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

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4. Parameters of the problem

Taking into account Eq. (4) we obtain for the cosine of the angle [FORMULA] between the magnetic field vector and the radial direction

[EQUATION]

Furthermore we shall assume that

[EQUATION]

where [FORMULA] and [FORMULA] in view of ULYSSES observations may depend on the colatitude [FORMULA] (see Forsyth et al., (1996). Then by use of Eq. (4) we shall have for the last factor on the right-hand side of Eq. (26)

[EQUATION]

where [FORMULA], and

[EQUATION]

It is known from ULYSSES observations that both [FORMULA] and [FORMULA] are latitude-dependent values (see e.g. Forsyth et al., (1996)). But we shall assume here that the ratio [FORMULA] essentially behaves as a constant. On the other hand we shall consider the magnitude of this value as a free parameter. By use of Eq. (4) and adopting an electron number density according to [FORMULA], where [FORMULA] = const, we can obtain

[EQUATION]

In Eq. (32) [FORMULA], and

[EQUATION]

Furthermore for this paper we shall specify pick-up ions as pick-up protons. The ratio [FORMULA] for protons can be written as

[EQUATION]

All calculations presented here were carried out using the following values for the basic parameters: [FORMULA] km/s, [FORMULA] km/s, [FORMULA] cm-3, [FORMULA]. Also it was assumed that [FORMULA] cm-1 (see Belcher & Davis, (1971); Jokipii & Coleman, (1968)), and [FORMULA] cm (Schlickeiser et al., (1991)). Then the dimensionless value L (see Eq. (25)) can be written as [FORMULA]. Calculations with [FORMULA] (the dissipative range is absent) were also carried out. What concerns the spatial dependence of [FORMULA] (see Eq. (29)) we assume that [FORMULA]. This dependence follows from the WKB theory for the transport of nondissipative Alfvén waves in the solar wind (Hollweg, (1974)) and is close to observations with the HELIOS spacecraft (Tu & Marsch, (1995)).

It can be shown from the definition (27) that at [FORMULA]

[EQUATION]

Since [FORMULA] we can admit here that [FORMULA]. Thus the diffusion coefficient [FORMULA] (see Eq. (26)) depends only on two free parameters, namely [FORMULA] and [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998
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