Parallel momentum balance and toroidal rotation in a tokamak

Plasma flow in toroidal geometry results in non‐trivial coupling of plasma flow, radial electric field and radial plasma pressure gradient. This coupling originates from combination of inertial and gyroviscous forces in toroidal geometry. Such effects have been recently studied as a sources of symmetry breaking and toroidal flow pinches. It is shown here that combination of geodesic curvature, radial electric field and pressure gradient leads to the instability of toroidal flow. An equilibrium profile of the toroidal rotation is determined from the balance of inertial and gyroviscous forces.