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Electromagnetic thin-wall model for simulations of plasma wall-touching kink and vertical modes

Published online by Cambridge University Press:  21 December 2015

Leonid E. Zakharov*
Affiliation:
LiWFusion, P.O. Box 2391, Princeton, NJ 08543, USA
Calin V. Atanasiu
Affiliation:
National Institute for Laser, Plasma and Radiation Physics, Atomistilor 409, P.O. Box MG-36, 077125 Magurele, Bucharest, Romania
Karl Lackner
Affiliation:
Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
Matthias Hoelzl
Affiliation:
Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
Erika Strumberger
Affiliation:
Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
*
Email address for correspondence: lzakharov@comcast.net

Abstract

The understanding of plasma disruptions in tokamaks and predictions of their effects require realistic simulations of electric current excitation in three-dimensional vessel structures by the plasma touching the walls. As discovered at JET in 1996 (Litunovski JET Internal Report contract no. JQ5/11961, 1995; Noll et al., Proceedings of the 19th Symposium on Fusion Technology, Lisbon (ed. C. Varandas & F. Serra), vol. 1, 1996, p. 751. Elsevier) the wall-touching kink modes are frequently excited during vertical displacement events and cause large sideways forces on the vacuum vessel which are difficult to withstand in large tokamaks. In disruptions, the sharing of electric current between the plasma and the wall plays an important role in plasma dynamics and determines the amplitude and localization of the sideways force (Riccardo et al., Nucl. Fusion, vol. 40, 2000, p. 1805; Riccardo & Walker, Plasma Phys. Control. Fusion, vol. 42, 2000, p. 29; Zakharov, Phys. Plasmas, vol. 15, 2008, 062507; Riccardo et al., Nucl. Fusion, vol. 49, 2009, 055012; Bachmann et al., Fusion Engng Des., vol. 86, 2011, pp. 1915–1919). This paper describes a flat triangle representation of the electric circuits of a thin conducting wall of arbitrary three-dimensional geometry. Implemented into the shell simulation code (SHL) and the source sink current code (SSC), this model is suitable for modelling the electric currents excited in the wall inductively and through current sharing with the plasma.

