which gives:

rmod = rtsw(b + exp(- (Xomax )optbu1 /rtsw)). (2.46.37)

By assuming that the radius of modulation region rmod for alpha-particle GOES data (effective rigidity 0.9 GV according to Table 2.46.2) is about the same as the radius of the Heliosphere rtsw , we obtain from Eq. 2.46.37 for rmod = rtsw = ro the following result:

For the most reliable value of b ~ 0.3 we obtain from Eq. 2.46.34 and Eq. 2.46.38 ro = 13.76X7.73X0.84 = 90 AU . (2.46.39)

We can compute regression coefficients A (indicating the natural logarithm of CR alpha-particle intensity out of the Heliosphere) and B (indicating the diffusion coefficient) in Eq. 2.46.29 for the values obtained by Eq. 2.46.34:


and according to Eq. 2.46.38

we obtain for the radial effective diffusion coefficient

and for the effective transport path (by using Table 2.46.2)

It should be noted that if the diffusion time lag is not taken into account, the result (Xomax) t ~ 19 av. months for alpha-particles in the energy interval 330500 MeV will be obtained instead of the value described by Eq. 2.46.34, in contradiction with results based on satellite proton data and on NM data (Dorman, 2001; Dorman et al., 2001a,b).

preliminary results, obtained for satellite alpha-particles data for other energy intervals 160-260 MeV and 60-160 MeV (values of (Adr) t and (Xomax) t)

show that in these cases the influence of SEp events was not totally excluded, and that there is a necessity of additional data cleaning.

2.46.10. Peculiarities in the solution of the inverse problem for small energy CR particles

The specific aspects in the solution of the inverse problem for small energy CR particles for long-term variations caused by propagation and modulation in the Heliosphere (convection-diffusion and drift processes) are the following:

• remarkable diffusion time-lag, increasing with decreasing particle energy, and

• remarkable drift modulation, whose relative role is also increasing with decreasing particle energy.

The obtained results for convection-diffusion and drift modulations have been used for the analysis of proton and alpha-particle satellite data. The results shown in Fig. 2.46.7 and Fig. 2.46.8 lead to the following conclusions:

• The procedure described here to obtain the expected convection-diffusion modulation, by taking into account the additional diffusion time lag in Heliosphere for small energy particles observed on satellites, and also by taking into account drift modulation based on Burger and Potgieter (1999), can be used to describe the long-term variation of galactic CR intensity at small energies;

• The procedure described above for excluding solar energetic particle events from satellite data for particles with energies Ek > 106 MeV and Ek > 100 MeV - made it possible to obtain from satellite data information on real long-term variation of galactic small-energy CR intensity, which can be compared with theoretical expectations;

• The Xo max values obtained from this comparison, Adr max, the dimension of modulation region and the effective radial diffusion coefficient are in good agreement with those obtained by Dorman (2001), Dorman et al. (2001a,b) on the basis of NM data, and with those expected by Burger and Potgieter (1999). This means that the dimension of modulation region is very close to the dimension of the Heliosphere.

• GOES data for small energy intervals 60-100 MeV, 30-60 MeV, and others, have been also analyzed. A contradictory dependence of the determined Xo max and Adr max on the energy has been obtained.

We think that the applied procedure for excluding events of CR increases for narrow small energy intervals is not enough accurate: these data still reflect an appreciable contribution of solar CR (without time-delay and with about opposite phase to variation of galactic CR) which leads to an appreciable decrease in the observed modulation and even to a change in phase. This could be the main reason for the contradictory determination of Xo max and Adr. It is necessary to develop more effective procedure for excluding the local CR influence on small energy particle intensity variation observed by satellites. To do that it will be important to use also satellite data of isotopes which are not contaminated by small energy solar CR.

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