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Fig. 3.6.10. 48 second averaged Heliospheric magnetic field magnitude observed by Voyager 1 (upper panel) near crossing of Termination shock on day 351 of 2004. Lower panel presents measurement of daily averaged higher frequency fluctuations up to 0.25 HZ over 16 min intervals. According to Ness et al. (2005).

Ness et al. (2005) came to conclusion that the Termination shock was observed by the Voyager 1 Magnetic Field Experiment in late 2004 when Voyager 1 crossed or was crossed by the Terminal shock at 94.0 AU and 35°N and entered the Heliosheath.

3.7. Radial CR pressure effects in the Heliosphere

3.7.1. On a necessity of including non-linear large-scale effects in studies of propagation of solar and galactic CR in interplanetary space.

In studies of a modulation of galactic CR and a propagation of solar CR, the solar wind is usually considered to be set, independent of intensity and gradients of CR whereas the effects of galactic CR is comparable, or even more than effects of the other factors also limiting solar wind propagation (re-charging, pressure of galactic magnetic field etc.). Therefore, it is necessary to take into account the inverse action of CR on the solar wind, i.e. to solve a self-consistent problem. Estimates of this action were obtained in Axford and Newman (1965), Dorman and Dorman (1968a,b,c, 1969, 1971), Sousk and Lenchek (1969), Dorman (1971b, 1972b), Holzer (1972), Belov et al. (1972), Dorman and Babayan (1975), Babayan and Dorman (1976, 1977a,b, 1979), Babayan et al. (1976), Dorman, Babayan et al. (1978a,b). In particular, in the work of Holzer (1972), there was considered the interaction of solar wind with neutral gas, galactic CR, thermal plasma and galactic magnetic field. The first two causes result in a volume force braking a supersonic flow. The second two causes provide the action of surface force and may result in arising of shock wave. The surface force has the normal and tangential components; therefore the shape of a heliospheric cavity, occupied by supersonic solar wind, will be stretched. A density of interstellar atomic hydrogen is, apparently, insufficient for the braking action to solar wind without forming a shock wave. It is expected that the penetration of interstellar neutral hydrogen into the Heliosphere result in a heating of solar wind at great distances from the Sun. This effect may however be at least partially, masked by dissipation processes and by a presence of jets in solar wind. It was noticed that penetration of interstellar gas into solar system can noticeably vary a state of ionization, for example, of helium.

The boundary of the Heliosphere, of the helio-pause, determined by the balance of pressure of radially outflowing solar wind plasma and interstellar magnetic field may be noticeably different from a spherical surface owing to anisotropy of a pressure of interstellar magnetic field along the surface. The Heliosphere has a tendency to be stretched along a local galactic magnetic field; the exact shapes and its dimension depend on the intensity of the interstellar magnetic field, the ion pressure in interstellar space, the density of interstellar hydrogen, and on the flux of the solar wind. Possible observable results of non-sphericity of Heliosphere are an additional contribution to anisotropy of galactic CR and anisotropic La distribution of a background radiation owed to scattering on 'hot' hydrogen atoms arising in the process of re-charging outside helio-pause (it is expected that the maximum intensity of this radiation will be observed along the direction of local galactic magnetic field).

3.7.2. Radial braking of solar wind and CR modulation: effect of galactic CR pressure

Babayan and Dorman (1976) obtained integer-differential equation describing non-linear interaction of galactic CR with solar wind for a spherically symmetric model of solar wind with assumption of isotropic diffusion. The equation was numerically solved by the Runge-Kutt method for interstellar spectrum of CR in the form of a power law on kinetic energy and the character of solar wind braking was determined in the minimum and maximum of solar activity depending on the value of Ek,min which determines the lower boundary of energy spectrum of primary CR

in interstellar space. A solution was obtained for the case in which the transport path for scattering A is independent of the distance to the Sun. It was noticed that the same method could be applied to solve the integro-differential equation for the solar wind velocity also in the case in which A is presented in the form of a product of two functions, one of which depends only on a distance to the Sun and the second depends only on the energy of cosmic radiation particles.

For a spherically symmetric model of solar wind with assumption of isotropic diffusion, Babayan and Dorman (1977a) obtained a self-consistent integro-differential equation describing action of galactic CR on the solar wind. The equations, describing solar wind propagation and including the effect of CR in spherically symmetric case, have the following form:

where r is a distance to the Sun; p, u are a density and velocity of solar wind; Pc is a pressure of CR. Gravitation plays a substantial role only up to the distances at which a transition of solar wind from subsonic to supersonic flow takes place (Parker, M1963). As this occurs at the distances of several solar radii, and we consider distances greater than 1 AU, on the right-hand side of Eq. 3.7.2 the terms are absent which describe the gravitational effect and a gradient of solar wind. The pressure of CR with isotropic distribution is

where n(Ek, r) is the energy spectrum of CR density at the distance r from the Sun;p and v are a momentum and velocity of particles. Substituting Eq. 3.7.3 in Eq. 3.7.2 and using Eq. 3.7.1, we obtain du dr

3r12u1p1 o dr

where r\ = 1 AU; u, p are respectivly the velocity and the density of the solar wind on the Earth's orbit. The factor dn/dr, in its turn, is determined by the character of the modulation of galactic CR in interplanetary space, i.e. is determined, finally, by the solar wind's velocity u(r) and by the transport path for particle scattering A(r). As was shown in Dorman (1967), the exact analytical solution of the problem of modulation in the two simplest cases when A = const and A rc r may be represented (with the relative accuracy to 10%) in the form:

where no (E^) is the energy spectrum of CR density outside solar wind, ro is the wind's dimension. Substituting Eq. 2.21.5 in Eq. 3.7.4 we have du dr ru

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