Guiding Center and Gyrokinetic Theory for Strong Shear Flows in General Magnetic Field Geometry

The guiding center and gyrokinetic theory of magnetized particle motion for the regime of large electric field gradients and strong shear flows is extended to include spatial and temporal variations in the magnetic field. Performing the calculation in a reference frame that moves with the guiding center simplifies the results. For small shear flows, the gyrofrequency is corrected by the parallel component of the guiding center vorticity. For large shear flows, the oscillation frequency depends on the gradient in the electric field in addition to the usual corrections due to the Banos drift. Moreover, the Larmor orbits deform from circular to elliptical trajectories, the drifts become anisotropic in response to external forces, and additional curvature drifts must be included. The polarization and magnetization are modified by the change in gyrofrequency, by the large drift flows, and must include self-consistent thermodynamic polarization. While several new physical effects are predicted, the theory is similar in mathematical form to the standard case and can readily be implemented within existing simulation tools.