Predictive control of the tokamak q profile to facilitate reproducibility of high-qmin steady-state scenarios at DIII-D

We consider control of the q profile while simultaneously regulating the plasma stored energy for the DIII-D tokamak. The main objective is to improve the shot-to-shot reproducibility and facilitate the accessibility of operating conditions that have steady-state potential, i.e. plasmas with large non-inductive current drive fractions. At DIII-D, non-inductive current sources including electron cyclotron current drive (ECCD) and neutral beam injection (NBI) allow the possibility of shaping the plasma current density distribution, and therefore enabling control of the q profile. A feedback controller is designed in a model predictive control framework to regulate the q profile while simultaneously regulating the plasma stored energy. The effectiveness of the control approach is demonstrated with experiments.

[1]  D. A. Humphreys,et al.  Towards model-based current profile control at DIII-D , 2007 .

[2]  Jay H. Lee,et al.  Model predictive control: Review of the three decades of development , 2011 .

[3]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[4]  O. Sauter,et al.  Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime , 1999 .

[5]  C. M. Greenfield,et al.  Optimizing the Beta Limit in DIII-D Advanced Tokamak Discharges , 2003 .

[6]  M. Steinbuch,et al.  Control of the tokamak safety factor profile with time-varying constraints using MPC , 2015 .

[7]  F. Felici,et al.  Real-time physics-model-based simulation of the current density profile in tokamak plasmas , 2011 .

[8]  Eugenio Schuster,et al.  Physics-based control-oriented modeling of the safety factor profile dynamics in high performance tokamak plasmas , 2013, 52nd IEEE Conference on Decision and Control.

[9]  F. Hinton,et al.  Theory of plasma transport in toroidal confinement systems , 1976 .

[10]  E. Joffrin,et al.  Chapter 6: Steady state operation , 2007 .

[11]  E. Joffrin,et al.  A control-oriented model of the current profile in tokamak plasma , 2007 .

[12]  Eugenio Schuster,et al.  Current profile control for the development of consistent discharges in DIII-D , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[13]  C. M. Greenfield,et al.  Optimization of DIII-D advanced tokamak discharges with respect to the β limita) , 2005 .

[14]  Aitor J. Garrido,et al.  Low Effort Nuclear Fusion Plasma Control Using Model Predictive Control Laws , 2015 .

[15]  Eugenio Schuster,et al.  Physics-model-based nonlinear actuator trajectory optimization and safety factor profile feedback control for advanced scenario development in DIII-D , 2015 .

[16]  Scott Kuindersma,et al.  An efficiently solvable quadratic program for stabilizing dynamic locomotion , 2013, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[17]  L. C. Woods.  Physics of plasmas , 2003 .

[18]  Sylvain Brémond,et al.  Validation of plasma current profile model predictive control in tokamaks via simulations , 2011 .

[19]  Bondeson,et al.  Stabilization of external modes in tokamaks by resistive walls and plasma rotation. , 1994, Physical review letters.

[20]  Alberto Bemporad,et al.  Predictive Control for Linear and Hybrid Systems , 2017 .

[21]  T.K. Fowler,et al.  Nuclear fusion , 1989, IEEE Potentials.

[22]  D. J. Campbell,et al.  Chapter 1: Overview and summary , 1999 .