E. Kolemen

Taming the plasma–material interface with the 'snowflake' divertor in NSTX

Experiments in several tokamaks have provided increasing support for the snowflake configuration as a viable tokamak heat exhaust concept. This white paper summarizes the snowflake properties predicted theoretically and studied experimentally, and identifies outstanding issues to be resolved in existing and future facilities before the snowflake divertor can qualify for the reactor interface.

Experimental vertical stability studies for ITER performance and design guidance

United States Department of Energy (DE-FC02-04ER54698, DEAC52- 07NA27344, and DE-FG02-04ER54235)

Snowflake divertor configuration studies in National Spherical Torus Experimenta)

Experimental results from NSTX indicate that the snowflake divertor (D. Ryutov, Phys. Plasmas 14, 064502 (2007)) may be a viable solution for outstanding tokamak plasma-material interface issues. Steady-state handling of divertor heat flux and divertor plate erosion remains to be critical issues for ITER and future concept devices based on conventional and spherical tokamak geometry with high power density divertors. Experiments conducted in 4–6 MW NBI-heated H-mode plasmas in NSTX demonstrated that the snowflake divertor is compatible with high-confinement core plasma operation, while being very effective in steady-state divertor heat flux mitigation and impurity reduction. A steady-state snowflake divertor was obtained in recent NSTX experiments for up to 600 ms using three divertor magnetic coils. The high magnetic flux expansion region of the scrape-off layer (SOL) spanning up to 50% of the SOL width λq was partially detached in the snowflake divertor. In the detached zone, the heat flux profile flatt...

Linear Stability of Ring Systems

We give a self-contained modern linear stability analysis of a system of n equal-mass bodies in circular orbit about a single more massive body. Starting with the mathematical description of the dynamics of the system, we form the linear approximation, compute all of the eigenvalues of the linear stability matrix, and finally derive inequalities that guarantee that none of these eigenvalues have a positive real part. In the end we rederive the result that Maxwell found for large n in his seminal paper on the nature and stability of Saturns rings, which was published 150 years ago. In addition, we identify the exact matrix that defines the linearized system even when n is not large. This matrix is then investigated numerically (by computer) to find stability inequalities. Furthermore, using properties of circulant matrices, the eigenvalues of the large 4n × 4n matrix are computed by solving n quartic equations, which further facilitates the investigation of stability. Finally, we implement an n-body simulator, and we verify that the threshold mass ratios that we derive mathematically or numerically do indeed identify the threshold between stability and instability. Throughout the paper we consider only the planar n-body problem so that the analysis can be carried out purely in complex notation, which makes the equations and derivations more compact, more elegant, and therefore, we hope, more transparent. The result is a fresh analysis that shows that these systems are always unstable for 2 ≤ n ≤ 6, and for n > 6 they are stable provided that the central mass is massive enough. We give an explicit formula for this mass-ratio threshold.

State-of-the-art neoclassical tearing mode control in DIII-D using real-time steerable electron cyclotron current drive launchers

Real-time steerable electron cyclotron current drive (ECCD) has been demonstrated to reduce the power requirements and time needed to remove 3/2 and 2/1 neoclassical tearing modes (NTMs) in the DIII-D tokamak. In a world first demonstration of the techniques required in ITER, the island formation onset is detected automatically, gyrotrons are turned on and the real-time steerable ECCD launcher mirrors are moved promptly to drive current at the location of the islands. This shrinks and suppresses the modes well before saturation using real-time motional Stark effect constrained equilibria reconstruction with advanced feedback and search algorithms to target the deposition. In ITER, this method will reduce the ECCD energy requirement and so raise Q by keeping the EC system off when the NTM is not present. Further, in the experiments with accurate tracking of pre-emptive ECCD to resonant surfaces, both 3/2 and 2/1 modes are prevented from appearing with much lower ECCD peak power than required for removal of a saturated mode.

Strike point control for the National Spherical Torus Experiment (NSTX)

This paper presents thefirst control algorithm for the inner- and outer-strike point position for a Spherical Torus (ST) fusionexperimentandtheperformanceanalysisofthecontroller. Aliquidlithiumdivertor(LLD)willbeinstalledon NSTX which is believed to provide better pumping than lithium coatings on carbon PFCs. The shape of the plasma dictates the pumping rate of the lithium by channelling the plasma to LLD, where the strike point location is the most important shape parameter. Simulations show that the density reduction depends on the proximity of the strike point to LLD. Experiments were performed to study the dynamics of the strike point, design a new controller to change the location of the strike point to the desired location and stabilize it. The most effective poloidal field (PF) coils in changing inner- and outer-strike points were identified using equilibrium code. The PF coil inputs were changed in a step fashion between various set points and the step response of the strike point position was obtained. From the analysis of the step responses, proportional‐integral‐derivative controllers for the strike points were obtained and the controller was tuned experimentally for better performance. The strike controller was extended to include the outer-strike point on the inner plate to accommodate the desired low outer-strike points for the experiment with the aim of achieving ‘snowflake’ divertor configuration in NSTX. (Some figures in this article are in colour only in the electronic version)

