Physics of penetration of resonant magnetic perturbations used for Type I edge localized modes suppression in tokamaks

Resonant Magnetic Perturbations (RMP) generated by external coils have been shown to be effective in eliminating Type I ELMs in DIII-D or significantly mitigating them in JET. At present, ELM control by RMP is strongly recommended for ITER since it could significantly increase the lifetime of the ITER divertor by reducing surface erosion caused by Type I ELMs. The present days extrapolations to ITER are mainly based on the experimental criterion and 'vacuum' field modelling suggesting that Type I ELMs are suppressed when edge plasma is ergodized. However, depending on plasma parameters and RMP spectrum and amplitude, the actual RMP field could be very different, especially in rotating plasmas where the generation of the current perturbations near rational surfaces could prevent reconnection leading to effective shielding of RMP. Also it is known from experiment that RMP penetration could produce significant slowing down of toroidal plasma rotation which potentially leads to MHD modes locking. The understanding of the rotating plasma response on RMPs is important in the optimization of the RMP coils spectrum in order to avoid a significant loss of plasma rotation in ITER The present paper describes physics of penetration of RMP into the toroidally rotating plasma. A new development of the non-linear cylindrical reduced MHD (RMHD) code was done to take into account toroidal rotation, resonant and global plasma braking due to the Neoclassical Toroidal Viscosity (NTV). In the present paper it is shown that RMP penetration time significantly increases for ITER-like parameters (∼ s) compared to present day tokamaks (∼ few ms in DIII-D). RMHD modelling for specific RMP coils in ITER and DIII-D demonstrated that central islands on the resonant surfaces are expected to be shielded due to the stronger rotation and lower resistivity compared to edge plasma which is expected to be ergodised in the pedestal region for both machines. It was demonstrated that non-resonant harmonics which do not produce islands in plasma are not screened by plasma rotation, hence they could play an important role in NTV braking mechanism. Latest RMP coil designs for ITER are analysed with respect to the minimisation of non-resonant NTV braking effect and the optimisation of the design. (author)