Analytical reduction of pitch-angle scattering in isotropic turbulence

The scattering of energetic particles in stochastic magnetic fields cannot be described using quasi-linear theories except for simple turbulence geometries. A promising candidate for the analytical description of such scattering processes is the second-order quasi-linear theory [A. Shalchi, Phys. Plasmas 12 (2005) 052905]. For isotropic turbulence, the theory has been evaluated only semi-numerically but the results are in good agreement with numerical simulations [R.C. Tautz, A. Shalchi, R. Schlickeiser, Astrophys. J. 685 (2008) L165]. Here, using well-established methods from the summation of Bessel functions, the equation for the pitch-angle Fokker-Planck coefficient is reduced to a few single and double integrals that are left to numerical evaluation. In doing so, the evaluation of transport parameters is facilitated, thus enabling one to conduct parameter studies.