Rotation velocity profile control by slow electromagnetic waves

Confinement of tokamak plasmas may depend on the rotation velocity profile, since velocity shear may suppress fluctuations. Slow electromagnetic waves are found to be a potentially attractive means for control of the velocity profile. The idea is to use antenna currents proportional to cos(mθ+nφ+ωt) for perturbing an axisymmetric tokamak. Here, θ and φ are the poloidal and toroidal angles of a tokamak, m and n integers, ω and t are frequency and time. The perturbation results in formation of islands at the surface where the safety factor, q, equals m/n; the islands rotate with the toroidal angular velocity ω/n. Away from the island surface, the configuration may be considered axisymmetric; here, flow in the toroidal direction is impeded only by ordinary viscosity, while flow in the poloidal direction, in addition, is impeded by the strong, neoclassical effect of collision between flowing and trapped particles. Therefore, here the flow is almost entirely in the toroidal direction. Plasma inside the islands is similarly inhibited from flowing in the helical direction of the islands because of trapped particles, and flow perpendicular to the helical direction is inhibited by ordinary viscosity when the islands are narrow. Therefore, one may expect that the plasma inside the rotating islands follow their rotation. The range of validity of these concepts was explored by studying helically symmetric equilibria for which plasma inside islands is exposed to forces imitating the viscous and neoclassical forces acting on the plasma inside rotating tokamak islands. It is found that the island width decreases as the total force is increased and that a maximum force is found as a function of the initial island width. It is conjectured that for island rotation velocities above that corresponding to the upper force limit, nonstationary flows which possibly break the assumed symmetry may be found in a real plasma. 1 ref