From Fig. 2.32.2 follows, that only two SNRs give significant contribution to observed proton flux in the high energy region: Loop-I gives from 60% to 70% and Loop-II from 12% to 7% (in dependence of energy). Lagutin et al. (2005) note that this result contradicts with observed very small amplitude of CR anisotropy, what can be owed either to not correctness of assuming about equal output of SN in CR protons (Eq. 2.32.16) or there are some other main sources of high energy CR (see the discussion also in Ptuskin, 1997; Cronin, 2001; Olinto, 2001; Hoerandel, 2004).

Fig. 2.32.2. Relative contribution of each nearby SNRs to proton flux near the solar system. According to Lagutin et al. (2005).

Lopus Loop

CTB13

s 149 STB 72

Loop III

Fig. 2.32.2. Relative contribution of each nearby SNRs to proton flux near the solar system. According to Lagutin et al. (2005).

2.33. CR propagation in large-scale anisotropic random and regular magnetic fields

In series of papers of Mel'nikov (1996, 2000, 2005a,b,c) kinetic coefficients and parallel (to the mean field) mean free paths of CR particles in large-scale anisotropic random magnetic field are obtained with using nonlinear collision integral, i.e., by taking into account the strong random scattering.

It follows from the analysis of experimental data performed by Matthaeus et al. (1990) and Bieber et al. (1996) that the distribution of interplanetary magnetic field fluctuations is anisotropic. In the weakly disturbed inner Heliosphere, the preferential direction of the magnetic field fluctuations is perpendicular to the regular magnetic field. The wave vectors of the fluctuations are also mainly perpendicular to the regular magnetic field, which gives rise to two-dimensional fluctuations. In the interplanetary medium the energy of the two-dimensional fluctuations can reach 85% of the energy of the random magnetic field. The parallel transport mean free paths of high energy particles in the interplanetary magnetic field, including the anisotropy of random fluctuations, were calculated numerically by Bieber et al. (1994), Teufel and Schlickeiser (2002, 2003), Teufel et al. (2003), Shalchi and Schlickeiser (2004) and analytically by Droge (2003). These authors used a quasi-linear random magnetic field approximation and introduced the cyclotron resonance broadening using a de-correlation in the correlation tensor of the random magnetic field. They showed that CR particles are scattered weakly by two-dimensional fluctuations. The calculated transport mean free paths of solar CR protons exceed their observed values by several tens or hundreds of times. Mel'nikov (2005a) shows that for nonlinear broadening of two-dimensional perturbations the random scattering frequency increases significantly, and the transport mean free path decreases.

2.33.2. Main equations and transforming of collision integral

Mel'nikov (2005a) has considered the kinetic coefficients and particle transport mean free paths over a wide energy range from 1 MeV to several GeV in the inner Heliosphere and at energies above 10 GeV in the outer Heliosphere, including those at the energies at which rg ~ L//, L^ where rg is the gyro-radius in the random magnetic field, and L^ and L// are the perpendicular and parallel (relative to the regular magnetic field) correlation lengths, respectively. It was used the following kinetic equation for the average particle distribution function F (r, p, t ) with the nonlinear collision integral (Mel'nikov, 1996, 2000):

dt or I

where

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