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50bs (R) = AD(R )D65 (R) = aR~Y, AD(R) = D(R) - D65 (R),

So (r) = AD0 (RVD65 (R) = (52 ± 8)R"L0±a\ AD0 (r) = Da (r) - D65 (R)

^tot(R) = ADtot(RVD0 (R) = aR-Y, ADtot(R) = D(r)-Do(r) (3.6.1)

where D65 (R) is the observed spectrum in the minimum of SA in 1965, and Do (r) is the CR spectrum out of the Heliosphere, in the interstellar space.

Fig.3.6.4. Rigidity spectra: of observed long term CR variations (a), of residual modulation (b) and of total CR modulation (c) during the various time intervals indicated on the curves.

Fig.3.6.4. Rigidity spectra: of observed long term CR variations (a), of residual modulation (b) and of total CR modulation (c) during the various time intervals indicated on the curves.

The residual modulation was found So (R ) = 6 .0 ±1.2 % at an effective rigidity

R ~ 10 GV (which is in good agreement with results in Fig. 3.6.2 for the hysteresis effect in Chicago neutron monitor data). The slope of the total spectrum modulation (the panel c in Fig. 3.6.4) gets steeper with increasing rigidity and the spectral index increases:

£tot (R)-R ~y; 0.4 at R = 2 ■ 5 GV; y = 1.1 at R = 5 ■ 10GV; Y = 1.6 at R = 10 ■ 25 GV. (3.6.2)

In the first approximation the effective transport path in the interplanetary space will be

where y is determined by Eq. 3.6.2. The tendency of increasing y with increasing rigidity R is seen also for CR propagation in the interstellar space for much higher energies 1°14-1°17 eV (Berezinsky at al., M199°) and for solar CR in the solar atmosphere and in interplanetary space for the much lower energy region eV (Dorman and Miroshnichenko, M1968; Dorman, M1978; Dorman and Venkatesan, 1993; Miroshnichenko, M2°°1). These intervals in the first approximation correspond to the product of magnetic field strength on the characteristic scale of turbulence in the space where CR propagate.

3.6.3. CR anisotropy in the Heliosphere

The information on possible types of galactic CR anisotropy in the interplanetary space and on their dependence on helio-latitude and radial distance as well as on the level of solar activity is very important for the problem of kinetic stream instability in the Heliosphere (in details see below Section 3.12). CR penetrate inside the Heliosphere and propagate in extended solar wind with frozen in regular spiral magnetic field with inhomogeneities. Fig. 3.6.5 (from Moraal, 1993) shows several mechanisms of CR anisotropy formation in the meridian plane: convection-diffusion, CR density gradient drift, terminal shock wave drift, polar drift and neutral current sheet drift.

Heliosphere Particle Density
Fig. 3.6.5. Meridian projection of a quarter Heliosphere showing the major galactic CR transport processes and mechanisms of anisotropy formation (according to Moraal, 1993).

The convection anisotropy is determined by the velocity of the solar wind and directed radially from the Sun; diffusion anisotropy is mainly along spiral magnetic field and directed towards the Sun. Resulting anisotropy increased with the radial distance (proportionally in the first approximation) and does not depend on the direction of the spiral interplanetary magnetic field. The direction and the value of the gradient density drift anisotropy depends on the directions of gradient and magnetic field and is proportional to the product of their particle Larmor radius and CR density gradient. The drift along the terminal shock wave gives important particle acceleration (formation of so called anomaly CR in low energy range). The neutral current sheet drift is very important for CR long term modulation; its direction changed every 11 years with changing of the sign of the Sun's general magnetic field: it is a main cause of the 22-year CR variation. In the vicinity of equatorial plane there is also a very important density drift mechanism cased by CR density gradient perpendicular to the ecliptic plane that gives some average anisotropy perpendicular to IMF and CR gradient. There are also North-South CR anisotropy caused by the some asymmetry in latitudinal distribution of solar activity and IMF (see review in Dorman, 2000). Ahluwalia and Dorman (1995a,b), Dorman and Ahluwalia (1995) show that observed anisotropy is mixed, produced by several mechanisms with different properties and different rigidity spectra. The observed galactic CR anisotropies reflect real CR fluxes and are determined by complicate CR density distribution in space and energy balance caused by many processes: CR convection, anisotropy diffusion, neutral sheet drift, curvature drift, drift in inhomogeneous magnetic field, drift along shock wave front with energy change and so on. Let us note that the main galactic CR anisotropy caused by the convection-diffusion mechanism is expected to increase with increasing radial distance, which is important for CR kinetic stream instability.

