Interaction of plasma rotation and resonant magnetic perturbation fields in tokamaks

The interaction between plasma rotation and perturbation fields is described by the ambipolarity constraint and the parallel momentum balance, both emanating from the revisited neoclassical theory, and the electrodynamical screening of the resonant perturbation field at the singular surfaces. This screening depends mainly on the slip between the rotating plasma and the resonant field. The neoclassical theory, valid in the collision dominated regime and accounting for gyro-viscosity, includes arbitrary plasma cross-sections, anomalous viscosity, ponderomotive forces, neutral beam injection (NBI), pressure anisotropization and a momentum source due to ergodicity which has a considerable impact on the plasma rotation as demonstrated in TEXTOR. To estimate the influence of the perturbation coils on the plasma rotation, the radial magnetic field (proportional to the helical flux function) is Fourier analysed (using 'intrinsic' coordinates) and the total field is used for field line tracing thus obtaining the ponderomotive momentum input and the extension Δ_e of the ergodic layer at the edge. Both procedures account for the full plasma geometry. Δ_e is assumed to be independent of the rotational state because of the boundary condition V_t = 0. In a second step the obtained velocity profiles are used to compute the screening at the singular layers and thus the reduction of the island width due to plasma rotation. The main results can be summarized as follows. Using in the case of TEXTOR shot #94092 the diffusion coefficient D_M = 2 × 10 ^-6 m (typical for the 12/4 configuration) the observed increase in v_t by Δv_t ≈ 5 km s^-1 can be reproduced. Inside the plasma the slip prevents any influence of the ponderomotive forces, thus yielding a constant increase in the v _t(r)-profile by Δv_t. Assuming in the case of the error field correction coils (n = 1) of JET the current I_hel = 30 kA and using for the plasma background the data of shot #67951 in the static case, an ergodized layer (Δ_e(n = 1) ≈ 20 cm in the vicinity of the unperturbed x-point) and large m = 2, m = 3 (n = 1) islands (W _m=2,n=1 = 10 cm) are obtained. In the n = 2 configuration the analogous parameters are Δ_e(n = 2) ≈ 18 cm and W _{m = 2,n = 2} = 4 cm i.e. Δ_e stays roughly the same and the island width is strongly reduced thus indicating the superiority of this configuration. Plasma rotation reduces the width W_m=2,n=1 to a small value. (However, tearing mode physics which may lead to mode locking is not included in this consideration.)