Astron. Astrophys. 335, 746-756 (1998)

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 (Schlickeiser, 1989)

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

In Eqs. (22)-(24) we have used the following denotations

where denotes the exponential integral

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
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