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b = (X2 +(2rL2X2 ))2 X2 + rL2X2 lX1 -(RrL2X2 Z^X + rL2X2 j

2 ( - (L2X2 ))2X2 + rL2X ) + (2^2X2 ))2X + ^X ) The results of calculations of A eff performed by Dorman and Sergeev (1976)

according to Eq. 1.9.9-Eq. 1.9.15, are presented in Fig. 1.9.1 for the values of the parameters a= 0.25, 0.5, 1 and 1.5; P = - 0.5, 0, 0.5, 1 and 1.5;

. Along the ordinate axis A eff/G is shown with

Fig. 1.9.1. Dependence of Aeff/G (where G = (/2/X2 )3 (X2 -X1)) on R/300h2X2 (where rigidity R in V, h2 in Gs, X2 in cm) for the model of inhomogeneities of a type of

"magnetic clouds" for a = 0.25, 0.5, 1.0 and 1.5 at Xy/X2 = 10-1, 10-2, 10-3 . The thick, dashed, dotted, dash-dotted, and thin lines correspond to P =1.5, 1.0, 0.5, 0, and -0.5 respectively.

Analysis of the above presented expressions (see also Fig. 1.9.1) shows that:

(1) If rL2 >> X then Aeff ^ l irrespective of the character of the inhomogeneity spectrum (at any a and p). Thus if the particle's radius of curvature

is in excess of the size of the largest inhomogeneity scale, then Aeff ^ R .

(2) If L = rL2(X2X << X1, i.e. rL2 << X1 (X1 /X2 , then in all cases Aeff approaches a constant value independent of particle rigidity R.

(3) In the region rL2 < X2 (but l > X1) the mode of the dependence of Aeff on R is determined by the parameters a and p. For example, at P= -1 for any a the dependence of Aeff on R is very weak (as r^i varies from X to zero the path

A eff decreases by a factor of only 2). At ยก3= 0 (which is probably the most realistic case), Aeff ^ R when a= 4/3. If, however, a> 5/3 then Aeff ^ R , and at a< 1 the path A eff has not in practice to be dependent on R. At 3= 0.5 a dependence close to Aeff ^ R will take place at 4/3 < a < 5/3 (approximately, at a = 4/3

Aeff ^ R23 , and at a = 5/3 Aeff ^ R43). At 3 = 1 (when the field strength in inhomogeneities is proportional to the inhomogeneity size, which is probably a fairly realistic case) Aeff ^ R2 for a> 7/3, Aeff ^ R32 for a= 2, Aeff ^ R for a = 5/3, Aeff ^

rV2 for a= 4/3, and, finally, is practically independent of R at a<

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