GENERALIZED GYROVISCOUS FORCE AND ITS EFFECT ON THE MOMENTUM BALANCE EQUATION

The perturbed nonlinear gyroviscous force (del.Pi(g), where PI(g) is the gyroviscous stress tensor) is calculated through order delta-2 [delta approximately (1/OMEGA) (delta/delta-t), k(perpendicular-to)rho approximately delta-1/2, where OMEGA is the particle gyrofrequency, k(perpendicular-to)rho denotes the finite Larmor radius effect] by solving the stress tensor evolution equation. The result shows that del.PI(g) mostly cancels the diamagnetic convective term nmV*.del(perpendicular-to) u (where V* is a generalized total diamagnetic flow) in the momentum balance equation. This formula generalizes the usual, widely used "gyroviscous cancellation" [in which the del.PI(g) cancels mostly the total time derivative of the diamagnetic flow (dV(d)/dt)] to include temperature variations and a perturbed stress tensor drift. It is proved that when temperature variations are neglected, the new formula reduces to the conventional form. When the temperature variations are considered, the new formula is simpler and more rigorous than the conventional one. A new polarization drift formula deduced from the new gyroviscous force is also derived.