Driven Rotation, Self-Generated Flow and Momentum Transport in Tokamak Plasmas*

.Plasma rotation can have a profound impact on turbulence, transport and MHD stability in tokamak plasmas. Toroidal velocity is governed by a balance between external torques  and the momentum flux gradient. There are several momentum sources, e.g. direct drive from neutral beam injection or radio frequency waves, and indirect drive from the electric field created by orbit shifts and losses. Sinks include neutral damping and magnetic braking (neo-classical toroidal viscosity). The momentum flux, Γ_φ, is dominated by the toroidal Reynolds stress which consists of three parts:

Γ_φ/m  =  −χ_φ∂v_φ/∂r  +  V_pv_φ  +  Π^res

where χ_φ is the momentum diffusivity (or viscosity), V_p is the momentum pinch (or convection) and Π^res is the residual stress. The latter component, which is independent of both the toroidal velocity v_φ and its spatial gradient ∂v_φ/∂r, has the unique characteristic that it can function as a momentum source (and so appears on both sides of the force balance), with the intrinsic torque density given by ∇·Π^res. Π^res is governed by turbulence which is often driven by spatial gradients of plasma parameters. Each of these terms and effects has a different plasma parameter dependence (such as density, temperature, neutral density, collisionality) and each can dominate in different regions of operational space. Examples of driven rotation and sinks will be treated, then self-generated flow in tokamaks arising from the residual stress will be discussed in detail. Two general categories of intrinsic rotation will be examined: that occurring in enhanced confinement regimes and that in L-mode plasmas, including the curious rotation reversal phenomenon (and its connection with confinement saturation and “non-local” heat transport cut-off). Momentum transport coefficients will also be described.