Chin. Phys. B, 2015, Vol. 24(3): 035202    DOI: 10.1088/1674-1056/24/3/035202
 PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES Prev   Next

# Start-up phase plasma discharge design of a tokamak via control parameterization method

Guo Shan (郭珊)a, Xu Ke (许珂)a, Xu Chao (许超)b, Ren Zhi-Gang (任志刚)b, Xiao Bing-Jia (肖炳甲)c
a Department of Mathematics, Zhejiang University, Hangzhou 310027, China;
b State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou 310027, China;
c Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China
Abstract  The tokamak start-up is a very important phase during the process to obtain a suitable equalizing plasma, and its governing model can be described as a set of nonlinear ordinary differential equations (ODEs). In this paper, we first estimate the parameters in the original model and set up an accurate model to express how the variables change during the start-up phase, especially how the plasma current changes with respect to time and the loop voltage. Then, we apply the control parameterization method to obtain an approximate optimal parameters selection problem for the loop voltage design to achieve a desired plasma current target. Computational optimal control techniques such as the variational method and the costate method are employed to solve the problem, respectively. Finally, numerical simulations are performed and the results obtained via different methods are compared. Our numerical parameterization method and optimization procedure turn out to be effective.
Keywords:  tokamak      start-up      optimal control      variational method
Received:  16 September 2014      Revised:  29 October 2014      Accepted manuscript online:
 PACS: 52.55.Fa (Tokamaks, spherical tokamaks) 02.60.Pn (Numerical optimization)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61104048 and 61473253) and the National High Technology Research and Development Program of China (Grant No. 2012AA041701).
Corresponding Authors:  Xu Chao     E-mail:  cxu@zju.edu.cn