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The component of the neoclassical electrostatic potential that is non-constant on the magnetic surface, that we denote by
, can affect radial transport of highly charged impurities, and this has motivated its inclusion in some modern neoclassical codes. The number of neoclassical simulations in which
is calculated is still scarce, partly because they are usually demanding in terms of computational resources, especially at low collisionality. In this paper the size, the scaling with collisionality and with aspect ratio and the structure of
on the magnetic surface are analytically derived in the
and superbanana-plateau regimes of stellarators close to omnigeneity; i.e. stellarators that have been optimized for neoclassical transport. It is found that the largest
that the neoclassical equations admit scales linearly with the inverse aspect ratio and with the size of the deviation from omnigeneity. Using a model for a perturbed omnigenous configuration, the analytical results are verified and illustrated with calculations by the code KNOSOS. The techniques, results and numerical tools employed in this paper can be applied to neoclassical transport problems in tokamaks with broken axisymmetry.
The collisionless axisymmetric zonal flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value zonal flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the zonal flow residual in gyrokinetic codes. Unlike the electrostatic potential, the parallel vector potential and the parallel magnetic field perturbations need not relax to flux functions for all possible initial conditions.
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