Abstract
A nonlinear gyrokinetic formalism is developed which admits mean velocities comparable to thermal speeds in arbitrary magnetic field geometry. The theory is fully electromagnetic and does not employ an eikonal ansatz. The moments of the gyrokinetic distribution function, as well as the gyrokinetic equation it satisfies, are derived to first order in the guiding center expansion parameter. This large mean velocity formulation is important whenever the E×B drift over the thermal speed cannot be ordered small. For example, upon summing over all species, the moment description yields a set of generalized magnetohydrodynamic equations which are valid to one order higher in the expansion parameter.
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