Perturbation theory based solution of the pitch-angle dependent cosmic ray diffusion equation

The motion of cosmic rays and energetic particles in general is described via transport equations. If a pitch-angle dependent description is desired, a Fokker-Planck equation provides the basis for exploring the particle motion. To date, no exact and pure analytical solution to the two-dimensional cosmic ray Fokker-Planck equation has been found. Previous attempts are either solutions of the pitch-angle averaged equation or the space integrated equation. Of course, numerical calculations can easily be performed but those are not very useful in astrophysical applications. In the current paper we employ perturbation theory in order to solve the cosmic ray Fokker-Planck equation. Corrections up to fourth-order to the eigenvalues and second-order eigenfunctions are computed. Our results are compared with previous solutions. Furthermore, we discuss applications such as estimating higher order correlations occurring in analytical treatments of perpendicular transport.