Fig. 2.34.2. The same as in Fig. 2.34.1, but for the modified anomalous diffusion (MAD) model of K__. From le Roux et al. (1999a).

(2.1) A_ x rg contributes mainly to Arr beyond ~ 20 AU so that Arr has a strong r-dependence upstream beyond ~ 30 AU.

(2.2) The drop in Arr across the termination shock is reduced (sin2y is less

sensitive to the shock jump than cos y).

(2.3) The R-dependence of Arr is determined by A//, giving it the same dependence as for the MQLT model.

(2.4) The negative r-dependence of Arr below R < 1 GV is weakened by the important contribution of A_ to Arr.

In Fig. 2.34.3 and Fig. 2.34.4 calculations of mean free paths are presented on the basis of the NP model.

Fig. 2.34.3. As in Fig. 2.34.1, but for the non-perturbative (NP) model of k_. From le Roux et al. (1999a).

The key results produced by the NP model are the following: (3.1) A__ contributes significantly to Arr beyond ~ 20 AU from the Sun below ~ 3 GV so that the r-dependence of Arr upstream is reduced compared to the MAD case for intermediate R-values (Fig. 2.34.3). This is because A__ is independent of rg (mz>> 1 in Eq. 2.34.5).

(3.2) For R << 3 GV beyond ~ 20 AU, A__ and therefore Arr is strongly dependent on r (a>T<< 1 in Eq. 2.34.5).

(3.3) Above ~ 3 GV beyond ~ 20 AU A// contributes the most to Arr.

(3.4) Consequently, Arr features a three interval R-dependence in the outer Heliosphere with the weakest dependence Arr ^ R for intermediate values of R < 3

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