P. J. Byrne’s research while affiliated with Columbia University and other places

We report scrape-off layer (SOL) current measurements during magnetohydrodynamic (MHD) mode activity, resonant magnetic perturbations (RMPs), and disruptions in the High Beta Tokamak-Extended Pulse (HBT-EP) device. Currents are measured via segmented plasma current Rogowski coils, jumpers running toroidally between otherwise-isolated vessel sections, and a grounded electrode in the scrape-off layer. These currents strongly depend on the plasma's major radius, and amplitude and phase of non-axisymmetric field components. SOL currents connecting through the vessel are seen to reach ∼0.2-0.5% of the plasma current during typical kink activity and RMPs. Plasma current asymmetries and scrape-off-layer currents generated during disruptions, which are commonly called halo currents, reach ∼4% of IP. Asymmetric toroidal currents between vessel sections rotate at tens of kHz through most of the current quench, then symmetrize once IP reaches ∼30% of its pre-disruptive value. Toroidal jumper currents oscillate between co- and counter-IP, with co-IP being dominant on average during disruptions. A relative increase in local plasma current measured by a segmented IP Rogowski coil correlates with counter-IP current in the nearest toroidal jumper. Measurements are interpreted in the context of two models that produce contrary predictions for the toroidal vessel current polarity during disruptions. Plasma current asymmetry measurements are consistent with both models, and SOL currents scale with plasma displacement toward the vessel wall. The design of an upcoming SOL current diagnostic and control upgrade is also briefly presented.

A new algorithm for feedback control of rotating, wall-stabilized kink modes in the High Beta Tokamak-Extended Pulse (HBT-EP) device maintains an accurate phase shift between the perturbation and the measured rotating mode through current control, with control power emphasizing fast rotation and phase jumps over fast amplitude changes. In HBT-EP, wall-stabilized kink modes become unstable above the ideal wall stability limit, and feedback suppression is aimed at delaying the onset of discharge disruption through reduction of the kink mode amplitude. Performance of the new feedback algorithm is tested under different experimental conditions, including variation of the plasma-wall coupling, insertion of a ferritic wall, changing mode rotation frequency over the range of 4-8 kHz using an internal biased electrode, and adjusting the feedback phase-angle to accelerate, amplify, or suppress the mode. We find the previously reported excitation of the slowly rotating mode at high feedback gain in HBT-EP is mitigated by the current control scheme. We also find good agreement between the observed and predicted changes to the mode rotation frequency and amplitude. When ferritic material is introduced, or the plasma-wall coupling becomes weaker as the walls are retracted from plasma, the feedback gain needs to be increased to achieve the same level of suppression. When mode rotation is slowed by a biased electrode, the feedback system still achieves mode suppression, and demonstrates wide bandwidth effectiveness.

High-resolution active and passive kink mode studies are conducted in a tokamak with an adjustable ferromagnetic wall near the plasma surface. Ferritic tiles made from 5.6 mm thick Hiperco® 50 alloy have been mounted on the plasma-facing side of half of the in-vessel movable wall segments in the High Beta Tokamak-Extended Pulse device [D. A. Maurer et al., Plasma Phys. Controlled Fusion 53, 074016 (2011)] in order to explore ferritic resistive wall mode stability. Low-activation ferritic steels are a candidate for structural components of a fusion reactor, and these experiments examine MHD stability of plasmas with nearby ferromagnetic material. Plasma-wall separation for alternating ferritic and non-ferritic wall segments is adjusted between discharges without opening the vacuum vessel. Amplification of applied resonant magnetic perturbations and plasma disruptivity are observed to increase when the ferromagnetic wall is close to plasma surface instead of the standard stainless steel wall. Rapidly rotating m / n = 3 / 1 external kink modes have higher growth rates with the nearby ferritic wall. Feedback suppression of kinks is still as effective as before the installation of ferritic material in vessel, in spite of increased mode growth rates.

The detailed measurements of the 3D plasma response to applied external magnetic perturbations in the presence of a rotating external kink are presented, and compared with the predictions of a single-helicity linear model of kink mode dynamics. The modular control coils of the High Beta Tokamak-Extended Pulse (HBT-EP) device are used to apply resonant m/n = 3/1 magnetic perturbations to wall-stabilized tokamak plasmas with a pre-existing rotating 3/1 kink mode. The plasma response is measured in high-resolution with the extensive magnetic diagnostic set of the HBT-EP device. The spatial structures of both the naturally rotating kink mode and the externally driven response are independently measured and observed to be identical, while the temporal dynamics are consistent with the independent evolution and superposition of the two modes. This leads to the observation of a characteristic change in 3D field dynamics as a function of the applied field amplitude. This amplitude dependence is found to be different for poloidal and radial fields. The measured 3D response is compared to and shown to be consistent with the predictions of the linear single-helicity model in the ``high-dissipation'' regime, as reported previously [M. E. Mauel et al., Nucl. Fusion 45, 285 (2005)].

