Toroidal and poloidal flows that stabilize MHD modes and suppress turbulent transport in tokamaks
Plasma rotation in a tokamak arises from a combination of external momentum input and intrinsic torques. Neutral beam injection is the dominant source of toroidal rotation in present-day experiments: fast ions born with a directed velocity transfer angular momentum to the bulk plasma through collisional drag. Toroidal velocities of 100–400 km/s are routinely achieved in beam-heated discharges, corresponding to Mach numbers of 0.1–0.5 relative to the ion thermal speed.1
Intrinsic rotation—spontaneous toroidal flow arising without external momentum input—is also significant and has been observed in radio-frequency-heated plasmas. It is driven by residual stress in the turbulent momentum flux, is typically co-current in direction, and scales roughly with the plasma stored energy. Understanding intrinsic rotation is critical because ITER and reactor-scale devices will have lower torque per unit volume from NBI than current experiments.2
Toroidal rotation provides a powerful stabilizing influence on macroscopic MHD instabilities. The resistive wall mode (RWM)—an external kink that would grow on the resistive timescale of a surrounding conducting wall—is stabilized when the plasma rotation exceeds a critical threshold, typically a few percent of the Alfvén speed. This stabilization arises because rotation-induced coupling between stable and unstable branches of the dispersion relation damps the mode energy.3
The E×B flow shear associated with radial gradients in toroidal and poloidal rotation is the primary mechanism for turbulence suppression. When the shearing rate ωE×B exceeds the linear growth rate of the dominant micro-instability (typically ion temperature gradient or trapped electron modes), turbulent eddies are decorrelated and transport barriers form. This is the physics behind the L–H transition, internal transport barriers, and quiescent H-mode operation.4
Because reactor plasmas will have weaker NBI torque per particle, intrinsic rotation and its scaling to large machines are active research frontiers. Techniques under study include optimized magnetic geometry to enhance intrinsic rotation, application of non-axisymmetric magnetic perturbations to brake or spin the plasma selectively, and compact torque injection with negative-ion or high-energy NBI.