The influence of the Kubo number on the transport of energetic particles

Abstract

We discuss the interaction between charged energetic particles and magnetized plasmas by using analytical theory. Based on the unified nonlinear transport (UNLT) theory we compute the diffusion coefficient across a large scale magnetic field. To achieve analytical tractability we use a simple Gaussian approach to model the turbulent magnetic fields. We show that the perpendicular diffusion coefficient depends only on two parameters, namely the Kubo number and the parallel mean free path. We combine the aforementioned turbulence model with the UNLT theory and we solve the corresponding integral equation numerically to show how these two parameters control the perpendicular diffusion coefficient. Furthermore, we consider two extreme cases, namely the case of strong and suppressed pitch-angle scattering, respectively. For each case we consider small and large Kubo numbers to achieve a further simplification. All our analytical findings are compared with formulas which are known in diffusion theory.

Impurity pinch generated by trapped particle driven turbulence

“…This fact reveals that QL approximation easily fails with more unstable plasma (high κ T ) and it converges into the valid limit K ∼ 1 by weakening the background instability (low κ T ). Although the Kubo number is not satisfied for our non-linear simulations, some examples have already shown that the QL framework could be applicable even with large Kubo number K > 1 [32,33].…”