Electric fields and transverse conductivity in a SOL of a tokamak

The self-consistent electric fields and current systems play extremely important role in many processes in a SOL. The impact of the self-consistent electric fields depends critically on the type of the transverse conductivity. In the present paper a new type of the transverse conductivity determined by the ion viscosity and inertia is analyzed. In fact this is the effective conductivity because the transverse ion current is not proportional to the electric field itself but to its spatial derivatives. Both classical perpendicular viscosity of Braginski and anomalous viscosity are analyzed. Two type of the events are considered. In the first group there are the local processes when the current system occupies a small part of the total volume of a SOL. It is shown that for such events as unipolar arc formation or probes in a SOL the local transverse conductivity produced by the perpendicular ion viscosity dominates over the ion-neutral conductivity. The second group is formed by the processes when the whole SOL is involved, and the transverse current is flowing between two flux surfaces. Such averaged conductivity is important in the biasing experiments and in the problem of global vector E x vector B convection. It is shown that averaged conductivity is to large extent determined by the anomalous shear viscosity and inertia. The averaged ion-neutral conductivity is also calculated but in contrast to the existing theories is not proportional to the ion-neutral collision frequency. It is demonstrated that the theory is in agreement with the absolute measurements and parametric dependence in TdeV tokamak, predicts the observed linear I-V dependence in probe measurements in SOL. The criterion of unipolar arc formation is also discussed. (orig.)