Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-28T00:36:24.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear translational symmetric equilibria relevant to the L–H transition

Published online by Cambridge University Press:  12 November 2012

Ap. KUIROUKIDIS  and
G. N. THROUMOULOPOULOS
Ap. KUIROUKIDIS
Affiliation:
Technological Education Institute of Serres, 62124 Serres, Greece
G. N. THROUMOULOPOULOS
Affiliation:
Department of Physics, University of Ioannina, Association Euratom-Hellenic Republic, 45110 Ioannina, Greece (gthroum@uoi.gr)
Get access Rights & Permissions [Opens in a new window]

Abstract

Nonlinear z-independent solutions to a generalized Grad–Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non-parallel to the magnetic field are constructed quasi-analytically. Through an ansatz, the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in Cartesian coordinates (x,y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L–H transition phenomenology. For flows parallel to the magnetic field, one equilibrium corresponding to the H state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity plays a stabilizing role.

Type
Papers
Information
Journal of Plasma Physics , Volume 79 , Issue 3 , June 2013 , pp. 257 - 265
Copyright
Copyright © Cambridge University Press 2012 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Apostolaki, D., Throumoulopoulos, G. N. and Tasso, H. 2008 In: 35th EPS Conference on Plasma Phys. Hersonissos, 9–13 June, ECA Vol. 32 (ed. Lalousis, P. and Moustaizis, S.). European Physical Society, p. 2.057.Google Scholar
Atanasiu, C. V., Gunter, S., Lackner, K. and Miron, I. G. 2004 Phys. Plasmas 11, 3510.CrossRefGoogle Scholar
Berk, H. L., Hammer, J. H. and Weitzner, H. 1981 Phys. Fluids 24, 1758.CrossRefGoogle Scholar
Betti, R. and Freidberg, J. P. 2000 Phys. Plasmas 7, 2439.CrossRefGoogle Scholar
Cerfon, A. J. and Freidberg, J. P. 2010 Phys. Plasmas 17, 032502.CrossRefGoogle Scholar
Clemente, R. A. and Farengo, R. 1984 Phys. Fluids 27, 776.CrossRefGoogle Scholar
de Vries, P. C., Joffrin, E., Brix, M., Challis, C. D., Crombé, K., Esposito, B., Hawkes, N. C., Giroud, C., Hobirk, J., Lönnroth, J.et al., 2009 Nucl. Fusion 49, 075007.CrossRefGoogle Scholar
Friedlander, S. and Vishik, M. M. 1995 Chaos 5, 416.CrossRefGoogle Scholar
Garcia, J. and Giruzzi, G. 2010 Phys. Rev. Lett. 104, 205003.CrossRefGoogle Scholar
Goedbloed, J. P. and Lifschitz, A. 1997 Phys. Plasmas 4, 3544.CrossRefGoogle Scholar
Grad, H. and Rubin, H. 1958 In: Proceedings of the Second United Nations Conference on the Peaceful Uses of Atomic Energy, Vol. 21. Geneva: United Nations, p. 190.Google Scholar
Greene, J. M. 1988 Plasma Phys. Control. Fusion 30, 327.CrossRefGoogle Scholar
Herrnegger, F. 1972 In: Proceedings of the Fifth European Conference on Controlled Fusion and Plasma Physics, Vol. I (ed Petit-Lancy). European Physical Society, p. 26.Google Scholar
Ilgisonis, V. I. and Pozdnyakov, Yu. I. 2004 Plasma Phys. Rep. 30, 988.CrossRefGoogle Scholar
Khater, A. H. and Moawad, S. M. 2009 Phys. Plasmas 16, 122506.CrossRefGoogle Scholar
