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 distributio n function is formulated incorporating the effects of stochastic accel eration 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, whic h satisfies f proportional to v (2(k+1)) for large velocity v, where k is the spectral index. The parameter re depends strongly on the relat ive wave intensity R. Taking into account the critical energy required for resonance of electrons with whistlers, we calculate a range of va lues of R for each of a number of different space plasmas for which ka ppa distributions can be expected to be formed. This study is one of t he first in the literature to provide a theoretical justification for the formation of generalized Lorentzian (or kappa) particle distributi on functions in space plasmas.