M.L. Walker

Real time equilibrium reconstruction for tokamak discharge control

A practical method for performing a tokamak equilibrium reconstruction in real time for arbitrary time varying discharge shapes and current profiles is described. An approximate solution to the Grad-Shafranov equilibrium relation is found which best fits the diagnostic measurements. Thus, a solution for the spatial distribution of poloidal flux and toroidal current density is available in real time that is consistent with plasma force balance, allowing accurate evaluation of parameters such as discharge shape and safety factor profile. The equilibrium solutions are produced at a rate sufficient for discharge control. This equilibrium reconstruction algorithm has been implemented on the digital plasma control system for the DIII-D tokamak. The first application of real time equilibrium reconstruction to discharge shape control is described.

Active feedback stabilization of the resistive wall mode on the DIII-D device

A proof of principle magnetic feedback stabilization experiment has been carried out to suppress the resistive wall mode (RWM), a branch of the ideal magnetohydrodynamic (MHD) kink mode under the influence of a stabilizing resistive wall, on the DIII-D tokamak device [Plasma Phys. and Contr. Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. The RWM was successfully suppressed and the high beta duration above the no wall limit was extended to more than 50 times the resistive wall flux diffusion time. It was observed that the mode structure was well preserved during the time of the feedback application. Several lumped parameter formulations were used to study the feedback process. The observed feedback characteristics are in good qualitative agreement with the analysis. These results provide encouragement to future efforts towards optimizing the RWM feedback methodology in parallel to what has been successfully developed for the n = 0 vertical positional control. Newly developed MHD codes have been extremely useful in guiding the experiments and in providing possible paths for the next step.

Design and simulation of extremum-seeking open-loop optimal control of current profile in the DIII-D tokamak

In a magnetic fusion reactor, the achievement of a certain type of plasma current profiles, which are compatible with magnetohydrodynamic stability at high plasma pressure, is key to enable high fusion gain and non-inductive sustainment of the plasma current for steady-state operation. The approach taken toward establishing such plasma current profiles at the DIII-D tokamak is to create the desired profile during the plasma current ramp-up and early flattop phases. The evolution in time of the current profile is related to the evolution of the poloidal flux, which is modeled in normalized cylindrical coordinates using a partial differential equation usually referred to as the magnetic diffusion equation. The control problem is formulated as an open-loop, finite-time, optimal control problem for a nonlinear distributed parameter system, and is approached using extremum seeking. Simulation results, which demonstrate the accuracy of the considered model and the efficiency of the proposed controller, are presented.

Experimental vertical stability studies for ITER performance and design guidance

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

Stabilization of the external kink and control of the resistive wall mode in tokamaks

One promising approach to maintaining stability of high beta tokamak plasmas is the use of a conducting wall near the plasma to stabilize low-n ideal magnetohydrodynamic instabilities. However, with a resistive wall, either plasma rotation or active feedback control is required to stabilize the more slowly growing resistive wall modes (RWMs). Previous experiments have demonstrated that plasmas with a nearby conducting wall can remain stable to the n=1 ideal external kink above the beta limit predicted with the wall at infinity. Recently, extension of the wall stabilized lifetime τL to more than 30 times the resistive wall time constant τw and detailed, reproducible observation of the n=1 RWM have been possible in DIII-D [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159] plasmas above the no-wall beta limit. The DIII-D measurements confirm characteristics common to several RWM theories. The mode is destabilized as the plasma rotation at the q=3 surfac...

Resistive wall stabilization of high-beta plasmas in DIII?D

Recent DIII?D experiments show that ideal kink-modes can be stabilized at high beta by a resistive wall, with sufficient plasma rotation. However, the resonant response to static magnetic field asymmetries by a marginally stable resistive wall mode can lead to strong damping of the rotation. Careful reduction of such asymmetries has allowed plasmas with beta well above the ideal MHD no-wall limit, and approaching the ideal-wall limit, to be sustained for durations exceeding 1?s. Feedback control can improve plasma stability by direct stabilization of the resistive wall mode or by reducing magnetic field asymmetry. Assisted by plasma rotation, direct feedback control of resistive wall modes with growth rates more than five times faster than the characteristic wall time has been observed. These results open a new regime of tokamak operation above the free-boundary stability limit, accessible by a combination of plasma rotation and feedback control.

Stabilization of the resistive wall mode in DIII–D by plasma rotation and magnetic feedback

Suppression of the resistive wall mode (RWM) has been successfully demonstrated in the DIII–D tokamak by using rotational stabilization in conjunction with a close-fitting vacuum vessel wall. The duration of the high-pressure discharge was extended to hundreds of times the wall skin time. Frequently, the plasma pressure reached the ideal-wall magnetohydrodynamic (MHD) kink limit. The confined pressure is up to twice as high as the no-wall ideal MHD kink limit. Near its marginal stability point, the RWM is found to resonate with residual non-axisymmetric fields (e.g. components of the error field). A magnetic feedback system has been used to identify and compensate for the residual non-axisymmetric fields. This is to the best of our knowledge, the first demonstration of the sustainment of a stable plasma with pressure at levels well above the no-wall pressure limit. This technique is expected to be applicable to other toroidal devices.

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.

Overview of KSTAR initial operation

Since the successful first plasma generation in the middle of 2008, three experimental campaigns were successfully made for the KSTAR device, accompanied with a necessary upgrade in the power supply, heating, wall-conditioning and diagnostic systems. KSTAR was operated with the toroidal magnetic field up to 3.6 T and the circular and shaped plasmas with current up to 700 kA and pulse length of 7 s, have been achieved with limited capacity of PF magnet power supplies.The mission of the KSTAR experimental program is to achieve steady-state operations with high performance plasmas relevant to ITER and future reactors. The first phase (2008–2012) of operation of KSTAR is dedicated to the development of operational capabilities for a super-conducting device with relatively short pulse. Development of start-up scenario for a super-conducting tokamak and the understanding of magnetic field errors on start-up are one of the important issues to be resolved. Some specific operation techniques for a super-conducting device are also developed and tested. The second harmonic pre-ionization with 84 and 110 GHz gyrotrons is an example. Various parameters have been scanned to optimize the pre-ionization. Another example is the ICRF wall conditioning (ICWC), which was routinely applied during the shot to shot interval.The plasma operation window has been extended in terms of plasma beta and stability boundary. The achievement of high confinement mode was made in the last campaign with the first neutral beam injector and good wall conditioning. Plasma control has been applied in shape and position control and now a preliminary kinetic control scheme is being applied including plasma current and density. Advanced control schemes will be developed and tested in future operations including active profiles, heating and current drives and control coil-driven magnetic perturbation.

CONTROL OF THE RESISTIVE WALL MODE IN ADVANCED TOKAMAK PLASMAS ON DIII-D

Resistive wall mode (RWM) instabilities are found to be a limiting factor in advanced tokamak regimes with low internal inductance. Even small amplitude modes can affect the rotation profile and the performance of these ELMing H mode discharges. Although complete stabilization of the RWM by plasma rotation has not yet been observed, several discharges with increased beam momentum and power injection sustained good steady state performance for record durations. The first investigation of active feedback control of the RWM has shown promising results: the leakage of radial magnetic flux through the resistive wall can be successfully controlled and the duration of the high beta phase can be prolonged. The results provide a comparative test of several approaches to active feedback control, and are being used to benchmark the analysis and computational models of active control.