3. Diffusion coefficients
In the present paper only ion interactions with nondispersive
parallel and antiparallel propagating Alfvén waves are
considered. In the case of nonrelativistic particles the quasilinear
Fokker-Planck coefficients can then be written in the following form
where is the ion gyrofrequency, is the Alfvén speed. The quantities and are connected with particle-resonating waves propagating outwards and inwards, respectively, and are given by the following expressions
In Eqs. (18) and (19) k is the wavenumber, and are the differential intensities of left-hand and right-hand circularly polarized Alfvén waves, respectively, so that the mean-squared amplitude of the associated fluctuations is
where corresponds to the largest scale of energy containing fluctuations and the signs correspond to parallel and antiparallel moving waves.
A representative power spectrum of hydromagnetic field fluctuations in the solar wind consists of the inertial and dissipative ranges (e.g. see Zhou & Matthaeus, (1990), Miller & Roberts, (1995)). It is assumed here that the dissipative range has an exponential form, so that the differential intensity can be written as (see Bieber et al., (1988); Smith et al., (1995); Schlickeiser et al., (1991))
where is the dissipative scale. In the following we will consider the case when left- and right-hand polarized waves have the same intensities, that is . If we now substitute Eqs. (18), (19), and (21) into Eqs. (15)-(17) taking into account that , we obtain
To derive Eq. (26) for the diffusion coefficient Eq. (20) has been used. The parameter is related to the cross helicity of Alfvénic turbulence as .
© European Southern Observatory (ESO) 1998
Online publication: June 18, 1998