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 x 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. Our generalized ordering takes ρi << ρθi ∼ LE ∼ Lp << R (here ρi is the thermal ion Larmor radius and ρθi = B/Bθ ρi), as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. We take k#perpendicular# ρi ∼ 1 for generality, and keep the relative fluctuation amplitudes e(delta)φ/Ti ∼ (delta)B/B up to the second order. Extending the electrostatic theory in the presence of high E x B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pull-back transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation