Integrated plasma control for advanced tokamaks

Tokamak plasma experiments on the DIII-D device (Luxon et al 2005 Fusion Sci. Tech. 48 807) demonstrate high-performance, negative central shear (NCS) equilibria with enhanced stability when the minimum safety factor exceeds 2, qualitatively confirming theoretical predictions of favorable stability in the NCS regime. The discharges exhibit good confinement with an L-mode enhancement factor H89 = 2.5, and are ultimately limited by the ideal-wall external kink stability boundary as predicted by ideal MHD theory, as long as tearing mode (TM) locking events, resistive wall modes (RWMs), and internal kink modes are properly avoided or controlled. Although the discharges exhibit rotating TMs, locking events are avoided as long as a threshold minimum safety factor value is maintained. Fast timescale magnetic feedback control ameliorates RWM activity, expanding the stable operating space and allowing access to values approaching the ideal-wall limit. Quickly growing and rotating instabilities consistent with internal kink mode dynamics are encountered when the ideal-wall limit is reached. The RWM events largely occur between the no- and ideal-wall pressure limits predicted by ideal MHD. However, evaluating kinetic contributions to the RWM dispersion relation results in a prediction of passive stability in this regime due to high plasma rotation. In addition, the ideal MHD stability analysis predicts that the ideal-wall limit can be further increased to by broadening the current profile. This path toward improved stability has the potential advantage of being compatible with the bootstrap-dominated equilibria envisioned for advanced tokamak (AT) fusion reactors.

The DIII-D research program is a science program aimed at an energy goal as stated in the mission statement: ''To establish the scientific basis for the optimization of the tokamak approach to fusion energy production.'' The focus is on advanced tokamak (AT) research with a goal aimed at discovering the ultimate potential of the tokamak. The research program is a multi-institutional, collaborative effort involving 60 institutions and about 300 researchers. The DIII-D tokamak has considerable plasma shape flexibility, plasma feedback control tools and algorithms and a full set of mature diagnostics for detailed studies of plasma stability, turbulence and transport, heating and current drive with neutral beams and electron cyclotron power available, and boundary and divertor physics. Along with these broad topical science areas (TSAs) of research several more focused areas of research, called thrusts, are chosen each year. This year the thrusts were on a high bootstrap fraction (fBS) AT scenario, stabilization of resistive wall modes (RWMs), internal transport barrier (ITB) control, understanding and control of the edge pedestal, and stabilization of neoclassical tearing modes (NTMs).

Active feedback stabilization of multiple resistive wall modes (RWMs) has been successfully proven in the EXTRAP T2R reversed field pinch. One of the features of plasma discharges operated with active feedback stabilization, in addition to the prolongation of the plasma discharge, is the sustainment of the plasma rotation. Sustained rotation is observed both for the internally resonant tearing modes (TMs) and the intrinsic impurity oxygen ions. Good quantitative agreement between the toroidal rotation velocities of both is found: the toroidal rotation is characterized by an acceleration phase followed, after one wall time, by a deceleration phase that is slower than in standard discharges. The TMs and the impurity ions rotate in the same poloidal direction with also similar velocities. Poloidal and toroidal velocities have comparable amplitudes and a simple model of their radial profile reproduces the main features of the helical angular phase velocity. RWMs feedback does not qualitatively change the TMs behaviour and typical phenomena such as the dynamo and the ‘slinky’ are still observed. The improved sustainment of the plasma and TMs rotation occurs also when feedback only acts on internally non-resonant RWMs. This may be due to an indirect positive effect, through non-linear coupling between TMs and RWMs, of feedback on the TMs or to a reduced plasma-wall interaction affecting the plasma flow rotation. Electromagnetic torque calculations show that with active feedback stabilization the TMs amplitude remains well below the locking threshold condition for a thick shell. Finally, it is suggested that active feedback stabilization of RWMs and current profile control techniques can be employed simultaneously thus improving both the plasma duration and its confinement properties.

The effort to understand the physics of the resistive wall mode (RWM) and develop methods to control this magnetohydrodynamic mode to allow achievement of higher pressure in advanced tokamak plasmas has been an example of successful multi-institutional collaboration at the DIII-D National Fusion Facility in San Diego, California. DIII-D research in this area has produced several advances and breakthroughs following a coordinated research plan involving a sequence of measurements, development of new analysis tools, and the installation of new diagnostic and feedback stabilization hardware: Suppression of the RWM by active magnetic feedback has been demonstrated using the DIII-D six-element error field correction coil, rotational stabilization of the RWM has been demonstrated and sustained for all values of the plasma pressure from the no-wall to the ideal-wall stability limits, improved RWM feedback stabilization has been shown using a new set of 12 internal control coils, and newly developed models of feedback have shown good agreement with the measurements. By so doing, the DIII-D work on RWM stabilization has become a cornerstone of the long-term advanced tokamak program and is having impact on the world fusion program. Presently both ITER and FIRE are including plans for RWM stabilization in their programs.

In this work, μ synthesis is employed to stabilize a model of the resistive wall mode (RWM) instability in the DIII-D tokamak. The General Atomics/FAR-TECH DIII-D RWM model, which replaces the spatial perturbation of the plasma with an equivalent perturbation of surface current on a spatially fixed plasma boundary, is used to derive a linear state-space representation of the mode dynamics. The spatial and current perturbations are equivalent in the sense that they both produce the same magnetic field perturbation at surrounding conductors. The key term in the model characterizing the magnitude of the instability is the time-varying uncertain parameter cpp, which is related to the RWM growth rate γ. Taking advantage of the structure of the state matrices, the model is reformulated into a robust control framework, with the growth rate of the RWM modeled as an uncertain parameter. A robust controller that stabilizes the system for a range of practical growth rates is proposed. The controller is tested through simulations, demonstrating significant performance increase over the classical proportional-derivative controller, extending the RWM growth rate range for which the system is stable and satisfies predefined performance constraints, and increasing the level of tolerable measurement noise. The simulation study shows that the proposed model-based DK controllers can successfully stabilize the mode when the growth rate varies over time during the discharge because of changes in the operating conditions such as pressure and rotation. In terms of robust stability, this method eliminates the need for growth-rate online identification and controller scheduling.Selected Full Papers from15th WORKSHOP ON

A new model-based dynamic resistive wall mode (RWM) identification and feedback control algorithm has been developed. While the overall RWM structure can be detected by a model-based matched filter in a similar manner to a conventional sensor-based scheme, it is significantly influenced by edge-localized-modes (ELMs). A recent study suggested that such ELM noise might cause the RWM control system to respond in an undesirable way. Thus, an advanced algorithm to discriminate ELMs from RWM has been incorporated into this model-based control scheme, dynamic Kalman filter. Specifically, the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] resistive vessel wall was modeled in two ways: picture frame model or eigenmode treatment. Based on the picture frame model, the first real-time, closed-loop test results of the Kalman filter algorithms during DIII-D experimental operation are presented. The Kalman filtering scheme was experimentally confirmed to be effective in discriminating ELMs from RWM. As a result, the actuator coils (I-coils) were rarely excited during ELMs, while retaining the sensitivity to RWM. However, finding an optimized set of operating parameters for the control algorithm requires further analysis and design. Meanwhile, a more advanced Kalman filter based on a more accurate eigenmode model has been developed. According to this eigenmode approach, significant improvement in terms of control performance has been predicted, while maintaining good ELM discrimination.

High-confinement (H-mode) operation is the choice for next-step tokamak devices based either on conventional or advanced tokamak physics. This choice, however, comes at a significant cost for both the conventional and advanced tokamaks because of the effects of edge localized modes (ELMs). ELMs can produce significant erosion in the divertor and can affect the beta limit and reduced core transport regions needed for advanced tokamak operation. Experimental results from DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] this year have demonstrated a new operating regime, the quiescent H-mode regime, which solves these problems. We have achieved quiescent H-mode operation that is ELM-free and yet has good density and impurity control. In addition, we have demonstrated that an internal transport barrier can be produced and maintained inside the H-mode edge barrier for long periods of time (>3.5 s or >25 energy confinement times τE), yielding a quiescent double barrier regime. By slowly ramping the input power, we have achieved βNH89=7 for up to 5 times the τE of 150 ms. The βNH89 values of 7 substantially exceed the value of 4 routinely achieved in the standard ELMing H mode. The key factors in creating the quiescent H-mode operation are neutral beam injection in the direction opposite to the plasma current (counter injection) plus cryopumping to reduce the density. Density and impurity control in the quiescent H mode is possible because of the presence of an edge magnetohydrodynamic (MHD) oscillation, the edge harmonic oscillation, which enhances the edge particle transport while leaving the energy transport unaffected.

