Explicit expressions for the neoclassical poloidal and toroidal rotation speeds of primary ion and impurity species are derived via the Hirshman and Sigmar moment approach. The rotation speeds of the primary ion can be significantly different from those of impurities in various interesting cases. The rapid increase of impurity poloidal rotation in the edge region of H-mode discharges in tokamaks can be explained by a rapid steepening of the primary ion pressure gradient. Depending on ion collisionality, the poloidal rotation speed of the primary ions at the edge can be quite small and the flow direction may be opposite to that of the impurities. This may cast considerable doubts on current L to H bifurcation models based on primary ion poloidal rotation only. Also, the difference between the toroidal rotation velocities of primary ions and impurities is not negligible in various cases. In Ohmic plasmas, the parallel electric field induces a large impurity toroidal rotation close to the magnetic axis, which seems to agree with experimental observations. In the ion banana and plateau regime, there can be non-negligible disparities between primary ion and impurity toroidal rotation velocities due to the ion density and temperature gradients. Detailed analytic expressions for the primary ion and impurity rotation speeds are presented, and the methodology for generalization to the case of several impurity species is also presented for future numerical evaluation.

A reduced set of neoclassical fluid equations, consisting of the parallel ion flow velocity ulI , the generalized potential F, the ion pressure p, and the parallel ion heat flow qll , is derived. The resultant equations are the extension of reduced fluid equations derived from Braginskii equations with the high collisionality to the equations relevant to a fusion plasma with low to intermediate collisionality. The linear Q mode dynamics is reinvestigated by using the resultant model equations. The effects of the perpendicular compressibility in the ion pressure response, the parallel heat flow, and the neoclassical viscosity are analyzed both analytically and numerically. It is stressed that the closure condition of neoclassical viscosity changes the sign of energy dissipation and seriously affects the stability of vi modes.