N

,(Ek ) = 2.2 x(Ek + mpc2 ) Yproton.sr-1.cm-2.s-1.GeV-1 (1.14.

is the differential energy spectrum of proton component of galactic CR outside the Heliosphere, the slope of the primary spectrum y = 2.75, u(r, t) is the solar wind velocity, and

is the diffusion coefficient, Ap (r, Ek, t) is the transport path for particle scattering, v(Ek ) is the particle velocity in dependence of kinetic energy per nucleon Ek :

According to numeral experimental data and theoretical investigations A i (Ek) has a wide minimum in the region 0.1-0.5 GeV/nucleon and increases with energy decreasing lower than this region as about ^ E-1 (caused by the 'tunnel' effect for particles with curvature radius in the interplanetary magnetic field smaller than the smallest scale of hydromagnetic turbulence, see in Dorman, M1975a, and above in Section 1.9) as well as with energy increasing over this interval as « EY, where y depends from the spectrum of the turbulence, and usually increases from 0 up to about 1 for high energy particles of a few GeV/nucleon and then up to about 2 for very high energy particles with radius of curvature in the IMF larger than the biggest scale of magnetic inhomogeneities in the IMF (according to investigations of galactic CR modulation in the Heliosphere it happens at Ek > 15 ■ 20 GeV/nucleon). For calculations of expected space-time distribution of gamma ray emissivity we try to describe this dependence approximately as

Ek E2

To determine the parameters E1; E2, E3 in Eq. 1.14.5 we used observations of solar CR events as well as observations of galactic CR modulation in interplanetary space. The time-dependence of galactic CR primary fluxes for effective rigidities R =2, 5, 10 and 25 GV were found in Belov et al. (1988, 1990) on the basis of ground measurements (muon and neutron components) as well as measurements in the stratosphere by balloons and in space by satellites and spacecrafts. The residual modulation (relative to the flux out of the Heliosphere) for R ~ 10 GV in the minimum and maximum of solar activity was determined as 6 and 24 % (what is in good agreement with results from hysteresis effect obtained on the basis of neutron monitor data (Dorman and Dorman, 1967a,b, 1968; Dorman, M1975b; Alania and Dorman, M1981; Alania et al., M1989; Dorman, Villoresi et al., 1997a,b). According to convection-diffusion model of CR cycle modulation, the slope of the residual spectrum AD(r)/D0 (RR~Y reflects the dependence

In Belov et al. (1988, 1990) the spectral index y was determined as y = 0.4 at 2-5 GV, y = 1.1 at 5-10 GV, and y = 1.6 at 10-25 GV. Eq. 1.14.5 will be in agreement with these results and with data on FEP events in smaller energy range if we choose E1 = 0.05 GeV/nucleon, E2 = 2 GeV/nucleon, and E3 = 5 GeV/nucleon.

The dependence of the transport path from the level of solar activity is characterized by A i (W). This parameter can be determined from investigations of galactic CR modulation in interplanetary space on the basis of observations by neutron monitors and muon telescopes for several solar cycles. According to Dorman and Dorman (1967a,b, 1968) A(w)<* W_1/3 for the period of high solar activity and A i (W )<* W_1 for the period of low solar activity. According to Dorman and Dorman (1967a,b, 1968), Dorman (M1975b), Dorman, Villoresi et al. (1997a,b), the hysteresis phenomenon in the connection of long-term CR intensity variation with solar activity cycle can be explained well by the analytical approximation of this dependence, taking into account the time lag r/u of electromagnetic processes in the interplanetary space relative to solar activity phenomena on the Sun caused these processes:

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Renewable Energy 101

Renewable Energy 101

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