UW-CPTC 09-6R Viscous Forces Due To Collisional Parallel Stresses For Extended MHD Codes

Various forms of the viscous force caused by collision-induced parallel viscous stresses within an inhomogeneous magnetized plasma are presented. New forms are proposed for initial value extended MHD codes to capture the “fast” (Braginskii) collisional viscous force effects on short time scales and multi-collisionality regime “residual” viscous forces on collision time scales and longer in axisymmetric toroidal plasmas. Collision-based viscosity coefficients are described in various collisionality regimes: high (Braginskii, Pfirsch-Schlüter), intermediate (plateau) and low (banana). Smoothed formulas for the residual viscous forces induced by electron and ion parallel stresses on the collision and longer time scales that encompass all these collisionality regimes are presented. Also, a generalized Ohm’s law that includes both the fast Braginskii-type viscous effects and the slow residual effects that lead to the neoclassical parallel Ohm’s law is proposed. Finally, suggestions are made for implementing and verifying viscous force effects in extended MHD codes. ∗[email protected]; http://www.cae.wisc.edu/~callen