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

• Published in: Geophysical research letters Vol. 25; no. 21; pp. 4099 - 4102
• Main Authors: Ma, Chun-yu, Summers, Danny
• Format: Journal Article
• Language: English
• Published: Washington, DC Blackwell Publishing Ltd 01.11.1998; American Geophysical Union
• Subjects: Astronomy; Earth, ocean, space; Exact sciences and technology; Fundamental aspects of astrophysics; Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations; Magnetohydrodynamics and plasmas; Energy spectra; Astrophysical plasma; Theoretical study; Particle acceleration; Fokker-Planck equation; Particle wave interaction; Coulomb interaction; Power law; Steady state solution; Whistler wave
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/1998GL900108

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.