Analytic slowing-down distributions as modified by turbulent transport

TL;DR

This paper derives analytic models for the velocity distribution of energetic particles in plasmas, accounting for turbulent transport effects, which are crucial for understanding plasma heating and stability.

Contribution

The paper introduces first-principles derived analytic distribution functions incorporating turbulence effects, characterized by a single parameter, simplifying complex multiscale plasma simulations.

Findings

Models reproduce key features of numerical solutions

A single parameter quantifies turbulence strength effects

Provides a heuristic for energetic particle redistribution

Abstract

The effect of electrostatic microturbulence on fast particles rapidly decreases at high energy, but can be significant at moderate energy. Previous studies found that, in addition to changes in the energetic particle density, this results in nontrivial changes to the equilibrium velocity distribution. These effects have implications for plasma heating and the stability of Alfv\'en eigenmodes, but make multiscale simulations much more difficult without further approximations. Here, several related analytic model distribution functions are derived from first principles with reasonable approximations. A single dimensionless parameter characterizes the relative strength of turbulence relative to collisions, and this parameter appears as an exponent in the model distribution functions. Even the most simple of these models reproduces key features of the numerical phase-space transport solution and provides a useful a priori heuristic for determining how strong the effect of turbulence is on the redistribution of energetic particles in toroidal plasmas.