3.6.4. Possible structure of the Heliosphere and expected nonlinear effects

A possible structure of the Heliosphere according to Dorman (1991) is shown on Fig. 3.6.6.

Heliosphere Particle Density
Fig. 3.6.6. Expected structure of the Heliosphere. According to Dorman (1991).

In the region of the inner planets the dynamic pressure of the solar wind is much larger than the CR pressure but at larger distances these pressures became of about the same order and the nonlinear effects then became important. The problem is what is the size of the Heliosphere. About 40 years ago many scientists came to the conclusion that the radius of the Heliosphere is not more than 10-15 AU, but from investigations of CR hysteresis phenomena we determine that this size must be not smaller than the size of effective modulation region for small energy particles, i. e. not smaller about 100 AU (see Section 3.6.1). If the size of the Heliosphere is as big as shown in Fig. 3.6.6, then the dynamical pressure of solar wind in the outer part of the Heliosphere becomes comparable with the CR pressure and it is necessary to take into account the influence of galactic CR pressure on the solar wind's propagation. This was first done by Axford and Newman (1965), and then by Dorman and Dorman (1968a,b,c, 1969), Babayan and Dorman (1977, 1979a,b, 1981, 1990). It was shown that the solar wind's radial deceleration by the pressure of galactic CR becomes important in the outer Heliosphere. The CR modulation in the interplanetary space is not spherically symmetric; the modulation is expected to be stronger in the low helio-latitude region. Therefore one expects that CR pressure in the high helio-latitude region will be higher than in the low helio-latitude region. If it is so, we shell expect the transverse compression of solar wind streams by CR pressure caused by the transverse CR density gradient (Dorman and Dorman, 1969; Babayan and Dorman, 1977).

3.6.5. Studies of the termination shock and heliosheath at > 92 AU: Voyager 1 magnetic field measurements

Now, about 40 years after our prediction (on the basis of investigation of the nature of CR-SA hysteresis effect) that the dimension of the Heliosphere is about 100 AU (Dorman and Dorman, 1967a-e), was obtained experimental evidence. According to Ness et al. (2005), the Heliospheric Magnetic Field (HMF) has been measured by twin Voyager spacecrafts, Voyager 1 and Voyager 2, which were launched in 1977. After encounters with the 4 giant outer planets, they have more or less continuously measured the Heliospheric Magnetic Field (HMF) from 1 to ~96 AU (at June 2005). Thus, magnetic field observations now cover well over a full 22 years long solar magnetic cycle. The temporal and spatial variations of the magnitude of the HMF have been found to be well described by parker's Archimedean spiral structure (parker, M1963) when due account is made for time variations of the source field strength and solar wind velocity. The HMF generally had the expected properties at these distances and epochs through several solar activity cycles until late in 2004 when Voyager 1 was at 94 AU and heliographic latitude of 35° N. The paper of Ness et al. (2005), summarizes HMF observations which demonstrate clearly that the theorized and long-sought Termination Shock (TS) associated with the interaction of the solar wind with the local interstellar medium was detected in mid-December 2004 by Voyager 1 at 94.0 AU at 35° N heliographic latitude: the magnitude of HMF increased by a factor of ~3-4 and fluctuations were enhanced significantly, it has been observing in-situ a new astrophysical plasma regime referred to as the Heliosheath (HS). It was note that observations of the HMF in 2002-2003 did not provide evidence for any crossings of the termination shock near 85 AU as earlier was proposed (Burlaga et al., 2003; Krimigis et al., 2003). Main results of Ness et al. (2005) are shown in Fig. 3.6.7-3.6.9.

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