CCS Method to Reproduce Tokamak Plasma Shape ( C auchy C ondition S urface)

1. CCS Method to Reproduce Tokamak Plasma Shape(Cauchy Condition Surface) F. Wang*1, K. Nakamura2, O. Mitarai3, K. Kurihara4, Y. Kawamata4, M. Sueoka4, K. N. Sato2, H. Zushi2, K. Hanada2, M. Sakamoto2, H. Idei2, M. Hasegawa2, S. Kawasaki2, H. Nakashima2, A. Higashijima2 Prepared and Presented by Wang Feng in ITC-16 Modified and Presented by Kazuo Nakamura in ASIPP • IGSES, Kyushu University • (Interdisciplinary Graduate School of Engineering Sciences) • 2) RIAM, Kyushu University • 3) Kyushu Tokai University • 4) Japan Atomic Energy Agency

2. Outline • Conventional Tokamak and Spherical Tokamak • CPD • Cauchy Condition Surface Method • Main Principle of CCS Method • Equations of Numerical Calculation • Motivation • Configuration of CPD • Magnetic Sensor Dependence • Cauchy-Condition Dependence • Plasma Current Profile Dependence • Summary and Future Work • Application of CCS Method to EAST

3. a R Conventional Tokamak a R Spherical Tokamak 1. Conventional Tokamak and Spherical Tokamak Spherical Tokamak (ST) Small Aspect Ratio (A=R/a) < 2 High natural elongation High natural triangularity Equilibrium and stability properties are much different with the conventional tokamaks

4. CPD (Compact PWI Experimental Device) RIAM, Kyushu University • Plasma major radius: 0.3 m • Plasma minor radius: 0.2 m • Toroidal field: 0.3 T @ R = 0.25 m • Operation period: 1.00 sec for Bt = 0.3 T • Operation cycle: 5 min • Plasma current: 150 kA Main parameters of CPD:

5. 2. Cauchy Condition Surface Method • Shape reproduction is important for plasma control in a tokamak, especially for non-circular and triangular plasmas. • Cauchy-Condition Surface (CCS) method [1] is a numerical approach to reproduce plasma shape. Its main features are as follows: 1) The CCS method can reproduce plasma shape with high precision corresponding to the number and types of available sensors. 2) The CCS method can identify plasma current with an error of less than 2%. 3) The CCS position and shape are insensitive to reproduction accuracy. This is advantageous in the application to the real-time plasma control. [1] K. Kurihara, Nuclear Fusion, Vol.33, No.3 (1993) 399-412. CCS method was proposed by Dr. Kurihara and tested on JT-60U.

6. CCS Actual Plasma Surface Main Principle of CCS Method B = grad F Cauchy-Condition Surface Dirichlet (Φ) ? Neumann (B) ? Vacuum field Magnetic Measurements Cauchy-Condition Surface Dirichlet (Φ) Neumann (B) Flux Distribution Outside CCS Actual Plasma Shape

7. Equations of Numerical Calculation (1) Dirichlet Neumann Vacuum field Flux Loops CCS && PF Coils (2) Magnetic Probes CCS && PF Coils (3) CCS CCS && PF Coils (4)

8. 3. Motivation • Motivation • As for the spherical tokamak, the aspect ratio is much smaller than normal tokamaks, so the shape reproduction precision of CCS method under a spherical tokamak device is checked. • In order to apply it in real-time plasma shape control, magnetic sensor dependence and current profile dependence is also studied. • Main Steps of Comparison 1. Various ideal flux surfaces corresponding to different plasma profiles are made by equilibrium code. 2. These plasma shapes are reproduced by using CCS method. 3. The original and reproduced shapes are compared.

9. 4. Configuration of CPD R: +0.1 ~ +0.8 Z: -0.7 ~ +0.7 PF Coils: 7 Flux Loops: 45 Mesh Size (RxZ): 140x280 Mesh Precision: 0.005m Ellipse for CCS Small radius: 0.03m Large radius: 0.05m

10. 5. Magnetic Sensor Dependence Reproduction with 45 flux loops Reproduction with 26 magnetic probes The CCS method can reproduce plasma shape of spherical tokamak solely with the measurements of flux loops.

11. 6. Cauchy-Condition Dependence CCS (M=6) CCS (M=8) CCS (M=10) In case of much elongated and triangular plasmas in spherical tokamak CPD, good precision can be achieved by changing the degrees of parametric freedom of Cauchy-Condition Surface.

12. 7. Plasma Current Profile Dependence (1) li=1.0 li=0.8 li=0.9 In case of circular plasma shape, normally the shape difference of circular plasma shape is less than 1% compared with major radius R.

13. 7. Plasma Current Profile Dependence (2) Shape Difference X Point difference Typical plasma shape reproduction (Ip = 100kA, IPF1=10kA, βp=0.5, li=0.7, κ=2.1)

14. Difference of X Point and Plasma Shape Difference of X Point Difference of Plasma Shape The differences between CCS method and ECODE are compared. In case of large elongated and triangular double-null plasma of CPD, normally the X point difference is less than 2%, and shape difference is less than 3% compared with major radius R.

15. 8. Summary and Future Work • Summary 1. The CCS method can reproduce plasma shape of spherical tokamak in good precision solely with the measurements of flux loops or magnetic sensors. 2. In case of much elongated and triangular plasmas in spherical tokamak, good precision can be achieved by increase in degrees of parametric freedom representing the Cauchy condition. 3. The CCS method can reproduce spherical tokamak plasma shape with good precision in different plasma current profiles (li=0.5 ~ 1.0). In case of large elongated and triangular double-null plasma, normally the X point difference is less than 2%, and shape difference is less than 3%. • Future Work In the real plasma discharge experiment, eddy current effect is important, especially at ramp-up stage of plasma current. The effect of eddy current will be taken into account in Cauchy Condition Surface method in future.

16. Application of CCS Method to EAST • Reproduction of plasma shape • Consideration of eddy current in startup • Real-time reproduction and display