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

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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)

[EQUATION]

[EQUATION]

[EQUATION]

where [FORMULA] is the ion gyrofrequency, [FORMULA] is the Alfvén speed. The quantities [FORMULA] and [FORMULA] are connected with particle-resonating waves propagating outwards and inwards, respectively, and are given by the following expressions

[EQUATION]

[EQUATION]

In Eqs. (18) and (19) k is the wavenumber, [FORMULA] and [FORMULA] 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

[EQUATION]

where [FORMULA] corresponds to the largest scale of energy containing fluctuations and the signs [FORMULA] 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))

[EQUATION]

where [FORMULA] 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 [FORMULA]. If we now substitute Eqs. (18), (19), and (21) into Eqs. (15)-(17) taking into account that [FORMULA], we obtain

[EQUATION]

[EQUATION]

[EQUATION]

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

[EQUATION]

[EQUATION]

where [FORMULA] denotes the exponential integral

[EQUATION]

To derive Eq. (26) for the diffusion coefficient [FORMULA] Eq. (20) has been used. The parameter [FORMULA] is related to the cross helicity [FORMULA] of Alfvénic turbulence as [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998
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