Performance and Upgrades for the Electron Cyclotron Heating System on DIII-D

The electron cyclotron heating (ECH) system on the DIII-D fusion reactor consists of six 110-GHz gyrotrons with 6 MW installed power for pulses limited administratively to 5 s in length. The transmission coefficient is better than -1.1 dB for four of the transmission lines, which is close to the theoretical value. A new depressed collector gyrotron was recently installed and is injecting up to 720 kW of power into DIII-D during 2013 tokamak operations. Three of the four dual waveguide launchers, which can steer the RF beams ±20° both poloidally and toroidally, were used for real-time neoclassical tearing mode control and suppression with increased poloidal scanning speed up to 60°/s and positioning accuracy of the beams of ±2 mm at the plasma center. The ECH capabilities on DIII-D are being steadily updated, leading to increased experimental flexibility and high reliability of the system. In the past year, the ECH system reliability reached 87% for 2352 successful individual gyrotron shots into DIII-D. Planning is under way for the addition of two new depressed collector gyrotrons, one at 110 GHz, 1.2 MW and another at 117.5 GHz, 1.5 MW generated power, both of which are in the test stage at Communications and Power Industries.

Novel aspects of plasma control in ITER

ITER plasma control design solutions and performance requirements are strongly driven by its nuclear mission, aggressive commissioning constraints, and limited number of operational discharges. In addition, high plasma energy content, heat fluxes, neutron fluxes, and very long pulse operation place novel demands on control performance in many areas ranging from plasma boundary and divertor regulation to plasma kinetics and stability control. Both commissioning and experimental operations schedules provide limited time for tuning of control algorithms relative to operating devices. Although many aspects of the control solutions required by ITER have been well-demonstrated in present devices and even designed satisfactorily for ITER application, many elements unique to ITER including various crucial integration issues are presently under development. We describe selected novel aspects of plasma control in ITER, identifying unique parts of the control problem and highlighting some key areas of research remaining. Novel control areas described include control physics understanding (e.g., current profile regulation, tearing mode (TM) suppression), control mathematics (e.g., algorithmic and simulation approaches to high confidence robust performance), and integration solutions (e.g., methods for management of highly subscribed control resources). We identify unique aspects of the ITER TM suppression scheme, which will pulse gyrotrons to drive current within a magnetic island, and turn the drive off following suppression in order to minimize use of auxiliary power and maximize fusion gain. The potential role of active current profile control and approaches to design in ITER are discussed. Issues and approaches to fault handling algorithms are described, along with novel aspects of actuator sharing in ITER.

Plasma modelling results and shape control improvements for NSTX

New shape control implementations and dynamics studies on the National Spherical Torus eXperiment (NSTX) (Ono et al 2000 Nucl. Fusion 40 557–61) are summarized. In particular, strike point position, X-point height and squareness control, and two new system-identification methods/control-tuning algorithms were put into operation. The PID controller for the strike point was tuned by analysing the step response of the strike point position to the poloidal coil currents, employing the Ziegler–Nichols method. An offline system identification of the plasma response to the control inputs based on ARMAX (Ljung 1999 System Identification: Theory for the User (Englewood Cliffs, NJ: Prentice-Hall)) input–output models was implemented. With this tool, rough estimates of the improvements were realized and several control improvements were identified. An online automatic relay-feedback PID tuning algorithm, which has the advantage of tuning the controller in one shot, was implemented, thus optimizing the use of experimental time. Using these new capabilities, all four upper/lower/inner/outer strike points were simultaneous controlled and a combined X-point height, strike point radius control was implemented. The new and improved control with better accuracy and robustness enabled successful plasma operations with the liquid lithium divertor. Additionally this year, the first independent squareness control was developed. This will enable better optimization of the NSTX shape for stability and high performance in the future.

Modeling and control of plasma rotation for NSTX using neoclassical toroidal viscosity and neutral beam injection

A model-based feedback system is presented to control plasma rotation in a magnetically confined toroidal fusion device, to maintain plasma stability for long-pulse operation. This research uses experimental measurements from the National Spherical Torus Experiment (NSTX) and is aimed at controlling plasma rotation using two different types of actuation: momentum from injected neutral beams and neoclassical toroidal viscosity generated by three-dimensional applied magnetic fields. Based on the data-driven model obtained, a feedback controller is designed, and predictive simulations using the TRANSP plasma transport code show that the controller is able to attain desired plasma rotation profiles given practical constraints on the actuators and the available measurements of rotation.