4. Parameters of the problem
where and in view of ULYSSES observations may depend on the colatitude (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)
It is known from ULYSSES observations that both and are latitude-dependent values (see e.g. Forsyth et al., (1996)). But we shall assume here that the ratio 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 , where = const, we can obtain
All calculations presented here were carried out using the following values for the basic parameters: km/s, km/s, cm-3, . Also it was assumed that cm-1 (see Belcher & Davis, (1971); Jokipii & Coleman, (1968)), and cm (Schlickeiser et al., (1991)). Then the dimensionless value L (see Eq. (25)) can be written as . Calculations with (the dissipative range is absent) were also carried out. What concerns the spatial dependence of (see Eq. (29)) we assume that . 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
Since we can admit here that . Thus the diffusion coefficient (see Eq. (26)) depends only on two free parameters, namely and .
© European Southern Observatory (ESO) 1998
Online publication: June 18, 1998