Chun-yu Ma, Danny Summers. 1998-10-26. Formation of Power-law Energy Spectra in Space Plasmas by Stochastic Acceleration due to Whistler-Mode Waves. https://doi.org/10.1029/1998gl900108

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