Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence
Authors: T.S. Hahm, Lu Wang and J. Madsen
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 Χ 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 ρι << ρϑ¡ ~ LE ~ Lp << R (here ρ¡ is the thermal ion Larmor radius and ρϑ¡ = [B over Bϑ] ρ¡), as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. We take κ⊥ ρi ~ 1 for generality, and keep the relative fluctuation amplitudes eδφ ⁄ Τι ~ δΒ ⁄ Β
up to the second order. Extending the electrostatic theory in the presence of high E Χ 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.
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Submitted to: Physics of Plasmas (August 2008)
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Download PPPL-4344 (pdf 460KB 28pp)
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