ATEP: an advanced transport model for energetic particles

Abstract

In this paper we report on the implementation and verification of a phase- space resolved energetic particle (EP) transport model. It is based on a first-principle theoretical framework, i.e. the system of non-linear gyrokinetic equations and the related transport equations. Its focus is primarily directed toward understanding the meso-scale character of EPs and its consequences. Compared to the conventional description of thermal radial transport via a one-dimensional radial diffusion equation, the newly developed model is three-dimensional using canonical constants-of-motion (CoM) variables. The model does not assume diffusive processes to be dominant a priori, instead the EP fluxes are self-consistently calculated and directly evolved in CoM space. We use the EP-Stability workflow and the HAGIS code to determine the phase space fluxes explicitly either in the limit of constant mode amplitudes or an energy-conserving quasi-linear model. As an application of the model the transport of neutral-beam-generated EPs due to a toroidal Alfv ́en eigenmode in an ITER plasma is investigated. As there are no sources and collisions taken into account so far (for an extension of the model see the companion paper ref. [1]), the results cannot be considered as an exhaustive study, but rather as a practical demonstration of the conceptual framework on the way to a comprehensive reduced description of burning plasmas.

Energetic particles transport in constants of motion space due to collisions in tokamak plasmas

“…More fundamentally, the kick model is a probabilistic approach, while the PSZS theory solves transport equations in phase space. However, the comparison is an important step for model validation in the future [27]. The RBQ (Resonance Broadened Quasilinear) model is built upon the foundation of the quasilinear and diffusive model, expanding to include the broadened resonance inherent in wave-particle interactions.…”

“…Based on this framework, a reduced EP transport code (named 'ATEP') is developed. The primary objective of ATEP is to systematically encompass the intricate physics embedded in the overarching equations, as detailed in [26,27]. The general ATEP model addresses comprehensive physics, recovering critical gradient models [28], the 'kick' model [29], and quasi-linear resonance broadening models [30,31] within appropriate limits.…”