Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

Abstract

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 ρ i ρ θi ∼ LE ∼ Lp R [here ρ i is the thermal ion Larmor radius and ρ θi =B(Bθ ρ i)], as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. k⊥ ρ i ∼1 is assumed for generality, and the relative fluctuation amplitudes eδφ Ti ∼δBB are kept up to the second order. Extending the electrostatic theory in the presence of high E×B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pullback transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation. © 2009 American Institute of Physics.