Estimation of possible additional acceleration of CR particles in the Heliosphere and in stellar winds

Let us consider first the situation with CR particles of small energy, about Ek ~ 100 MeV/nucleon. In our Heliosphere there is solar wind with average velocity u^ ~ 4 x 10 cm/sec (background plasma) and characterized in the maximum of solar activity by a transport path 4 ~ 3 x 10 cm for CR with energy Ek ~ 100 MeV/nucleon. The dimension of the Heliosphere r0 ~ 100 AU, so the life-time inside the Heliosphere of these particle will be T ~ r0 / 2vA1 ~ 3 x 10 sec ~ 1 year (Dorman and Dorman, 1967a,b; Dorman, 1991; Dorman et al., 1997a,b,c,d).

on the other hand, in the periods of high solar activity there are also shock waves, magnetic clouds, and high speed streams moving with an average velocity u20 ~ 108 cm/sec. The CR particle scattering on these objects can be characterized in the periods of high solar activity by 4 ~ 1013 cm. Then according to Eq. 4.20.21 the characteristic time of particle acceleration will be Tac ~3 x107 sec ~ 1 year. According to Eq. 4.20.23 in this case there can be expected additional acceleration of small energy particles in exp(T/Tac)~ few times.

For low level of solar activity 4 increases and T decreases; there will also be a big increase of 4, so Tac will increase. Therefore in periods of low solar activity we expect T/Tac << 1 and the additional acceleration considered even for CR particles with energy ~ 100 MeV/nudeon will be not effective.

For particles of higher energy with > 1 GeV/nucleon the value of /ยก1 > 1013 cm in a maximum of solar activity, and are expect T ~ r212v 4 < 3 x 10 sec. Then in this case T/Tac << 1 even in periods of high level of solar activity and additional acceleration is not effective. We came to the conclusion that the mechanism of CR particle acceleration considered can be effective in the Heliosphere only for small energy particles in periods of high solar activity.

In stellar winds the effectiveness of the mechanism of additional particle acceleration considered will depend on the ratio T/Tac which can be determined from the values of 4,42,0,u20 - u10 as

and the increase of the particle's energy will be determined according to Eq. 4.20.27 as exp((/ Tac).

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