Krasheninnikov, S. I., Soboleva, T. K. and Catto, P. J. 2002 Phys. Lett. A 298, 171.CrossRefGoogle Scholar
Kuiroukidis, Ap 2010 Plasma Phys. Control. Fusion 52, 015002.CrossRefGoogle Scholar
Kuiroukidis, Ap and Throumoulopoulos, G. N. 2011 Plasma Phys. Control. Fusion 53, 125005.CrossRefGoogle Scholar
Kuiroukidis, Ap and Throumoulopoulos, G. N. 2012 Phys. Plasmas 19, 022508.CrossRefGoogle Scholar
Malfliet, W. 2004 J. Comput. Appl. Math. 164–165, 529.CrossRefGoogle Scholar
Maschke, E. K. 1972 Plasma Phys. 15, 535.CrossRefGoogle Scholar
Mashke, E. K. and Perrin, H. 1984 Phys. Lett. A 102, 106.CrossRefGoogle Scholar
Mc Carthy, P. J. 1999 Phys. Plasmas 6, 3554.CrossRefGoogle Scholar
Mukhopadhyay, S. 2000 Bull. Am. Phys. Soc. 45, 364.Google Scholar
Poulipoulis, G., Throumoulopoulos, G. N. and Tasso, H. 2005 Phys. Plasmas 12, 042112.CrossRefGoogle Scholar
Shafer, M. W., McKee, G. R., Austin, M. E.Burrell, K. H., Fonck, R. J. and Schlossberg, D. J. 2009 Phys. Rev. Lett. 103, 075004.CrossRefGoogle Scholar
Shafranov, V. D. 1958 Sov. Phys. JETP 6, 545; (1957) Zh. Eksp. Teor. Fiz. 33, 710.Google Scholar
Shi, B. 2011 Nucl. Fusion 51, 023004.CrossRefGoogle Scholar
Simintzis, Ch., Throumoulopoulos, G. N., Pantis, G. and Tasso, H. 2001 Phys. Plasmas 8, 2641.CrossRefGoogle Scholar
Solano, E. R. 2004 Plasma Phys. Control. Fusion 46, L7.CrossRefGoogle Scholar
Solovév, L. S. 1968 Sov. Phys. JETP 26, 400; 1976 Zh. Eksp. Teor. Fiz. 53, 626.Google Scholar
Srinivasan, R., Lao, L. L. and Chu, M. S. 2010 Plasma Phys. Control. Fusion 52, 035007.CrossRefGoogle Scholar
Tasso, H. and Throumoulopoulos, G. N. 1998 Phys. Plasmas 5, 2378.CrossRefGoogle Scholar
Tasso, H. and Throumoulopoulos, G. N. 2012 J. Plasma Physics 78, 1.CrossRefGoogle Scholar
Terry, P. W. 2000 Rev. Mod. Phys. 72, 109.CrossRefGoogle Scholar
Throumoulopoulos, G. N. and Pantis, G. 1996 Plasma Phys. Control. Fusion 38, 1817.CrossRefGoogle Scholar
Throumoulopoulos, G. N. and Tasso, H. 1997 Phys. Plasmas 4, 1492.CrossRefGoogle Scholar
Throumoulopoulos, G. N. and Tasso, H. 2007 Phys. Plasmas 14, 122104.CrossRefGoogle Scholar
Throumoulopoulos, G. N. and Tasso, H. 2010 Phys. Plasmas 17, 032508.CrossRefGoogle Scholar
Throumoulopoulos, G. N. and Tasso, H. 2012 Phys. Plasmas 19, 014504.CrossRefGoogle Scholar
Throumoulopoulos, G. N., Weitzner, H. and Tasso, H. 2006 Phys. Plasmas 13, 122501.CrossRefGoogle Scholar
Throumoulopoulos, G. N., Tasso, H. and Poulipoulis, G. 2008 J. Plasma Physics 74, 327.CrossRefGoogle Scholar
Throumoulopoulos, G. N., Tasso, H. and Poulipoulis, G. 2009 J. Phys. A: Math. Theor. 42, 335501.CrossRefGoogle Scholar
Tsui, K. H. and Navia, C. E. 2012 Phys. Plasmas 19, 012505.CrossRefGoogle Scholar
Tsui, K. H., Navia, C. E., Serbeto, A. and Shigueoka, H. 2011 Phys. Plasmas 18, 072502.CrossRefGoogle Scholar
Vladimirov, V. A. and Ilin, K. I. 1998 Phys. Plasmas 5, 4199.CrossRefGoogle Scholar
Weening, R. H. 2000 Phys. Plasmas 7, 3654.CrossRefGoogle Scholar
Yavorskij, V. A., Schoepf, K., Andrushchenko, Zh. N., Cho, B. H., Goloborod'ko, V. Ya. and Reznyk, S. N. 2001 Plasma Phys. Control. Fusion 43, 249.CrossRefGoogle Scholar