On the efficiency of intrinsic rotation generation in tokamaks

A theory of the efficiency of the plasma flow generation process is presented. A measure of the efficiency of plasma self-acceleration of mesoscale and mean flows from the heat flux is introduced by analogy with engines, using the entropy budget defined by thermal relaxation and flow generation. The efficiency is defined as the ratio of the entropy destruction rate due to flow generation to the entropy production rate due to ∇T relaxation (i.e., related to turbulent heat flux). The efficiencies for two different cases, i.e., for the generation of turbulent driven E×B shear flow (zonal flow) and for toroidal intrinsic rotation, are considered for a stationary state, achieved by balancing entropy production rate and destruction rate order by order in O (k_||/k_⊥), where k is the wave number. The efficiency of intrinsic toroidal rotation is derived and shown to be ^eIR ∼ (Mach)_th² ∼0.01. The scaling of the efficiency of intrinsic rotation generation is also derived and shown to be ρ*² (q²/ŝ²) (R ²/L_T²) = ρ*² (L _s²/L_T²), which suggests a machine size scaling and an unfavorable plasma current scaling which enters through the shear length.