Spontaneous poloidal spin-up of tokamak plasmas: Reduced equations, physical mechanism, and sonic regimes

A theoretical description of the spontaneous (Stringer) poloidal spin-up of tokamak plasmas is given. A set of reduced equations is derived to investigate various aspects of the phenomenon. A simple physical description of the instability mechanism is given. The theory of the instability is extended to show that the spin-up persists even under conditions where the growth rate is sonic. A nonlinear evolution equation for unstable poloidal rotation is obtained which shows that the instability mechanism loses its efficacy when the poloidal speed exceeds the poloidal sound speed, thus resulting in nonlinear saturation of the rotation at this level.