R.D. Johnson

Development of ITER-relevant plasma control solutions at DIII-D

The requirements of the DIII-D physics program have led to the development of many operational control results with direct relevance to ITER. These include new algorithms for robust and sustained stabilization of neoclassical tearing modes with electron cyclotron current drive, model-based controllers for stabilization of the resistive wall mode in the presence of ELMs, coupled linear–nonlinear algorithms to provide good dynamic axisymmetric control while avoiding coil current limits, and adaptation of the DIII-D plasma control system (PCS) to operate next-generation superconducting tokamaks. Development of integrated plasma control (IPC), a systematic approach to modelbased design and controller verification, has enabled successful experimental application of high reliability control algorithms requiring a minimum of machine operations time for testing and tuning. The DIII-D PCS hardware and software and its versions adapted for other devices can be connected to IPC simulations to confirm control function prior to experimental use. This capability has been important in control system implementation for tokamaks under construction and is expected to be critical for ITER.

Model-based dynamic resistive wall mode identification and feedback control in the DIII-D tokamak

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...

Plasma shape control on the National Spherical Torus Experiment (NSTX) using real-time equilibrium reconstruction

Plasma shape control using real-time equilibrium reconstruction has been implemented on the National Spherical Torus Experiment (NSTX). The rtEFIT code originally developed for use on DIII-D was adapted for use on NSTX. The real-time equilibria provide calculations of the flux at points on the plasma boundary, which are used as input to a shape control algorithm known as isoflux control. The flux at the desired boundary location is compared with a reference flux value, and this flux error is used as the basic feedback quantity for the poloidal field coils on NSTX. The hardware that comprises the control system is described, as well as the software infrastructure. Examples of precise boundary control are also presented.

First-principles-driven model-based current profile control for the DIII-D tokamak via LQI optimal control

In tokamak fusion plasmas, control of the spatial distribution profile of the toroidal plasma current plays an important role in realizing certain advanced operating scenarios. These scenarios, characterized by improved confinement, magnetohydrodynamic stability, and a high fraction of non-inductively driven plasma current, could enable steady-state reactor operation with high fusion gain. Current profile control experiments at the DIII-D tokamak focus on using a combination of feedforward and feedback control to achieve a targeted current profile during the ramp-up and early flat-top phases of the shot and then to actively maintain this profile during the rest of the discharge. The dynamic evolution of the current profile is nonlinearly coupled with several plasma parameters, motivating the design of model-based control algorithms that can exploit knowledge of the system to achieve desired performance. In this work, we use a first-principles-driven, control-oriented model of the current profile evolution in low confinement mode (L-mode) discharges in DIII-D to design a feedback control law for regulating the profile around a desired trajectory. The model combines the magnetic diffusion equations with empirical correlations for the electron temperature, resistivity, and non-inductive current drive. To improve tracking performance of the system, a nonlinear input transformation is combined with a linear-quadratic-integral (LQI) optimal controller designed to minimize a weighted combination of the tracking error and controller effort. The resulting control law utilizes the total plasma current, total external heating power, and line averaged plasma density as actuators. A simulation study was used to test the controllers performance and ensure correct implementation in the DIII-D plasma control system prior to experimental testing. Experimental results are presented that show the first-principles-driven model-based control schemes successful rejection of input disturbances and perturbed initial conditions, as well as target trajectory tracking.

Toroidal current profile control during low confinement mode plasma discharges in DIII-D via first-principles-driven model-based robust control synthesis

In order for ITER to be capable of operating in advanced tokamak operating regimes, characterized by a high fusion gain, good plasma confinement, magnetohydrodynamic stability and a non-inductively driven plasma current, for extended periods of time, several challenging plasma control problems still need to be solved. Setting up a suitable toroidal current density profile in the tokamak is key for one possible advanced operating scenario characterized by non-inductive sustainment of the plasma current. At the DIII-D tokamak, the goal is to create the desired current profile during the ramp-up and early flat-top phases of the plasma discharge and then actively maintain this target profile for the remainder of the discharge. The evolution in time of the toroidal current profile in tokamaks is related to the evolution of the poloidal magnetic flux profile, which is modelled in normalized cylindrical coordinates using a first-principles, nonlinear, dynamic partial differential equation (PDE) referred to as the magnetic diffusion equation. The magnetic diffusion equation is combined with empirical correlations developed from physical observations and experimental data from DIII-D for the electron temperature, the plasma resistivity and the non-inductive current drive to develop a simplified, control-oriented, nonlinear, dynamic PDE model of the poloidal flux profile evolution valid for low confinement mode discharges. In this work, we synthesize a robust feedback controller to reject disturbances and track a desired reference trajectory of the poloidal magnetic flux gradient profile by employing the control-oriented model of the system. A singular value decomposition of the static gain matrix of the plant model is utilized to identify the most relevant control channels and is combined with the dynamic response of system around a given operating trajectory to design the feedback controller. A general framework for real-time feedforward + feedback control of magnetic and kinetic plasma profiles was implemented in the DIII-D Plasma Control System and was used to demonstrate the ability of the feedback controller to control the toroidal current profile evolution in the DIII-D tokamak. These experiments constitute the first time ever a first-principles-driven, model-based, closed-loop magnetic profile controller was successfully implemented and tested in a tokamak device.

