It is seen from Eq. 2.6.21 for D3 that D3 is divergent at the value v = 2 of the index of the spectral function of turbulence. This is connected with the circumstance that at v = 2 a particle interacts with the waves of vanishing amplitudes, and when there is a sufficiently weak dependence of the amplitude on the scale of pulsations, the effective time of a particle interaction with a wave tends to zero.

Actually integrating over k, one should cut off the integral at the wave length corresponding to a particle Larmor radius. At v = 2 this results in a logarithmic dependence of the diffusion coefficient on the momentum in the momentum space (Tverskoy, 1967a).

2.6.3. The case of small wave lengths

In this case a >> 1, and the expressions for Db D2, D3 are

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