Electromagnetic Gyrokinetic Turbulence Simulations in the Tokamak Edge With Discontinuous Galerkin Methods

Noah Mandell, Princeton University

Photo of Noah Mandell

Gkeyll, a full-F continuum gyrokinetic code, is being developed to study plasma turbulence in the edge and scrape-off-layer (SOL) region of fusion devices. This region involves large-amplitude fluctuations, electromagnetic effects and plasma interactions with material walls due to open magnetic field lines. All of these effects make the edge more computationally challenging than the core region. Gkeyll models the turbulence by solving the 5-D full-F gyrokinetic system in Hamiltonian form using an energy-conserving high-order discontinuous Galerkin (DG) scheme. I will present new simulations that self-consistently include the effects of electromagnetic fluctuations of the background magnetic field on the turbulence in the SOL. These simulations are the first continuum gyrokinetic simulations on open field lines to include electromagnetic effects.

I also will present some of the implementation details of the DG scheme in Gkeyll. We choose a modal basis composed of orthonormalized Serendipity polynomials, which makes tensor products sparse. We use a computer algebra system (like Mathematica) to calculate the (sparse) tensor products in the DG weak form of the gyrokinetic equation. This system then generates the solver kernels that form the back end of Gkeyll: thousands of lines of machine-written C code containing no loops. This lets our algorithm take full advantage of the sparsity and also makes the implementation quadrature-free. The result is an O(10) speed-up over a previous implementation, which used a nodal Serendipity basis with Gaussian quadrature.

Abstract Author(s): Noah Mandell, Greg Hammett, Ammar Hakim