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 ρi⪡ρθi∼LE∼Lp⪡R [here ρi is the thermal ion Larmor radius and ρθi=B∕(Bθρi)], as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. k⊥ρi∼1 is assumed for generality, and the relative fluctuation amplitudes eδϕ∕Ti∼δB∕B 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 gyro...

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