Real Time Equilibrium Reconstruction Algorithm in HT-7U Tokamak

1. ASIPP HT-7 Real Time Equilibrium Reconstruction Algorithm in HT-7U Tokamak • H.Z. Wang, Q.C. Huang, J.R. Luo, W.P. Zhao, J.Z. Li, F. Wang • (E-mail: hzwang@ipp.ac.cn)

2. ASIPP HT-7 Outline 1. The different plasma shape control methods 2. Real time equilibrium algorithm research in HT-7U 3. Summary

3. ASIPP HT-7 plasma shape control methods 1.Filament/element method: ISX-B 、 JT-60 2.local and global expansion methods: JET、FTU、 JT-60U 3.statistical methods: KSTAR 4.RTEFIT method: D-IIID、JET、TEXT-U、 JT-60U

4. ASIPP HT-7 Plasma is represented by a set of discrete filaments at pre- specified locations so the plasma effect express as: The method developed separates the problem intotwo parts, the magnetostatics part and the force balance part. filament/element method

5. ASIPP HT-7 The basis of the method is five 6th order expansions of the poloidal flux, one each at the top, bottom, inboard, upper belt and lower belt limiters of the vessel. The ex- pansions are given by . The coefficients aiiare determined by imposing the va- cuum equationand by fitting ; to the local flux and magnetic field measurements. In addition, the five expansions are constrained to match at chosen tie points around the vessel. local and global expansion methods

6. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U For the HT7U project, aiming at both advanced tokamak regime and long pulse operations, it is essential to control not only the position and shape but also the equilibrium profiles of plasmas. For the advanced plasma control, the accurate and fast identification of plasma equilibrium as well as plasma position has to be preceded. The purpose of the present work is to extract plasma equilibrium para- meters, especially position and shape parameters, in a fast time-scale for real-time plasma control.

7. ASIPP HT-7 Here is the polodial current enclosed between a flux surface and the central symmetric axis, is the plasma Pressure. Real Time Equilibrium Algorithm Research in HT-7U

8. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U The equilibrium constraints relates the two–dimensional toroidal current density function to the two one– dimensional free functions P and F and their parameters can be determined from all the measures data M by minimizing: Here and are the computed values and the uncertainty of the corresponding measured quantities, respectively,and nm is thenumber of measured data.

9. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U This minimization problem is non-linear and can be linearized problems interleaved with the equilibrium calculations using the Pichard iteration scheme, also the two free functions P and F are parameterized as and using the basis functions . where is the normalized poloidal flux and , are the poloidal flux at the plasma boundary and axis.

10. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U platform：CPU PIII 866 memory 256M OS：Redhat Linux 7.3 program：Fortan 77 (1) complete equilibrium construct ：about 1022ms (2) equilibrium construct known PF ：895ms (3) equilibrium construct known PF and no probe：498ms (4) equilibrium construct known PF and no probe： 310ms (33* 33 grids)

11. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U It is too long time to be used to control! Reason: The most consume time is how to get the normalized poloidal Flux (because we must solve Grad-Shafranov Equation 120ms/one) Another most time is iteration calculation

12. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U A premise of the real time algorithm is that if the differences between the starting point equilibrium and a good reconstruction are small enough then after only one iteration the solution will be close enough to the well- converged reconstruction to be adequate for discharge control. An additional premise is that one iteration will be sufficient to allow the real time algorithm to follow changes in the equilibrium as the discharge evolves.

13. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U Had the normalized poloidal flux, parameters and of toroidal current density can be determined from all the measures data by minimizing method(this time is about 1ms so it can be used to control in real time) Two premises guarantee that in real time control, the normalized poloidal flux is known as starting point Equilibrium.

14. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U The basic idea of HT-7U is to control the polodial flux and in some cases the polodial magnetic field, at a number of points at the plasma boundary. The coordinates of these points are preprogrammed, and they define the desired evolution of the plasmas boundary. The coordinates of these points are preprogrammed, and they define the desired evolution of the plasmas boundary . is the magnetic flux produced by the plasma. is the magnetic flux produced by all the currents except plasma (including the induce current in the vacuum chamber)

15. ASIPP HT-7 Real Time Equilibrium Algorithm Research in HT-7U

16. HT-7 ASIPP

17. ASIPP HT-7 Summary • It is practical to use such algorithm nearly identical to a standard equilibrium reconstruction technique in real time for identification of HT-7U tokamak discharge parameters. • Equilibrium parameters can be evaluated directly from a solution to the Grad-Shafranov tokamak equilibrium relation. Even parameters such as the safety factor profile can be evaluated in real time.

18. HT-7 ASIPP THANKS