Interest in real-time control of magnetic field errors and magnetohydrodynamic (MHD) instabilities has been growing in the last decades due to the demanding stability requirements of high-performance scenarios in fusion devices. In this framework, the RFX-mod experiment (Sonato et al 2003 Fusion Eng. Des. 66 161) plays an important role. One of the main goals of RFX-mod is to explore high-plasma current regimes up to 2 MA for the first time in a reversed-field pinch. To this aim, RFX-mod is equipped with an advanced active coil system for the control of error fields and MHD modes, such as tearing and resistive-wall modes. As far as tearing modes are concerned, both controlling their edge radial magnetic field and maintaining them into slow (∼10–100 Hz) rotation are crucial to reduce both the plasma–wall interaction and the core magnetic stochasticity. In this paper, a model-based optimization of the RFX-mod feedback control is presented. The aim is to find an optimal gain set for a spectrum of multiple tearing modes, which produces the lowest possible value of the edge radial magnetic field, maintaining at the same time the modes into slow rotation and avoiding coil current saturations. These optimal gains have first been calculated offline by simulating the non-linear dynamics of a spectrum of tearing modes interacting through viscous and electromagnetic torques, using an adaptation to the RFX-mod multiple-shell layout of the model described in Zanca (2009 Plasma Phys. Control. Fusion 51 015006). This gain set has been obtained by scanning the proportional and derivative gains and has been tested in an extensive experimental campaign, showing good agreement with the model. With this approach, a reduction in the edge radial magnetic field up to 15%, with respect to discharges in which an empirical optimization was used, has been obtained. The above model proved to be a powerful tool to tune a multi-mode controller offline, which allowed us to save a large amount of experimental time.

An investigation is presented of the effect of an error field on the growth of a resistive wall mode (RWM). This issue is of importance to many toroidal confinement devices, but particularly to the proposed International Thermonuclear Experimental Reactor (ITER) [ITER Physics Basis, Nucl. Fusion 39, 2175 (1999)], where if advanced tokamak performance is required, then the RWM instability is especially vulnerable. The paper includes a discussion of error field amplification when RWM marginal stability is approached, and it is pointed out that error field current is the fixed quantity in this calculation, not the error field flux, which is essentially an eigenvalue of the calculation. The key issue concerns the effect of plasma rotation on the RWM. The distinction is made between the resistive wall tearing mode (RWTM), which is stabilized by modest plasma rotation, and the ideal RWM, which is not. The importance of the joint torques that are present when an error field and an RWM of the same helicity coexist is investigated. Using torque balance a simulation is presented of the effect of reducing error field amplitude on the duration of a stable discharge. This shows features in accord with experimental observations from the DIII-D device [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p.159].

Steady-state operation of the advanced tokamak reactor relies on maintaining plasma stability with respect to the resistive wall mode (RWM). Active magnetic feedback and plasma rotation are the two methods proposed and demonstrated for this purpose. A comprehensive modeling effort including both magnetic feedback and plasma rotation is needed for understanding the physical mechanisms of the stabilization and to project to future devices. For plasma with low rotation, a complete solution for the feedback issue is obtained by assuming the plasma obeys ideal magnetohydrodynamics (MHDs) and utilizing a normal mode approach (NMA) [M. S. Chu et al., Nucl. Fusion 43, 441 (2003)]. It is found that poloidal sensors are more effective than radial sensors and coils inside of the vacuum vessel more effective than outside. For plasmas with non-negligible rotation, a comprehensive linear nonideal MHD code, the MARS-F has been found to be suitable. MARS-F [Y. Q. Liu et al., Phys. Plasmas 7, 3681 (2000)] has been benchmarked in the ideal MHD limit against the NMA. The effect of rotation stabilization of the plasma depends on the plasma dissipation model. Broad qualitative features of the experiment are reproduced. Rotation reduces the feedback gain required for RWM stabilization. Reduction is significant when rotation is near the critical rotation speed needed for stabilization. The International Thermonuclear Experimental Reactor (ITER) [R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 (2002)] (scenario IV for advanced tokamak operation) may be feedback stabilized with β above the no wall limit and up to an increment of ∼50% towards the ideal limit. Rotation further improves the stability.

