O. Katsuro-Hopkins

Advances in global MHD mode stabilization research on NSTX

Stabilizing modes that limit plasma beta and reduce their deleterious effect on plasma rotation are key goals for the efficient operation of a fusion reactor. Passive stabilization and active control of global kink/ballooning modes and resistive wall modes (RWMs) have been demonstrated on NSTX and research is now advancing towards understanding the stabilization physics and reliably maintaining the high beta plasma for confident extrapolation to ITER and a fusion component test facility based on the spherical torus. Active n = 1 control experiments with an expanded sensor set, combined with low levels of n = 3 field phased to reduce error fields, reduced resonant field amplification and maintained plasma rotation, exceeded normalized beta = 6 and produced record discharge durations limited by magnet system constraints. Details of the observed RWM dynamics during active control show the mode being converted to a rotating kink that stabilizes or saturates and may lead to tearing modes. Discharges with rotation reduced by n = 3 magnetic braking suffer beta collapse at normalized beta = 4.2 approaching the no-wall limit, while normalized beta greater than 5.5 has been reached in these plasmas with n = 1 active control, in agreement with the single-mode RWM theory. Advanced state-space control algorithms proposed for RWM control in ITER theoretically yield significant stabilization improvements. Values of relative phase between the measured n = 1 mode and the applied correction field that experimentally produce stability/instability agree with RWM control modelling. Experimental mode destabilization occurs over a large range of plasma rotation, challenging the notion of a simple scalar critical rotation speed defining marginal stability. Stability calculations including kinetic modifications to the ideal MHD theory are applied to marginally stable experimental equilibria. Plasma rotation and collisionality variations are examined in the calculations. Intermediate rotation levels are less stable, consistent with experimental observations. Trapped ion resonances play a key role in this result. Recent experiments have demonstrated magnetic braking by non-resonant n = 2 fields. The observed rotation damping profile is broader than found for n = 3 fields. Increased ion temperature in the region of maximum braking torque increases the observed rate of rotation damping, consistent with the theory of neoclassical toroidal viscosity at low collisionality.

Resistive wall mode stabilization with internal feedback coils in DIII-D

A set of twelve coils for stability control has recently been installed inside the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] vacuum vessel, offering faster time response and a wider range of applied mode spectra than the previous external coils. Stabilization of the n=1 ideal kink mode is crucial to many high beta, steady-state tokamak scenarios. A resistive wall converts the kink to a slowly growing resistive wall mode (RWM). With feedback-controlled error field correction, rotational stabilization of the RWM has been sustained for more than 2.5 s. Using the internal coils, the required correction field is smaller than with the external coils, consistent with a better match to the mode spectrum of the error field. Initial experiments in direct feedback control have stabilized the RWMs at higher beta and lower rotation than could be achieved by the external coils in similar plasmas, in qualitative agreement with numerical modeling. The new coils have also allowed wall stabilization in plasmas with...

Enhanced ITER resistive wall mode feedback performance using optimal control techniques

In order to achieve the highest plasma pressure limits in ITER, resistive wall kink mode stabilization is required. A novel resistive wall mode linear observer and feedback controller designed using model reduction and optimal control theory and employing only proportional gain are described here that allow operation of ITER up to Cβ = 86% of the ideal wall limit using the present design external control coils. The full VALEN finite element ITER model containing ~3000 modes was reduced to a minimum of 8 modes making real-time controller implementation possible. We find an order of magnitude reduction of the required control coil current and voltage in the presence of white noise from the no-wall limit to the optimal feedback system performance limit as compared with a traditional, classical controller.

Equilibrium and global MHD stability study of KSTAR high beta plasmas under passive and active mode control

The Korea Superconducting Tokamak Advanced Research, KSTAR, is designed to operate a steady-state, high beta plasma while retaining global magnetohydrodynamic (MHD) stability to establish the scientific and technological basis of an economically attractive fusion reactor. An equilibrium model is established for stability analysis of KSTAR. Reconstructions were performed for the experimental start-up scenario and experimental first plasma operation using the EFIT code. The VALEN code was used to determine the vacuum vessel current distribution. Theoretical high beta equilibria spanning the expected operational range are computed for various profiles including generic L-mode and DIII-D experimental H-mode pressure profiles. Ideal MHD stability calculations of toroidal mode number of unity using the DCON code shows a factor of 2 improvement in the wall-stabilized plasma beta limit at moderate to low plasma internal inductance. The planned stabilization system in KSTAR comprises passive stabilizing plates and actively cooled in-vessel control coils (IVCCs) designed for non-axisymmetric field error correction and stabilization of slow timescale MHD modes including resistive wall modes (RWMs). VALEN analysis using standard proportional gain shows that active stabilization near the ideal wall limit can be reached with feedback using the midplane segment of the IVCC. The RMS power required for control using both white noise and noise taken from NSTX active stabilization experiments is computed for beta near the ideal wall limit. Advanced state-space control algorithms yield a factor of 2 power reduction assuming white noise while remaining robust with respect to variations in plasma beta.

Experiments and modelling of external kink mode control using modular internal feedback coils

We report on recent advances in modelling and experiments on resistive wall mode feedback control. The first experimental demonstration of feedback suppression of rotating external kink modes near the ideal wall limit in a tokamak is described [1]. This was achieved using an optimized control system employing a low latency digital controller and directly coupled modular feedback coils. The magnitude of plasma dissipation affecting kink mode behaviour has also been experimentally quantified for the first time using measurements of the radial eigenmode structure of the poloidal field fluctuations associated with the rotating kink mode. New capabilities of the VALEN code [2] are also reported. These include the ability to simulate multiple plasma modes and mode rotation in the model of the feedback control loop. Results from VALEN modelling of resistive wall mode feedback control in ITER are also presented, showing a significant improvement in performance with internal coils. Evidence for a lack of mode rigidity in HBT-EP is given, and plans to address this and other issues related to coil coverage and coil modularity are presented.

Analysis of resistive wall mode LQG control in NSTX with mode rotation

Stabilization of the Resistive Wall Mode (RWM) in the NSTX tokamak is important to achieve high-beta plasmas. This paper numerically investigates state-space control algorithms for improved performance of RWM control using the existing six external control coils with off-midplane poloidal magnetic field sensors in NSTX. Experimentally βN = 5.6 was achieved with the present proportional gain controller. The proposed LQG controller is capable of reaching βN = 6.7 for slowly rotating plasma modes and the ideal wall limit N = 7:06 for plasma modes with higher natural rotation speed.