Electromagnetic full-$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods

Abstract

We present an energy-conserving discontinuous Galerkin scheme for the full-$f$ electromagnetic gyrokinetic system in the long-wavelength limit. We use the symplectic formulation and solve directly for $\partial A_{\parallel }/\partial t$, the inductive component of the parallel electric field, using a generalized Ohm's law derived directly from the gyrokinetic equation. Linear benchmarks are performed to verify the implementation and show that the scheme avoids the Ampère cancellation problem. We perform a nonlinear electromagnetic simulation in a helical open-field-line system as a rough model of the tokamak scrape-off layer using parameters from the National Spherical Torus Experiment (NSTX). This is the first published nonlinear electromagnetic gyrokinetic simulation on open field lines. Comparisons are made to a corresponding electrostatic simulation.

38 pages, 11 figures

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Cited by in corpus (23)

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• Magnetic flutter effect on validated edge turbulence simulations
• Verification of a Fully Implicit Particle-in-Cell Method for the $v_{\parallel }$ Formalism of Electromagnetic Gyrokinetics in the XGC Code
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• A Two-dimensional Numerical Study of Ion-Acoustic Turbulence
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• Discontinuous Galerkin schemes for a class of Hamiltonian evolution equations with applications to plasma fluid and kinetic problems
• Polarization and magnetization in collisional and turbulent transport processes
• A Parallel-Kinetic-Perpendicular-Moment Model for Magnetized Plasmas
• A $\delta f$ PIC method with Forward-Backward Lagrangian reconstructions
• Pseudo-spectral solver versus grid-based solver: A quantitative accuracy test using GMHD3D and PLUTO4.4
• Mapped discontinuous Galerkin interpolations and sheared boundary conditions
• Reduction of transport due to magnetic shear in gyrokinetic simulations of the scrape-off layer
• Verification of a hybrid gyrokinetic model using the advanced semi-Lagrange code ssV