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Fig. 3.7.7. The character of a decrease of solar wind velocity u with a distance from the Sun

r including the process of re-charging at u = 3x10 cm/sec, N1 = 5 cm , ß = 0,

NHo = 0.1cm (a), NHo = 0.5 cm (b), and NHo = 1.0 cm (c); curves: 1 -

no x Ek2'5, Wc = 1 eV/cm3 ; 2 - no E-2-5, Wc = 2.67 eV/cm3 ; 3 - no ~ E-3 0,

Wc = 1 eV/cm3 ; 4 - no ~ E-3 0, Wc = 7.11 eV/cm3 ; 5 - no R"2 5, Wc = 1 e^cm3 .

The calculations for Fig. 3.7.7 were made for various values of the interstellar density of energy of CR: curves 1, 3 and 5 correspond to Wc = 1 eV/cm-3, and curves 2 and 4 are related to the values Wc = 2.67 and 7.11 eV/cm-3. A character of dependence of u/u on r is substantially dependent on Wc, Nho and on a form of interstellar energy spectrum. In Fig. 3.7.8 the dependences of u/u on r are presented for Nho = 0.5 cm-3 at Wc = 1 eV/cm-3 and the spectrum form ^ E- for ß= 0, 0.5 and 1.

Fig.3.7.8. The character of a decrease of solar wind velocity u with distance from the Sun r, including re-charging process depending on parameters ¡3 at u = 3 x10 cm/sec, N1 = 5 cm-3 , NHo = 0.5 cm-3 , n0 ~ £-3 0 , Wc = 1 e^cm3 . Curves 1, 2 and 3 correspond to ¡3= 0, 0.5 and 1.

Fig.3.7.8. The character of a decrease of solar wind velocity u with distance from the Sun r, including re-charging process depending on parameters ¡3 at u = 3 x10 cm/sec, N1 = 5 cm-3 , NHo = 0.5 cm-3 , n0 ~ £-3 0 , Wc = 1 e^cm3 . Curves 1, 2 and 3 correspond to ¡3= 0, 0.5 and 1.

It is seen from Fig. 3.7.8 that with a growth of parameter 3 in Eq. 3.7.8, the dimension of the region occupied by solar wind should be somehow increased: the distance where u/u is decreased by an order, equals 72, 100, and 112 AU, respectively, at 3 = 0, 0.5, and 1.

The character of CR modulation at Nh0 = 0.5 cm-3 is seen from Fig. 3.7.9 for particles with the rigidity R from 0.5 to 100 GV.

A comparison with the results of Section 3.7.2 (where it was assumed Nh0 = 0) shows that including of the process of re-charging results in some weakening of the modulation depth; it is caused by more rapid deceleration of solar wind with a growth of Nh0 .

Fig. 3.7.9. Modulation depth of CR n/no depending on a distance to the Sun r for particles with the rigidity R = 0.5, 1, 5, 10, and 100 GV (Curves 1-5, respectively) at Nh = 0.5 cm-3 , 0= 0, u = 3 x107 cm/sec, N1 = 5 cm-3 , no - E-2'5 , Wc = 1 eV/cm3 .

Fig. 3.7.9. Modulation depth of CR n/no depending on a distance to the Sun r for particles with the rigidity R = 0.5, 1, 5, 10, and 100 GV (Curves 1-5, respectively) at Nh = 0.5 cm-3 , 0= 0, u = 3 x107 cm/sec, N1 = 5 cm-3 , no - E-2'5 , Wc = 1 eV/cm3 .

3.8. Expected change of solar wind Mach number accounting the effects of radial CR pressure and re-charging with neutral interstellar atoms

If we introduce the Mach number M = u/Vs , where vs AyPglp}11 (3-8.!)

is the sound velocity, then on the basis of Eq. 3.7.13, taking into account the analytical solution of Eq. 3.7.11 for CR isotropic diffusion, we obtain:

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Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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