Type
Research Article
Copyright
© Cambridge University Press 2015 

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References

Atanasiu, C. V., Moraru, A. & Zakharov, L. E. 2009 Influence of a nonuniform resistive wall on the RWM stability in a tokamak. In American Physical Society Plasma 51st Annual Meeting, Atlanta, USA, 2–6 November UP8:00088 2009.Google Scholar
Atanasiu, C. V. & Zakharov, L. E. 2013 Response of a partial wall to an external perturbation of rotating plasma. Phys. Plasmas 20, 092506.CrossRefGoogle Scholar
Bachmann, C., Sugihara, M., Rocella, R., Sannazzaro, G., Gribov, Yu., Riccardo, V., Hender, T. C., Gerasimov, S. N., Putasso, G., Belov, A. et al. 2011 Specification of asymmetric VDE loads of the ITER tokamak. Fusion Engng Des. 86, 19151919.Google Scholar
Berzak, H. L., Menard, J., Majeski, R., Lundberg, D. P., Granstedt, E., Jacobson, C., Kaita, R., Kozub, T. & Zakharov, L. E. 2012 Plasma equilibrium reconstructions in the lithium tokamak experiment. Nucl. Fusion 52, 063025.Google Scholar
Chance, M. S. 1997 Vacuum calculations in azimuthally symmetric geometry. Phys. Plasmas 4, 2161.Google Scholar
Chance, M. S., Chu, M. S., Okabayashi, M. & Turnbull, A. D. 2002 Theoretical modelling of the feedback stabilization of external MHD modes in toroidal geometry. Nucl. Fusion 42, 295.Google Scholar
Chu, M. S., Chance, M. S., Glasser, A. H. & Okabayashi, M. 2003 Normal mode approach to modelling of feedback stabilization of the resistive wall mode. Nucl. Fusion 43, 441.Google Scholar
Gerasimov, S. N., Abreu, P., Baruzzo, M., Drozdov, V., Dvornova, A., Havlicek, J., Hender, T. C., Hronova, O., Kruezi, U. et al. & JET EFDA Contributors 2015 JET and COMPASS asymmetrical disruptions. Nucl. Fusion 55, 113006.CrossRefGoogle Scholar
Gerasimov, S. N., Hender, T. C., Morris, J., Riccardo, V., Zakharov, L. E.& JET EFDA Contributors 2014 Plasma current asymmetries during disruptions in JET. Nucl. Fusion 54, 073009.Google Scholar
Hoelzl, M., Huysmans, G. T. A., Merkel, P., Atanasiu, C. V., Lackner, K., Nardon, E., Aleuynikova, K., Liu, F., Strumberger, E., McAdams, R. et al. 2014 Non-linear simulations of MHD instabilities in Tokamaks including Eddy current effects and perspectives for the extension to Halo currents. J. Phys.: Conf. Ser. 561, 012011.Google Scholar
Hoelzl, M., Merkel, P., Huysmans, G. T. A., Nardon, E., McAdams, R. & Chapman, I. 2012 Coupling the JOREK and STARWALL codes for non-linear resistive-wall simulations. J. Phys.: Conf. Ser. 401, 012010.Google Scholar
Huysmans, G. T. A. & Czarny, O. 2007 MHD stability in X-point geometry: simulation of ELMs. Nucl. Fusion 47, 659.CrossRefGoogle Scholar
In, Y. et al. 2009 Model-based dynamic resistive wall mode identification and feedback control in the DIII-D tokamak. Phys. Plasmas 13, 062512.Google Scholar
Litunovski, R.1995, The observation of phenomena during plasma disruption and the interpretation of the phenomena from the point of view of the toroidal asymmetry of forces, JET Internal Report contract no. JQ5/11961.Google Scholar
Merkel, P., Nührenberg, C. & Strumberger, E. 2004 Resistive wall modes of 3D equilibria with multiply-connected walls. In 31st EPS Conference on Plasma Physics (Europhysics Conference Abstracts Vol 28G), P1.208.Google Scholar
Merkel, P. & Sempf, M. 2006 Feedback stabilization of resistive wall modes in the presence of multiply connected wall structures. In (TH/P3-8) Proceedings of 21st IAEA Fusion Energy Conference, Chengdu, China, 2006.Google Scholar
Merkel, P. & Strumberger, E.2015, Linear MHD stability studies with the STARWALL code, arXiv:1508.04911.Google Scholar
Noll, P., Andrew, P., Buzio, M., Litunovski, R., Raimondi, T., Riccardo, V. & Verrecchia, M. 1996 Present understanding of electromagnetic behaviour during disruptions at JET. In Proceedings of the 19th Symposium on Fusion Technology, Lisbon (ed. Varandas, C. & Serra, F.), vol. 1, p. 751. Elsevier.Google Scholar
Pustovitov, V. D. 2008 General formulation of the resistive wall mode coupling equations. Phys. Plasmas 15, 072501.CrossRefGoogle Scholar
Riccardo, V., Arnoux, G., Beaumont, P., Hacquin, S., Horbrk, J., Howell, D., Huber, A., Joffrin, E., Koslowski, R., Lam, N. et al. 2009 Progress in understanding halo current at JET. Nucl. Fusion 49, 055012.Google Scholar
Riccardo, V., Noll, P. & Walker, S. P. 2000 Forces between plasma, vessel and TF coils during AVDEs at JET. Nucl. Fusion 40, 1805.Google Scholar
Riccardo, V. & Walker, S. P. 2000 Parametric analysis of asymmetric vertical displacement events at JET. Plasma Phys. Control. Fusion 42, 29.Google Scholar
Sovinec, C. R., Glasser, A. H., Gianakon, T. A., Barnes, D. G., Nebel, R. A., Kruger, S. E., Schnack, D. D, Plimpton, S. J., Tarditi, A. et al. & the NIMROD Team 2004 Nonlinear magnetohydrodynamics simulation using high-order finite elements. J. Comput. Phys. 195, 355.CrossRefGoogle Scholar
Strumberger, E., Merkel, P., Sempf, M. & Günter, S. 2008 On fully three-dimensional resistive wall mode and feedback stabilization computations. Phys. Plasmas 15, 056110.Google Scholar
Tseitlin, L. A. 1970 Eddy currents in thin plates and shells. Sov. Phys. Tech. Phys. 10, 1733.Google Scholar
Xiong, H., Xu, G., Wang, H., Zakharov, L. E. & Li, X. 2015 First measurements of Hiro currents in vertical displacement event in tokamaks. Phys. Plasmas 22, 060702.Google Scholar
Zakharov, L. E. 2008 The theory of the kink mode during the vertical plasma disruption events in tokamaks. Phys. Plasmas 15, 062507.Google Scholar
Zakharov, L. E., Galkin, S. A., Gerasimov, S. N.& JET-EFDA Contributors 2012 Understanding disruptions in tokamaks. Phys. Plasmas 19, 055703.Google Scholar
Zakharov, L. E. & Li, X. 2015 Tokamak magneto-hydrodynamics and reference magnetic coordinates for simulations of plasma disruptions. Phys. Plasmas 22, 062511.Google Scholar