Backstepping Control of the Toroidal Plasma Current Profile in the DIII-D Tokamak

One of the most promising devices for realizing power production through nuclear fusion is the tokamak. To maximize performance, it is preferable that tokamak reactors achieve advanced operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic stability, and a largely noninductively driven plasma current. Such scenarios could enable steady-state reactor operation with high fusion gain, the ratio of produced fusion power to the external power provided through the plasma boundary. For certain advanced scenarios, control of the spatial profile of the plasma current will be essential. The complexity of the current profile dynamics, arising due to nonlinearities and couplings with many other plasma parameters, motivates the use of model-based control algorithms that can account for the system dynamics. A first-principles-driven, control-oriented model of the current profile evolution in low-confinement mode (L-mode) discharges in the DIII-D tokamak is employed to address the problem of regulating the current profile evolution around desired trajectories. In the primarily inductive L-mode discharges considered in this paper, the boundary condition, which is dependent on the total plasma current, has the largest influence on the current profile dynamics, motivating the design of a boundary feedback control law to improve the system performance. The backstepping control design technique provides a systematic method to obtain a boundary feedback law through the transformation of a spatially discretized version of the original system into an asymptotically stable target system with desirable properties. Through a nonlinear transformation of the available physical actuators, the resulting control scheme produces references for the total plasma current, total power, and line averaged density, which are tracked by existing dedicated control loops. Adaptiveness is added to the control scheme to improve upon the backstepping controllers disturbance rejection and tracking capability. Prior to experimental testing, a Simserver simulation was carried out to study the controllers performance and ensure proper implementation in the DIII-D Plasma Control System. An experimental test was performed on DIII-D to test the ability of the controller to reject input disturbances and perturbations in initial conditions and to demonstrate the feasibility of the proposed control approach.

Integrated magnetic and kinetic control of advanced tokamak plasmas on DIII-D based on data-driven models

The first real-time profile control experiments integrating magnetic and kinetic variables were performed on DIII-D in view of regulating and extrapolating advanced tokamak scenarios to steady-state devices and burning plasma experiments. Device-specific, control-oriented models were obtained from experimental data using a generic two-time-scale method that was validated on JET, JT-60U and DIII-D under the framework of the International Tokamak Physics Activity for Integrated Operation Scenarios (Moreau et al 2011 Nucl. Fusion 51 063009). On DIII-D, these data-driven models were used to synthesize integrated magnetic and kinetic profile controllers. The neutral beam injection (NBI), electron cyclotron current drive (ECCD) systems and ohmic coil provided the heating and current drive (H&CD) sources. The first control actuator was the plasma surface loop voltage (i.e. the ohmic coil), and the available beamlines and gyrotrons were grouped to form five additional H&CD actuators: co-current on-axis NBI, co-current off-axis NBI, counter-current NBI, balanced NBI and total ECCD power from all gyrotrons (with off-axis current deposition). Successful closed-loop experiments showing the control of (a) the poloidal flux profile, Ψ(x), (b) the poloidal flux profile together with the normalized pressure parameter, βN, and (c) the inverse of the safety factor profile, , are described.

Next-generation plasma control in the DIII-D tokamak

OAK A271 NEXT-GENERATION PLASMA CONTROL IN THE DIII-D TOKAMAK. The advanced tokamak (AT) operating mode which is the principal focus of the DIII-D tokamak requires highly integrated and complex plasma control. Simultaneous high performance regulation of the plasma boundary and internal profiles requires multivariable control techniques to account for the highly coupled influences of equilibrium shape, profile, and stability control. This paper describes progress towards the DIII-D At mission goal through both significantly improved real-time computational hardware and control algorithm capability.

Real-time control of DIII–D plasma discharges using a Linux alpha computing cluster

Abstract This paper describes an upgrade for the real-time computing system responsible for monitoring and controlling plasma, discharges in the DIII–D tokamak (J.L. Luxon, L.G. Davis, Fusion Technol. 8 (1985) 441) at General Atomics (GA). The current system employs six CSPI i860 VME format processors working in parallel to acquire data in real-time and perform feed back control of plasma shape and position parameters. Work has commenced on integration of a new computing system based on commonly available PCI bus based processors that communicate over the 2 Gbit/s Myrinet (Myricom, Inc., CA, USA) network. The new system will greatly improve the processing power available to the algorithms required for computing plasma equilibrium reconstructions in real-time. A factor of 20 anticipated performance increase will allow for improved accuracy and frequency response for plasma shape estimation and control. The migration from VME to PCI Myrinet computer clustering will improve the data acquisition capabilities by opening up access to additional DIII–D temperature and density diagnostics. The upgrade will increase the inter-processor communication speed and provide the flexibility to integrate additional processors to match the cost and computing needs of the tokamak research program.

Plasma Startup Design of Fully Superconducting Tokamaks EAST and KSTAR With Implications for ITER

Recent commissioning of two major fully superconducting (SC)-shaped tokamaks, Experimental Advanced Superconducting Tokamak (EAST) and Korean Superconducting Tokamak Advanced Research (KSTAR), represents a significant advance in magnetic fusion research. The key to commissioning success in these complex and unique tokamaks was as follows: 1) use of a robust, flexible plasma control system (PCS) based on the validated DIII-D design; 2) use of the TokSys design and modeling environment, which is tightly coupled with the DIII-D PCS architecture for first-plasma scenario development and plasma diagnosis; and 3) collaborations with experienced internationally recognized teams of tokamak operations and control experts. We provide an overview of the generic modeling environment and plasma control tools developed and validated within the DIII-D experimental program and applied through an international collaborative program to successfully address the unique constraints associated with the startup of these next-generation tokamaks. The unique characteristics of each tokamak and the machine constraints that must be included in device modeling and simulation, such as SC coil current slew rate limits and the presence of nonlinear magnetic materials, are discussed, along with commissioning and initial operational results. Lessons learned from the startup experience in these devices are summarized, with special emphasis on ramifications for International Thermonuclear Experimental Reactor (ITER).