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All issues Volume 46 / No 5 (September-October 2012) ESAIM: M2AN, 46 5 (2012) 1081-1106 References
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Issue
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
Page(s) 1081 - 1106
DOI https://doi.org/10.1051/m2an/2011078
Published online 13 February 2012
  1. G. Allaire, Numerical Analysis and Optimization : An Introduction to Mathematical Modelling and Numerical Simulation in Numerical Mathematics and Scientific Computation series. Oxford University Press (2007). [Google Scholar]
  2. D. Biskamp, Nonlinear Magnetohydrodynamics. Cambridge University Press (1992). [Google Scholar]
  3. J. Blum, Numerical simulation and optimal control in plasma physics, with application to Tokamaks. Series in Modern Applied Mathematics. Wiley/Gauthier-Villard (1989). [Google Scholar]
  4. J. Blum, Numerical identification of the plasma current density in a Tokamak fusion reactor : the determination of a non-linear source in an elliptic pde, invited conference, in Proceedings of PICOF02. Carthage, Tunisie (2002). [Google Scholar]
  5. J. Blum, T. Gallouet and J. Simon, Existence and control of plasma equilibirum in a Tokamak. SIAM J. Math. Anal. 17 (1986) 1158–1177. [CrossRef] [MathSciNet] [Google Scholar]
  6. J. Blum, C. Boulbe and B. Faugeras, Real time reconstruction of plasma equilibrium in a Tokamak, International conference on burning plasma diagnostics. Villa Manoastero, Varenna (2007). [Google Scholar]
  7. H. Brezis and H. Berestycki, On a free boundary problem arising in plasma physics. Nonlinear Anal. 4 (1980) 415–436. [CrossRef] [MathSciNet] [Google Scholar]
  8. S. Briguglio, G. Wad, F. Zonca and C. Kar, Hybrid magnetohydrodynamic-gyrokinetic simulation of toroidal Alfven modes. Phys. Plasmas 2 (1995) 3711–3723. [CrossRef] [Google Scholar]
  9. S. Briguglio, F. Zonca and C. Kar, Hybrid magnetohydrodynamic-particle simulation of linear and nonlinear evolution of Alfven modes in tokamaks. Phys. Plasmas 5 (1998) 3287–3301. [CrossRef] [Google Scholar]
  10. L.A. Caffarelli and S. Salsa, A geometric approach to free boundary problems, Graduate Studies in Mathematics. AMS, Providence, RI 68 (2005). [Google Scholar]
  11. F. Chen, Introduction to plasma physics and controlled fusion. Springer, New York (1984). [Google Scholar]
  12. O. Czarny and G. Huysmans, MHD stability in X-point geometry : simulation of ELMs. Nucl. Fusion 47 (2007) 659–666. [CrossRef] [Google Scholar]
  13. O. Czarny and G. Huysmans, Bézier surfaces and finite elements for MHD simulations. J. Comput. Phys. 227 (2008) 7423–7445. [Google Scholar]
  14. E. Deriaz, B. Després, G. Faccanoni, K.P. Gostaf, L.-M. Imbert-Gérard, G. Sadaka and R. Sart, Magnetic equations with FreeFem++, The Grad-Shafranov equation and the Current Hole. ESAIM Proc. 32 (2011) 76–94. [Google Scholar]
  15. J.I. Diaz and J.F. Padial, On a free-boundary problem modeling the action of a limiter on a plasma. Discrete Contin. Dyn. Syst. Suppl. (2007) 313–322. [Google Scholar]
  16. J.I. Diaz and J.-M. Rakotoson, On a two-dimensional stationary free boundary problem arising in the confinement of a plasma in a Stellarator. C. R. Acad. Sci. Paris, Sér. I 317 (1993) 353–359. [Google Scholar]
  17. E. Feireisl, Dynamics of viscous compressible fluids. Oxford University Press (2004). [Google Scholar]