It is well known that stabilization of the resistive wall mode (RWM) may allow fusion power to be significantly increased for a given magnetic field in advanced tokamak operation. The principle of stabilization of the RWM by rotation has been established both experimentally and theoretically. Recent experimental results have indicated stabilization of the RWM has been achieved with very small levels of rotation using balanced neutral beam injection. The framework of Connor et al (Connor et al 1988 Phys. Fluids 31 577) is used to develop two ideal plasma analytic toroidal models where stepped pressure profiles and careful ordering of terms are used to simplify the analysis. The first model has one resonant layer in the plasma and two resistive walls and the second has two resonant layers and one resistive wall. The RWM can be stabilized with slow rotation (∼0.5%ΩA, where ΩA is the Alfvénic rotation frequency) of a secondary resistive wall. A secordary rotating resistive wall can only stabilize the plasma if a perfectly conducting wall at that location would stabilize the plasma. Differential rotation in the plasma is investigated by rotating two resonant layers in the plasma at different rates. It is found in this model that differential rotation of the outer resonant surface can stabilize the RWM, with no rotation required at the inner surface. However, stabilization is not possible with the outer surface static and the inner surface rotating. Experimental rotation profiles for balanced neutral beam shots have higher levels of rotation near the plasma edge showing differential rotation between the outer surface and the wall may be part of the RWM stabilization mechanism.

The stabilization of the resistive wall mode (RWM) instability in the DIII-D tokamak is necessary to maintain conditions for the plasma experiment. Stability has been achieved in experiments using proportional/derivative (PD) gain controllers. However, the stability range in terms of the mode growth rate ? is limited. Employing an optimal feedback controller in conjunction with a state estimator designed to reject sensor colored noise, the stability region of the system is greatly extended. Using experimental results, the power spectral density of the measurement noise is used to model the colored noise as a noise transfer function with a white noise input. The Linear Quadratic Gaussian (LQG) control technique is applied and results are compared to a traditional PD controller through simulations.

The Madison Symmetric Torus (MST) is a toroidal device that, when operated as a standard tokamak, does not have major disruptions. Unlike most tokamaks, the MST plasma is surrounded by a close fitting highly conducting wall, with a resistive wall penetration time two orders of magnitude longer than in JET or DIII-D, and three times longer than in ITER. The MST can operate with edge qa⩽2 , unlike standard tokamaks. Simulations presented here indicate that the MST is unstable to resistive wall tearing modes (RWTMs) and resistive wall modes (RWMs). They could in principle cause disruptions, but the predicted thermal quench (TQ) time is much longer than the experimental pulse time. If the MST TQ time were comparable to measurements in JET and DIII-D, theory and simulations predict that disruptions would have been observed in MST. This is consistent with the modeling herein, predicting that disruptions are caused by RWTMs and RWMs. In the low qa∼2 regime of MST, the RWTM asymptotically satisfies the RWM dispersion relation. The transition from RWTM to RWM occurs smoothly at qa=m/n , where m,n are poloidal and toroidal mode numbers.

This is a project to develop and apply analytic and computational tools to answer physics questions relevant to the onset of non-ideal magnetohydrodynamic (MHD) instabilities in toroidal magnetic confinement plasmas. The focused goal of the research is to develop predictive tools for these instabilities, including an inner layer solution algorithm, a resistive wall with control coils, and energetic particle effects. The production phase compares studies of instabilities in such systems using analytic techniques, PEST- III and NIMROD. Two important physics puzzles are targeted as guiding thrusts for the analyses. The first is to form an accurate description of the physics determining whether the resistive wall mode or a tearing mode will appear first as β is increased at low rotation and low error fields in DIII-D. The second is to understand the physical mechanism behind recent NIMROD results indicating strong damping and stabilization from energetic particle effects on linear resistive modes. The work seeks to develop a highly relevant predictive tool for ITER, advance the theoretical description of this physics in general, and analyze these instabilities in experiments such as ASDEX Upgrade, DIII-D, JET, JT-60U and NTSX. The awardee on this grant is the University of Tulsa. The research efforts are supervised principally by Dr. Brennan. Support is included for two graduate students, and a strong collaboration with Dr. John M. Finn of LANL. The work includes several ongoing collaborations with General Atomics, PPPL, and the NIMROD team, among others.

The maximum operational high beta in single-null divertor (SND) long pulse tokamak discharges in the DIII-D tokamak with a cross-sectional shape similar to the proposed International Thermonuclear Experimental Reactor (ITER) device is found to be limited by the onset of resistive instabilities that have the characteristics of neoclassically destabilized tearing modes. There is a soft limit due to the onset of an m/n=3/2 rotating tearing mode that saturates at low amplitude and a hard limit at slightly higher beta due to the onset of an m/n=2/1 rotating tearing mode that grows, slows down and locks. By operating at higher density and thus collisionality, the practical beta limit due to resistive tearing modes approaches the ideal magnetohydrodynamic (MHD) limit