Reevaluation of the Braginskii viscous force for toroidal plasma

The model by Braginskii [1] (Braginskii, S. I. 1965 Transport processes in plasma. In: Review of Plasma Physics, Vol. 1 (ed. M.A. Leontovich). New York, NY: Consultants Bureau, pp. 205-311) for the viscous stress tensor is used to determine the shear and gyroviscous forces acting within a toroidally confined plasma. Comparison is made to a previous evaluation, which contains an inconsistent treatment of the radial derivative and neglects the effect of the pitch angle. Parallel viscosity contributes a radial shear viscous force, which may develop for sufficient vertical asymmetry to the ion velocity profile. An evaluation is performed of this radial viscous force for a tokamak near equilibrium, which indicates qualitative agreement between theory and measurement for impure plasma discharges with strong toroidal flow.