For the amplitude and the polarization vector, one has
A(kn) ∝
√
G(kn) and e
⊥ ·e
z = 0, respectively, with the primed coordinates
determined by a rotation matrix with random angles so
that k ˆez for slab modes and random k directions for isotropic
modes. From the integration of the Newton-Lorentz equation
for the particle motion, various diffusion coefficients can then
be calculated by averaging over an ensemble of particles and
by determining the mean square displacement. For example, the
scattering mean free path in the direction parallel to the background
magnetic field can be obtained as λ = (3/v) (Δz)2
/(2t)
for large times (cf. Sect. 3).