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We present an energy-conserving discontinuous Galerkin scheme for thefull-$f$ electromagnetic gyrokinetic system in the long-wavelength limit. Weuse the symplectic formulation and solve directly for $\partialA_\parallel/\partial t$, the inductive component of the parallel electricfield, using a generalized Ohm's law derived directly from the gyrokineticequation. Linear benchmarks are performed to verify the implementation and showthat the scheme avoids the Amp\`ere cancellation problem. We perform anonlinear electromagnetic simulation in a helical open-field-line system as arough model of the tokamak scrape-off layer using parameters from the NationalSpherical Torus Experiment (NSTX). This is the first published nonlinearelectromagnetic gyrokinetic simulation on open field lines. Comparisons aremade to a corresponding electrostatic simulation.

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