A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

Journal Article · 12 May 2023 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2023.112220 · OSTI ID:1975402

Huang, Kun ^[1]; Abdelmalik, Michael ^[2]; Breizman, Boris ^[3]; Gamba, Irene M. ^[3]

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1. University of Texas at Austin, TX (United States); Institute for Fusion Studies, The University of Texas at Austin
2. Eindhoven University of Technology (The Netherlands)
3. University of Texas at Austin, TX (United States)

We propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form and use a discretization that preserves conservation properties independent of the wave emission probability. The discrete operators, combined with a consistent quadrature rule, preserve all the conservation laws rigorously. The proposed scheme is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle distribution by continuous basis functions and use discontinuous basis functions for the wave spectral energy density, which enables the application of a positivity-preserving technique. We adopt the marching simplex algorithm, designed initially for computer graphics, for numerical integration on the resonance manifold. Furthermore, the numerical examples with a bump-on-tail initial configuration show how the unstable waves produce strong momentum space diffusion.

• Research Organization: University of Texas at Austin, TX (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0016283
• OSTI ID: 1975402
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 488; ISSN 0021-9991
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English