Description
The HALO (HAgis LOcust) code [1] is a full orbit implementation of the perturbative delta-f approach, allowing nonlinear modelling of any bulk plasma eigenmode at arbitrary frequency using the Vlasov–Maxwell system of equations. HALO tracks a population of weighted markers through Hamiltonian orbits in phase space under the influence of a discrete spectrum of fixed-frequency, time-evolving eigenmodes, while self-consistently using marker motion to perturbatively update the mode amplitudes.
However, it is well understood that the nonlinear evolution of toroidal Alfvén eigenmodes (TAEs) seen in experiments generally requires collisions and sources/sinks to be modelled in order to reproduce the experimentally observed behaviour, including asymmetric frequency chirping. For example, such asymmetry can arise because drag and pitch-angle diffusion lead to asymmetries in the evolution of “holes” and “clumps”: features of the distribution function near the mode resonance [2], indicating that the inclusion of collisional effects is vital to modelling current experimental campaigns on MAST-U and future burning plasmas [3][4].
We present an adaptation of a finite-difference finite-volume scheme for the linear Fokker-Planck-Landau (FPL) collision operator implemented into HALO. We examine the convergence and stability properties of the linearised form of the algorithm derived by Yoon & Chang [5] and Hager et al. [6]. We detail its parallelisation across multiple GPUs in HALO with further attention to marker-grid interpolation, solver numerics, and positivity preservation. Benchmarks are made with analytical results for relaxation to a Maxwellian and for anisotropic slowing-down, as well as against Monte Carlo collisions in the 3D3V code LOCUST [7].
[1] Fitzgerald M, Buchanan J, Akers R J, Breizman B N, and Sharapov S.E., 2020, Comp. Phys. Comms, 252, 106773
[2] Lilley M K, Breizman B N, and Sharapov S E 2010 Phys. Plasmas 17 092305
[3] Rivero-Rodríguez J F, et al 2024, Nucl. Fusion 64 086025
[4] Slaby S et al., 2019, Nucl. Fusion 59 046006
[5] Yoon E S, and Chang C S, 2014, Phys. Plasmas 21, 032503
[6] Hager R, et al. 2016, J. Comp. Phys. 315, pp 644-660
[7] Ward S H, et al. 2021 Nucl. Fusion 61 086029