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Mitigation of Kink Modes in Pedestal

Mitigation of Kink Modes in Pedestal. Z. T. Wang 1,2 , Z. X. He 1 , J. Q. Dong 1 , X. L. Xu 2 ， M. L. Mu 2 , T. T. Sun 2 , J. Huang 2 , S. Y. Chen 2 , C. J. Tang 2 1. Southwestern Institute of Physics, Chengdu 610041, China

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Mitigation of Kink Modes in Pedestal

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  1. Mitigation of Kink Modes in Pedestal Z. T. Wang 1,2 , Z. X. He 1, J. Q. Dong 1 , X. L. Xu 2，M. L. Mu2, T. T. Sun2, J. Huang2, S. Y. Chen2, C. J. Tang2 1. Southwestern Institute of Physics, Chengdu 610041, China 2. College of Physics Science and Technology, Sichuan University, Chengdu 610065, China The Second A3 Foresight Workshop on Spherical Torus Jan. 6-8, 2014, Tsinghua University, Beijing, China

  2. Kink modes are investigated in pedestal for shaped tokamaks. Aanalytic combining criterion is presented. • For large poloidal mode number the modes are highly localized in both poloidal and radial directions. The modes increase rapidly when they approach to the resonant surface. They are typical of ELMs.

  3. There seems to be a second stable region when current gradient is large. It is pointed by Wesson [10] that “There is no way of avoiding this destabilizing current density gradient…. Fortunately the current density gradient also provides a strong stabilizing effect, namely shear of magnetic field”. • Several mitigation methods for controlling ELMS are proposed. The principle of the mitigation could apply for spherical torus.

  4. In the recent results given by Webster and Gimblett，the peeling mode could occur, but growth rate can be arbitrarily small near the separatrix. • Numerical calculations have suggested that a plasma equilibrium with an X-point-as it found with all ITER-like tokamaks is stable to the peeling mode [1-3]. • We extend Zakharov’ work [5] to the shaped tokamaks.

  5. Based on energy principle, The potential energy is written in a form: • (1) • In the Hamada coordinates , the potential energy is turned out to be where

  6. In the neighborhood of the magnetic axis, the square root of volume is taken as small parameter [8]. To the lowest order we have, (5) • We consider the step current proposed by Shafranov [13],

  7. (40) • We get a combining criterion [9], • When Eq.(40) is the sufficient criterion of Lortz [8-9] and Eq.(40) is the necessary criterion of Mercier [7], Eq.(40) is the result of present Paper.

  8. We define triangularity, • (12) • The potential energy • (13) • We can get an analytical criterion, • Where ι is rotation transform, the reciprocal of the safety factor q. (14)

  9. The growth rates of the unstable modes can be given by • (15)

  10. Numerical solution • For large tokamaks, such as, ITER, JET, DⅢ-D , JT-60, HL-2M there are large elongation and triangularity. We choose the parameters, • We get the growth rates versus in Fig. 1. Fig.2 gives the growth rate related to the current gradient. Both pressure gradient and current gradient are the drives of the kink modes. The elongation is essentially destabilizing. The growth rates versus elongation is given in Fig. 3. The triangularity has stabilizing effects in Fig. 4. The mode structure is presented in Fig.5. • There are two stable regions in Fig. 6.

  11. Fig. 1. The growth rates versus Fig. 2 . The growth rate versus

  12. Fig. 3. The growth rates versus elongation Fig. 4. The growth rates versus triangularity.

  13. Fig.5. The mode structure near the resonant surface where Fig. 6. There are two stable regions

  14. Summary • Using the energy principle we derive a combined criterion of kink • Numerical results show that the growth rates vary with elongation which essentially has destabilizing effects. The triangularity has stabilizing effects. • Changing elongation and triangularity by shaping coils may mitigate kink modes which may related to the ELMs. Changing the pedestal current by current drives can also mitigate the modes. • We can trigger more small elms avoiding a large type-1 elm, reduce the particle and heat roads to the plasma facing materials.

  15. Thanks for your attention !

  16. References • [1] J. W. Connor, R. J. Hastie, H. R. Wilson, and R. L. Miller, Phys. Plasmas , 2687(1998). • [2] A. J. Webster and C. G. Gimblett, Phys. Plasmas 16, 082502(2009). • [3] S. Yu. Medvedev, A. Degeling, O. Sauter and L. Villard, 2003, Proc. 30th EPS Conf. on Controlled Fusion and Plasma Physics (St.Petersburg,7–11 July,2003) vol. 27A (ECA) P-3.129. • [4] G. T. A. Huysmans, Plasma Phys. Control. Fusion 47, 2107(2005). • [5] L. E. Zakharov, Nucl. Fusion 18, 335(1978). • [6] I. A. Bernsein et al, Proc. R. Soc. London Ser. A244, 17(1958). • [7] G. Mercier, Nucl. Fusion Suppl. Part 2, 801(1962). • [8] ] D. Lortz, Nucl. Fusion 13, 817(1973). • [9] D. Lortz, Nucl. Fusion 13, 821(1973). • [10] J. A. Wesson, Nucl. Fusion 18, 87(1978). • [11] S. Hamada, Nucl. Fusion, 2, 23 (1962). • [12] D. Lortz, Nucl. Fusion 15, 49(1975). • [13] V. D. Shafranov, Zh. Tekh. Fiz. 40, 241(1970).

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