[en] The resistive wall mode instability limits the achievable plasma pressure in present and future advanced tokamak scenarios. We investigate the effect of drift kinetic resonance damping, due to plasma thermal particles, on the stability of this mode. A self-consistent toroidal kinetic damping model is developed and incorporated into the MHD code, MARS-F. The new code (MARS-K) allows study of the kinetic effects in both a perturbative and non-perturbative manner. The primary difference between these two approaches is that the former normally uses the no-wall ideal kink eigenmode structure to compute the kinetic energy perturbation, whilst the latter takes into account self-consistently the modification of the RWM eigenfunction by the kinetic effects. The perturbative approach in MARS-K is benchmarked against another, also perturbative calculation using the ideal MHD code MISHKA and the drift-orbit particle-following code HAGIS. The perturbative approach normally predicts a significant modification of the perturbed total energy (fluid + vacuum + wall + drift kinetic) by the kinetic contribution, which in many cases leads to a complete stabilization of the mode. However, the non-perturbative approach in many cases studied results in a partial stabilization, due to the fact that the drift kinetic energy is sensitive to the mode structure, that is modified by the kinetic effects. Therefore, the predicted RWM stability can be significantly different, depending on whether the kinetic terms are included self-consistently. Detailed comparison of the self-consistent modelling with the experimental results (JET and DIII-D) is in progress. Predictive simulations of the RWM stability will be made for the ITER advanced plasmas, using the new damping model. (author)

[en] Active feedback stabilization of high-β tokamaks is studied using a new, rigorous construction of the transfer functions, based on an expansion in the resistive wall eigenmodes of the unstabilized, toroidal equilibrium. It is shown that a simple control system using poloidal sensors can give robust stabilization for equilibria within a wide range of plasma currents and rotation speeds. The required coil voltages are modest, even for the two-wall structure of ITER. (author). Letter-to-the-editor

[en] A significant improvement of the resistive wall mode (RWM) feedback stabilization is achieved by optimizing the poloidal locations and the linear combination of an array of sensors, detecting the radial magnetic flux. The optimization is based on the full knowledge of the dynamic response of both unstable and stable RWMs. The optimal solution is robust against the variation of plasma parameters.

[en] The effects of the fusion born α particles on the stability of the RWM are numerically investigated for one of the advanced steady state scenarios in ITER. The α contribution is found to be generally stabilizing, compared with the thermal particle kinetic contribution alone. The same conclusion is achieved following both a perturbative and self-consistent approach. The latter generally predicts less stabilization than the former. At high enough plasma pressure, the self-consistent approach predicts two unstable branches for the ITER plasma studied here. The stabilizing effect from α particles is found to be generally weak, in particular in terms of the modification of the stability boundary. The effect is more pronounced only at fast enough plasma rotation frequency, roughly matching the α precession frequency, which is in the order of a few per cent of the toroidal Alfven frequency for ITER. A simple, energy principle based, fishbone-like dispersion relation is proposed to gain a qualitative understanding of the numerical results.

[en] Two possible ways of modifying the linear tearing mode index, by active magnetic feedback and by drift kinetic effects of deeply trapped particles, are analytically investigated. Magnetic feedback schemes, studied in this work, are found generally stabilizing for Δ^′. The drift kinetic effects from both thermal particles and hot ions tend to reduce the power of the large solution from the outer region. This generally leads to a destabilization of Δ′ for the toroidal analytic equilibria considered here.

[en] A uniform framework, based on the frequency dependent plasma response model (PRM), is proposed to study the physics and control of the resistive wall mode (RWM). The PRM is constructed, respectively, from the Fitzpatrick-Aydemir model, from a cylindrical theory with multiple RWM, and, finally, from toroidal calculations. Based on the PRM, several important aspects of the RWM physics are studied, including the interplay between active feedback and plasma rotation to stabilize the mode, the efficiency of external versus internal active coils for the mode control and the resonant field amplification effect due to a rotationally damped RWM

[en] Optimal correction of the intrinsic, static error field (EF) by the correction coils in MAST is numerically studied, based on linear, full MHD plasma response computed in full toroidal geometry. Various optimization criteria are proposed, and the results are compared with empirical optima from representative EF correction (EFC) experiments. The two best criteria are thus identified, one aiming at minimization of the net toroidal resonant electromagnetic torque produced on the plasma column by the EF, the other corresponds to the full cancellation of the 2/1 resonant field harmonic at the q = 2 surface, including the plasma response. Neither the vacuum field based criterion nor the singular value decomposition (including plasma response) based criteria produce satisfactory predictions for the EFC in MAST. (paper)

[en] The plasma response to resonant magnetic perturbation (RMP) and nonresonant perturbation fields is computed within a linear, full toroidal, single-fluid resistive magnetohydrodynamic framework. The response of resonant harmonics depends sensitively on the plasma resistivity and on the toroidal rotation. The response of nonresonant harmonics is not sensitive to most of the plasma parameters, except the equilibrium pressure. Both midplane and the off midplane odd parity RMP coils trigger a similar field response from the plasma. The RMP fields with different toroidal mode numbers trigger qualitatively similar plasma response. A simple model of the electron diamagnetic flow suggests significant effects both in the pedestal region and beyond.

[en] The misalignment of field coils in tokamaks can lead to toroidal asymmetries in the magnetic field, which are known as intrinsic error fields. These error fields often lead to the formation of locked modes in the plasma, which limit the lowest density that is achievable. Measurements on MAST suggest that the dominant source of the intrinsic error field is due to the P4 and P5 poloidal field coils. A direct measurement of the toroidal asymmetry of the fields from these coils has been made, which has then been parametrized in terms of distortions to the coils. Empirically the error fields are corrected using error field correction coils, where the optimum correction is found by determining the current required to ensure that the discharge is furthest from the onset of a locked mode. Assuming that the dominant n = 1 error field is produced by the P4 and P5 coils, the empirically derived corrections have been compared with the known distortion of these coils. In the vacuum approximation there is a factor of ∼3 difference between the predicted and empirically determined correction. When the plasma response is included better agreement is obtained, but there are still some cases where the agreement is not good. The results suggest that other effects may be important. These include on the experimental side additional unmeasured sources of the error field or on the theory side the non-linear coupling of the error field to the plasma. (paper)

[en] Within the single fluid theory for a toroidal, resistive plasma, the favorable average curvature effect [Glasser et al., Phys. Fluids 18, 875 (1975)], which is responsible for the strong stabilization of the classical tearing mode at finite pressure, can also introduce a strong screening effect to the externally applied resonant magnetic field. Contrary to conventional understanding, this screening, occurring at slow plasma rotation, is enhanced when decreasing the plasma flow speed. The plasma rotation frequency, below which this screening effect is observed, depends on the plasma pressure and resistivity. For the simple toroidal case considered here, the toroidal rotation frequency has to be below ∼10⁻⁵ω_A, with ω_A being the Alfvén frequency. In addition, the same curvature effect leads to enhanced toroidal coupling of poloidal Fourier harmonics inside the resistive layer, as well as reversing the sign of the electromagnetic torque at slow plasma flow.