Abstract. We present a new recursive procedure to find a full f electrostatic gyrokinetic equation correct to first order in an expansion of gyroradius over magnetic field characteristic length. The procedure provides new insights into the limitations of the gyrokinetic quasineutrality equation. We find that the ion distribution function must be known at least to second order in gyroradius over characteristic length to calculate the long wavelength components of the electrostatic potential selfconsistently. Moreover, using the example of a steady-state θ-pinch, we prove that the quasineutrality equation fails to provide the axisymmetric piece of the potential even with a distribution function correct to second order. We also show that second order accuracy is enough if a more convenient moment equation is used instead of the quasineutrality equation. These results indicate that the gyrokinetic quasineutrality equation is not the most effective procedure to find the electrostatic potential if the long wavelength components are to be retained in the analysis.
An efficient and systematic treatment of classical and neoclassical transport in all regimes of collisionality is formulated that permits toroidal rotation speeds on the order of the ion thermal speed for arbitrary aspect ratio, cross section, and poloidal magnetic field strength. A more convenient, but somewhat unconventional, form of the reduced kinetic equation is derived that is shown to extend the previous form by properly retaining electric field modifications. The generalized kinetic description is exploited to evaluate explicitly the radial fluxes of toroidal angular momentum and energy in a pure plasma via a variational formulation. The specific results obtained in the Pfirsch–Schlüter regime are substantially more general than previous evaluations; also, significant improvements are made in the banana regime.
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