Mark D. Boyer

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.

Fusion nuclear science facilities and pilot plants based on the spherical tokamak

A fusion nuclear science facility (FNSF) could play an important role in the development of fusion energy by providing the nuclear environment needed to develop fusion materials and components. The spherical torus/tokamak (ST) is a leading candidate for an FNSF due to its potentially high neutron wall loading and modular configuration. A key consideration for the choice of FNSF configuration is the range of achievable missions as a function of device size. Possible missions include: providing high neutron wall loading and fluence, demonstrating tritium self-sufficiency, and demonstrating electrical self-sufficiency. All of these missions must also be compatible with a viable divertor, first-wall, and blanket solution. ST-FNSF configurations have been developed simultaneously incorporating for the first time: (1) a blanket system capable of tritium breeding ratio TBR ≈ 1, (2) a poloidal field coil set supporting high elongation and triangularity for a range of internal inductance and normalized beta values consistent with NSTX/NSTX-U previous/planned operation, (3) a long-legged divertor analogous to the MAST-U divertor which substantially reduces projected peak divertor heat-flux and has all outboard poloidal field coils outside the vacuum chamber and superconducting to reduce power consumption, and (4) a vertical maintenance scheme in which blanket structures and the centerstack can be removed independently. Progress in these ST-FNSF missions versus configuration studies including dependence on plasma major radius R0 for a range 1 m–2.2 m are described. In particular, it is found the threshold major radius for TBR = 1 is ⩾ R 1.7 0 m, and a smaller R0 = 1 m ST device has TBR ≈ 0.9 which is below unity but substantially reduces T consumption relative to not breeding. Calculations of neutral beam heating and current drive for non-inductive ramp-up and sustainment are described. An A = 2, R0 = 3 m device incorporating high-temperature superconductor toroidal field coil magnets capable of high neutron fluence and both tritium and electrical self-sufficiency is also presented following systematic aspect ratio studies. J.E. Menard et al Fusion nuclear science facilities and pilot plants based on the spherical tokamak Printed in the UK 106023 NUFUAU

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.

Multivariable robust control of the plasma rotational transform profile for advanced tokamak scenarios in DIII-D

The tokamak is a high order, distributed parameter, nonlinear system with a large number of instabilities. Therefore, accurate theoretical plasma models are difficult to develop. However, linear plasma response models around a particular equilibrium can be developed by using data-driven modeling techniques. This paper introduces a linear model of the rotational transform ι profile evolution based on experimental data from the DIII-D tokamak. The model represents the response of the ι profile to the electric field due to induction as well as to heating and current drive (H&CD) systems. The control goal is to use both induction and H&CD systems to regulate the plasma ι profile around a particular target profile. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed sensitivity H∞ control design problem is formulated to synthesize a stabilizing feedback controller without input constraint that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is then augmented with an anti-windup compensator, which keeps the given profile controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop unmodified when no saturation is present. Finally, computer simulations and experimental results illustrate the performance of the model-based profile controller.

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.

A two-time-scale model-based combined magnetic and kinetic control system for advanced tokamak scenarios on DIII-D

System identification techniques have been successfully used to obtain linear dynamic plasma response models around a particular equilibrium in different tokamaks. This paper identifies a two-time-scale dynamic model of the rotational transform ι profile and βN in response to the electric field due to induction as well as to heating and current drive (H&CD) systems based on experimental data from DIII-D. The control goal is to regulate the plasma ι profile and βN around a particular target value. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed sensitivity H∞ control design problem is solved to determine a stabilizing feedback controller that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is augmented with an anti-windup compensator, which keeps the given controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop unmodified when no saturation is present. Experimental results illustrate the performance of the proposed controller, which is one of the first profile controllers integrating magnetic and kinetic variables ever implemented in DIII-D.

Zero-dimensional nonlinear burn control using isotopic fuel tailoring for thermal excursions

The control of plasma density and temperature are among the most fundamental problems in fusion reactors and will be critical to the success of burning plasma experiments like ITER. While stable burn conditions exist, it is possible that economic and technological constraints will require future commercial reactors to operate with low temperature, high density plasma, a burn condition that may be unstable. The instability is due to the fact that for low temperatures, the fusion heating increases as the plasma temperature rises. An active control system will be essential for stabilizing such operating points. In this work a spatially averaged (zero-dimensional) nonlinear transport model for the energy and the densities of deuterium and tritium fuel ions, as well as the alpha-particles, is used to synthesize a nonlinear feedback controller for stabilizing the burn condition of a fusion reactor. Whereas previous efforts assume an optimal 50:50 mix of deuterium and tritium fuel, this controller makes use of ITERs planned isotopic fueling capability and controls the densities of these ions separately. Also, unlike previous work which used impurity injection to mitigate thermal excursions, this design exploits the ability to modulate the DT fuel mix to control the plasma heating. By moving the isotopic mix in the plasma away from the optimal 50:50 mix, the reaction rate is slowed and the alpha-particle heating is reduced to desired levels. A zero-dimensional simulation study is presented to show the ability of the controller to bring the system back to the desired equilibrium from a given set of perturbations.

Nonlinear burn condition control in tokamaks using isotopic fuel tailoring

One of the fundamental problems in tokamak fusion reactors is how to control the plasma density and temperature in order to regulate the amount of fusion power produced by the device. Control of these parameters will be critical to the success of burning plasma experiments like ITER. The most previous burn condition control efforts use either non-model based control designs or techniques based on models linearized around particular operating points. Such strategies limit the potential operational space and must be carefully retuned or redesigned to accommodate changes in operating points or plasma parameters. In this work, a nonlinear dynamic model of the spatial averages of energy and ion species densities is used to synthesize a nonlinear feedback controller for stabilizing the burn condition. The nonlinear model-based control strategy guarantees a much larger operational space than previous linear controllers. Because it is not designed around a particular operating point, the controller can be used to move from one burn condition to another. The proposed scheme first attempts to use regulation of the auxiliary heating power to reject temperature perturbations, then, if necessary, uses isotopic fuel tailoring as a way to reduce fusion heating during positive temperature perturbations. A global model of hydrogen recycling is incorporated into the model used for design and simulation, and the proposed control scheme is tested for a range of recycling model parameters. As we find the possibility of changing the isotopic mix can be limited for certain unfavorable recycling conditions, we also consider impurity injection as a back-up method for controlling the system. A simple supervisory control strategy is proposed to switch between the primary and back-up control schemes based on stability and performance criteria. A zero-dimensional simulation study is used to study the performance of the control scheme for several scenarios and model parameters. Finally, a one-dimensional simulation is done to test the robustness of the control scheme to spatially varying parameters.