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

Abstract

The spatio-temporal evolution of the energetic particles in the transport time scale in tokamak plasmas is a key issue of the plasmas confinement, especially in burning plasmas. In order to include sources and sinks and collisional slowing down processes, a new solver, ATEP-3D was implemented to simulate the evolution of the EP distribution in the three-dimensional constants of motion (CoM) space. The Fokker-Planck collision operator represented in the CoM space is derived and numerically calculated. The collision coefficients are averaged over the unperturbed orbits to capture the fundamental properties of EPs. ATEP-3D is fully embedded in ITER IMAS framework and combined with the LIGKA/HAGIS codes. The finite volume method and the implicit Crank-Nicholson scheme are adopted due to their optimal numerical properties for transport time scale studies. ATEP-3D allows the analysis of the particle and power balance with the source and sink during the transport process to evaluate the EP confinement properties.

ATEP: an advanced transport model for energetic particles

“…However, the new non-linear equilibria can be used as input to particle tracking codes that are able to deliver detailed loss information. The IMAS integrated 'FINDER' tool used here as a HAGIS-wrapper for calculating the orbit averages is also employed to determine the orbit-averaged collision coefficients, using the collisional version of the HAGIS code [22,38].…”

“…Finally, the transport equation evolution is quite fast, however the Courant criterion for the explicit solver may require small time steps. The implicit solver [22] resolves this problem, but still needs parallelisation for larger CoM grids. The time-advanced F EP on the CoM grid is remapped into the marker-space by updating the individual weights of markers belonging to a certain CoM position according to the change of phase space density at that position.…”

“…In summary, all ingredients for solving the PSZS transport equation and its interfaces to other transport codes have been established. For details on the collisional part, please refer to the companion paper [22].…”

“…For simplicity, we assume here that the flow is incompressible (∇ • v P ϕ ,E = 0). This assumption will be relaxed when the upgraded solver [22] will be also available for the PSZS transport part. Within the constant-amplitude limit of equation ( 1) and the first promising results, using a bounce averaged collision operator in the same CoM formulation and code framework, are reported in [22].…”

“…Whereas this paper neglects sources and collisions, i.e. the formulation is reduced to a 2d transport problem, we demonstrate in a companion paper [22] how the neoclassical part of the problem can be included within the same conceptual framework, leading to a comprehensive 3d EP transport model resolving the time scales needed for the reduced modelling of burning plasmas. It should be emphasised that the omission of sources and collisions in this work limits significantly the physical validity of some results, especially in the cases where simulations on transport time scales ≳10 ms are considered.…”