An advanced adaptive control algorithm is used to study the control of external kink modes that are excited in the HBT-EP tokamak and have a natural toroidal rotation frequency near 8 kHz. The controller's system model is parametrized and the parameters are adjusted in real-time to match the measured plasma evolution. Depending upon a programmed phase angle, active feedback control is shown to either suppress or amplify the controlled amplitude by an amount comparable to the variations observed over a variety of plasma discharges. With negative feedback, the maximum amplitude is reduced to 40% of the uncontrolled value. With positive feedback, the amplitude increases to 155%. Intermediate feedback phases lead to an acceleration or deceleration of the mode rotation frequency in addition to changes in mode amplitude. As the feedback gain increases, the level of both mode suppression and mode amplification also increases. However, for sufficiently high gain, kink mode suppression becomes limited by the excitation of an additional, slowly rotating 1.4 kHz mode having the same helical structure as the uncontrolled kink. High gain amplification is limited by disruptive loss of plasma current. Experimental results are compared with numerical simulations based on a single helicity model, and qualitative agreement is found.

Feedback control has become a crucial tool in the research on magnetic confinement of plasmas for achieving controlled nuclear fusion. We present the first experimental results from a novel feedback control system that, for the first time, employs a graphics processing unit (GPU) for microsecond-latency, real-time control computations. The system was tested on the HBT-EP tokamak using an adaptive control algorithm for control of rotating magnetic perturbations. The algorithm assumes that perturbations of known shape are rotating rigidly, but dynamically derives and updates the rotation frequency to improve phase and gain accuracy of the control signals. Experiments were set up to control four rotating n = 1 perturbations at different poloidal angles. The perturbations are treated as coupled in frequency but independent of amplitude and phase, so that the system effectively controls a helical n = 1 perturbation with unknown poloidal spectrum. The control system suppresses the amplitude of the dominant 8 kHz mode by up to 60%. Deviation from the optimal feedback phase combines suppression with a speed up or slow down of the mode rotation frequency. The feedback performance is found to exceed previous results obtained with an FPGA- and Kalman-filter based control system without requiring any tuning of system model parameters.

We present high-resolution detection and control of the 3D magnetic boundary in the High Beta Tokamak-Extended Pulse (HBT-EP) device. Measurements of non-axisymmetric radial and poloidal fields are made using 216 magnetic sensors positioned near the plasma surface. Control of 3D fields is accomplished using 40 independent saddle coils attached to the passive stabilizing wall. The control coils are energized with high-power solid-state amplifiers, and massively parallel, high-throughput feedback control experiments are performed using low-latency connections between PCI Express analogue input and output modules and a graphics processing unit. The time evolution of unstable and saturated wall-stabilized external kink modes are studied with and without applying magnetic perturbations using the control coils. The 3D dynamic structure of the magnetic field surrounding the plasma is determined through biorthogonal decomposition using the full set of magnetic sensors without the need to fit either a Fourier or a model-based basis. Naturally occurring external kinks are composed of multiple independent helical modes. Smooth transitions between dominant poloidal mode numbers are observed for simultaneous n = 1 and n = 2 modes as the edge safety factor changes. Relative amplitudes of coexistent m/n = 3/1 and 6/2 modes depend on the plasma's major radius and edge safety factor. When stationary 3/1 magnetic perturbations are applied, the resonant response can be linear, saturated, or disruptive, depending upon the perturbation amplitude and the edge safety factor; increased plasma–wall interactions from the perturbed plasma are proposed as a saturation mechanism. Initial feedback experiments have used 40 sensors and 40 control coils, producing mode amplification or suppression, and acceleration or deceleration depending on the feedback phase angle.

A unique in situ calibration technique has been used to spatially calibrate and characterize the extensive new magnetic diagnostic set and close-fitting conducting wall of the High Beta Tokamak-Extended Pulse (HBT-EP) experiment. A new set of 216 Mirnov coils has recently been installed inside the vacuum chamber of the device for high-resolution measurements of magnetohydrodynamic phenomena including the effects of eddy currents in the nearby conducting wall. The spatial positions of these sensors are calibrated by energizing several large in situ calibration coils in turn, and using measurements of the magnetic fields produced by the various coils to solve for each sensor's position. Since the calibration coils are built near the nominal location of the plasma current centroid, the technique is referred to as an "artificial plasma" calibration. The fitting procedure for the sensor positions is described, and results of the spatial calibration are compared with those based on metrology. The time response of the sensors is compared with the evolution of the artificial plasma current to deduce the eddy current contribution to each signal. This is compared with simulations using the VALEN electromagnetic code, and the modeled copper thickness profiles of the HBT-EP conducting wall are adjusted to better match experimental measurements of the eddy current decay. Finally, the multiple coils of the artificial plasma system are also used to directly calibrate a non-uniformly wound Fourier Rogowski coil on HBT-EP.

We report on the design of a new plasma control system for the HBT-EP tokamak that utilizes a graphical processing unit (GPU) to magnetically control the 3D perturbed equilibrium state [1] of the plasma. The control system achieves cycle times of 5 μs and I/O latencies below 10 μs for up to 96 inputs and 64 outputs. The number of state variables is in the same order. To handle the resulting computational complexity under the given time constraints, the control algorithms are designed for massively parallel processing. The necessary hardware resources are provided by an NVIDIA Tesla M2050 GPU, offering a total of 448 computing cores running at 1.3 GHz each. A new control architecture allows control input from magnetic diagnostics to be pushed directly into GPU memory by a D-TACQ ACQ196 digitizer, and control output to be pulled directly from GPU memory by two D-TACQ AO32 analog output modules. By using peer-to-peer PCI express connections, this technique completely eliminates the use of host RAM and central processing unit (CPU) from the control cycle, permitting single-digit microsecond latencies on a standard Linux host system without any real-time extensions.