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The use of the standard approaches for evaluating a neoclassical radial electric field Er, i.e., the Ampere (or gyro-Poisson) equation, requires accurate calculation of the difference between the gyroaveraged electron and ion particle fluxes (or densities). In the core of a tokamak, the nontrivial difference appears only in high-order corrections to a local Maxwellian distribution due to the intrinsic ambipolarity of particle transport. The evaluation of such high-order corrections may be inconsistent with the accuracy of the standard long wavelength gyrokinetic equation (GKE), thus imposing limitations on the applicability of the standard approaches. However, in the edge of a tokamak, charge-exchange collisions with neutrals and prompt ion orbit losses can drive non-intrinsically ambipolar particle fluxes for which a nontrivial (Er-dependent) difference between the electron and ion fluxes appears already in a low order and can be accurately predicted by the long wavelength GKE. The parameter regimes, where the radial electric field dynamics in the tokamak edge region is dominated by the non-intrinsically ambipolar processes, thus allowing for the use of the standard approaches, are discussed. [ABSTRACT FROM AUTHOR]

An additional contribution to the ion viscosity for a collisional plasma is evaluated and found to be the same order as other temperature gradient terms in the collisional perpendicular viscosity. The new contribution arises because of an explicitly collisional portion of the ion distribution function. The evaluation of the Pfirsch-Schlüter radial electric field in a collisional tokamak of arbitrary cross section is extended to retain the new contribution. In a spherical tokamak this new contribution must be retained in determining the radial electric field, while in a conventional tokamak it is small by 1/q2, where q is the safety factor. [ABSTRACT FROM AUTHOR]

The neoclassical electric field in a tokamak is determined by the conservation of toroidal angular momentum. In the steady state in the absence of momentum sources and sinks it is explicitly evaluated by the condition that radial flux of toroidal angular momentum vanishes. For a collisional or Pfirsch-Schlüter short mean-free path ordering with subsonic plasma flows we find that there are two limiting cases of interest. The first is the simpler case of a strongly up-down asymmetric tokamak for which the lowest order gyroviscosity does not vanish and must be balanced by the leading order collisional viscosity in order to determine the radial electric field. The second case is the more complicated case of an up-down symmetric tokamak for which the gyroviscosity must be evaluated to higher order and again balanced by the lowest order collisional viscosity to determine the radial electric field. In general, both the lowest and the next order contributions from the gyroviscosity must be retained. [ABSTRACT FROM AUTHOR]

A concise and complete differential equation determining the Pfirsch–Schlüter radial electric field in an up-down symmetric tokamak is presented in the limit of weak poloidal magnetic field. [ABSTRACT FROM AUTHOR]