1. CREC in the AC operation theory via simulation and experiment
Shaojie Wang, Jun Yu, and Jiangang Li

2. Contents Introduction Theoretical Model Simulations vs Experiments
Experiment A
Experiment B
Expect New Experiments
Summary

3. Introduction
Grad-Shafranov equation lays the foundation for the research of the tokamak equilibrium theory.
V.D. Shafranov (1957);
R. Lust and A. Schluter (1957);
H. Grad and H. Rubin (1959).

4. N. C. Hawkes et al., Phys. Rev. Lett. 87, 115001 (2001);
Recent experiments indicate that a tokamak may be operated with nearly zero or negative toroidal current density in a finite central region (current hole).
N. C. Hawkes et al., Phys. Rev. Lett. 87, (2001);
T. Fujita et al., Phys. Rev. Lett. 87, (2001).

5. G. T. A. Huysmans et al., Phys. Rev. Lett. 87, 245002 (2001);
To understand the behavior of the CRECs (current reversal equilibrium configurations), a torrent of the theoretical research began.
G. T. A. Huysmans et al., Phys. Rev. Lett. 87, (2001);
M. S. Chu et al., Phys. Plasmas 9, 5036 (2002);
G. W. Hammett et al., Phys. Plasmas 10, 4048 (2003);
A. A. Martynov et al., Phys. Rev. Lett. 91, (2003).

6. AC operation experiments have been performed in a number of tokamak devices in the past decade.
O. Mitarai et al., Nucl. Fusion 27, 604 (1987); O. Mitarai et al., Fusion Technol. 15, 204 (1989);
O. Mitarai et al., Fusion Technol. 20, 285 (1991); B. Tubbing et al., Nucl. Fusion 32, 967 (1992);
O. Mitarai et al.,Nucl. Fusion 32, 1801 (1992); O. Mitarai et al.,PPCF 35, 711 (1993);
X. Yang et al. Chin. Phys.Lett. 12, 362 (1995); O. Mitarai et al., Nucl. Fusion 36, 1335 (1996);
X. Yang et al., Nucl. Fusion 36, 1669 (1996); J. Cabral et al., Nucl. Fusion 37, 1575 (1997);
J. Huang et al., Rev. Sci. Instrum. 68, 2711 (1997); X. Yang et al., Nucl. Fusion 40, 2023 (2000).

7. Introduction
Theoretical Model
Simulations vs Experiments
Experiment A
Experiment B
Expect New Experiments
Summary

8. Theoretical Model
The Grad-Shafranov-Helmholtz equation was proposed to describe the equilibrium configurations including CRECs.
Shaojie Wang, Phys. Rev. Lett. 93, (2004).

9. An exact analytical solution was found in the cylindrical coordinate system with a possible physical interpretation given.
Shaojie Wang and Jun Yu, Phys. Plasmas 12, (2005).

10. Introduction
Theoretical Model
Simulations vs Experiments
Experiment A
Experiment B
Expect New Experiments
Summary

11. Simulations vs Experiments
Using the exact solution of the theoretical model, we can simulate the equilibrium configuration.

12. Introduction
Theoretical Model
Simulations vs Experiments
Experiment A
Experiment B
Expect New Experiments
Summary

13. Experiment A
The radial profiles of toroidal current density and pressure in a small tokamak have been given.
S. Iizuka et al., Phys. Rev. Lett. 53, 918 (1984).

15. Net current is about zero when .
Major radius
Minor radius
Total current peak value
Loop voltage peak value
Magnetic diffusion time
Toroidal magnetic field
Current density peak value
Pressure value (averaged)

16. We can calculate the corresponding parameters in our simulation model.

19. Introduction
Theoretical Model
Simulations vs Experiments
Experiment A
Experiment B
Expect New Experiments
Summary

20. Experiment B
The CRECs with two oppositely flowing plasma current components have been found in the CT-6B tokamak.
Jianguo Huang et al., Nucl. Fusion 40, 2023 (2000)

25. Net current is about zero when .
Major radius
Minor radius
Total current peak value
Negative and positive currents on the low and high field side at the values
Loop voltage peak value
Toroidal magnetic field
Current density peak value
Electron temperature

26. We can calculate the corresponding parameters in our simulation model.

29. The theoretical model agrees well with the experimental results.
values in the CRECs with central current density reversal are higher than that in the CRECs with two oppositely flowing plasma current.

30. Introduction
Theoretical Model
Simulations vs Experiments
Experiment A
Experiment B
Expect New Experiments
Summary

31. Expect New Experiments
Theoretical Model via Computer Simulation had been compared to the Experimental Results.

34. The CRECs with central current density reversal are expected in the further experiments with the higher-frequency alternating current provided.

35. Contents Introduction Theoretical Model Simulations vs Experiments
Experiment A
Experiment B
Expect New Experiments
Summary

36. Summary
Theoretical model agrees well with the known experimental results.
The CRECs with central current density reversal are expected in the further experiments.