## R 2UiW2

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).

### 4.7.1. Small-angle scattering

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

Ho l

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. 4.7.1. The scattering angle 9for different values of ratio ho/Ho (from 0.01 up to 1.0 from bottom to the top) in dependence of 2rgjl = 2R/300Hol for the scattering by inhomogeneities of type j = 1. Fig. 4.7.2. The same as in Fig. 4.7.1 but for j = 2.