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

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 δA∥/δt, 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 Ampere 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.