Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov-Maxwell system. Generalized ordering takes i i L E L p R here i is the thermal ion Larmor radius and i = B / B i , as typically observed in the tokamak H-mode edge, with L E and L p being the radial electric field and pressure gradient lengths. k i 1 is assumed for generality, and the relative fluctuation amplitudes e / T i B / B are kept up to the second order.