The Parallel Diffusion Coefficient of Energetic Particles in a Spatially Varying Magnetic Field

In the theory of energetic particle transport, the spatial variation of large-scale magnetic fields gives rise to a so-called adiabatic focusing term in the pitch-angle-dependent transport equation. This focusing term leads to the effect of convection, but it also alters the parallel spatial diffusion coefficient. Over the past few decades researchers have tried to derive analytical forms for the parallel diffusion coefficient as a function of the focusing length. Two different results have been derived contradicting each other. In the current paper we revisit this problem and provide the final solution. We combine previously developed numerical methods such as the subspace approach, allowing us to compute the parallel diffusion coefficient as a function of the focusing length with very high precision within a very short computational time. Most importantly, we derive an exact formula for the diffusion coefficient by employing analytical theory. The new formula agrees perfectly with the numerically obtained results proofing its validity.