4.7. Statistical acceleration by scattering on small angles
In the above the statistical acceleration of particles in case of large-angle scatterings was considered. When treating the acceleration processes in the space plasmas, however, it is of great interest to consider also the small-angle scattering. First, we shall analyze the small- angle scattering (Section 4.7.1), then determine the energy change in an elementary scattering event (Sections 4.7.2-4.7.4), and finally, estimate the total energy change along the transport scattering path (Section 4.7.5).
The particles are scattered through small angles by magnetic clouds when the particle Larmor radius in inhomogeneities p > l, where l is the characteristic scale of inhomogeneities. In this case the characteristic scattering angle of a particle with rigidity R is (see Section 1.8)
where h is the magnetic field intensity in inhomogeneities.
Let the energy change in an elementary scattering event be determined at first. The small-angle scattering also takes place during interactions of the particles with sufficiently high energies with inhomogeneities of types j = 1, 2, and 3 which are disturbances against the background of homogeneous field (considered in Chapter 1, Section 1.9). If in the Cartesian system x, y, z the homogeneous field Ho = (Ho,0,0), then the disturbance h = (0,h(x),0). In this case, according to Parker (1964), h(X) = ho exp(- x2/l2 h + (-1) - - X]
where j = 0, 1, 2 is the type of inhomogeneity. The fields h(X) in inhomogeneities of types j = 1, 2, and 3 were shown in Fig. 1.8.4 in Chapter 1. In this case, according to Parker (1964) the scattering angle is
2 R300Ho exp l s2 0
where l is in cm, R in V, and Ho in Gs. The mode of the dependence of 9 on R for j = 1, 2, and 3 is shown in Table 1.8.1 (see Chapter 1, Section 1.8.6) and in Fig. 4.7.1-4.7.3.
Fig. 4.7.2. The same as in Fig. 4.7.1 but for j = 2.
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