Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks

In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co-I (p) direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with P (RF) absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.