  18. J. Freidberg, Plasma physics and fusion energy. Cambridge (2007). [Google Scholar]
  19. A. Friedman, Variational principles and free-boundary problems. Wiley-interscience publication, Wiley, New York (1982). [Google Scholar]
  20. T. Fujita, Tokamak equilibria with nearly zero central current : the current hole (review article). Nucl. Fusion 50 (2010). [Google Scholar]
  21. T. Fujita, T. Oikawa, T. Suzuki, S. Ide, Y. Sakamoto, Y. Koide, T. Hatae, O. Naito, A. Isayama, N. Hayashi and H. Shirai, Plasma equilibrium and confinement in a Tokamak with nearly zero central current density in JT-60U. Phys. Rev. Lett. 87 (2001) 245001–245005. [CrossRef] [PubMed] [Google Scholar]
  22. J.F. Gerbeau, C. Le Bris and T. Lelièvre, Mathematical methods for the magnetohydrodynamics of liquid metals. Oxford University Press, USA (2006). [Google Scholar]
  23. G. Huysmans, T.C. Hender, N.C. Hawkes and X. Litaudon, MHD stability of advanced Tokamak scenarios with reversed central current : an explanation of the “Current Hole”. Phys. Rev. Lett. 87 (2001) 245002–245006. [CrossRef] [PubMed] [Google Scholar]
  24. G.T.A. Huysmans, S. Pamela, E. van der Plas and P. Ramet, Non-linear MHD simulations of edge localized modes (ELMs). Plasma Phys. Control. Fusion 51 (2009) 124012. [CrossRef] [Google Scholar]
  25. B.B. Kadomtsev and O.P. Pogutse, Non linear helical perturbations of a plasma in a Tokamak. Sov. Phys.-JETP 38 (1974) 283–290. [Google Scholar]
  26. S.-E. Kruger, C.C. Hegna and J.D. Callen, Generalized reduced magnetohydrodynamic equations. Phys. Plasmas 5 (1998) 4169–4183. [CrossRef] [Google Scholar]
  27. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Études Mathématiques. Dunod (1969). [Google Scholar]
  28. P.-L. Lions, Mathematical topics in fluid mechanics. Incompressible models, edited by Oxford Science Publication 1 (1996). [Google Scholar]
  29. P.-L. Lions, Mathematical topics in fluid mechanics. Compressible models, edited by Oxford Science Publication 2 (1998). [Google Scholar]
  30. H. Lütjens and J.-F. Luciani, The XTOR code for nonlinear 3D simulations of MHD instabilities in tokamak plasmas. J. Comput. Phys. 227 (2008) 6944–6966. [CrossRef] [Google Scholar]
  31. H. Lütjens and J.-F. Luciani, XTOR-2F : A fully implicit NewtonKrylov solver applied to nonlinear 3D extended MHD in tokamaks. J. Comput. Phys. 229 (2010) 8130–8143. [CrossRef] [Google Scholar]
  32. K. Miyamoto, Plasma physics and controlled nuclear fusion. Springer (2005). [Google Scholar]
  33. B. Nkonga, Private communication (2010). [Google Scholar]
  34. M.N. Rosenbluth, D.A. Monticello, H.R. Strauss and R.B. White, Dynamics of high β plasmas. Phys. Fluids 19 (1976) 1987. [CrossRef] [Google Scholar]
  35. R. Smaltz, Reduced, three-dimensional, nonlinear equations for high-β plasmas including toroidal effects. Phys. Lett. A 82 (1981) 14–17. [Google Scholar]
  36. H.R. Strauss, Nonlinear three-dimensional magnetohydrodynamics of noncircular Tokamaks. Phys. Fluids 19 (1976) 134–140. [Google Scholar]
  37. H.R. Strauss, Dynamics of high β plasmas. Phys. Fluids 20 (1977) 1354–1360. [CrossRef] [Google Scholar]
  38. R. Temam, Remarks on a free boundary value problem arising in plasma physics. Commun. Partial Differ. Equ. 2 (1977) 563–585. [CrossRef] [Google Scholar]
  39. R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. North-Holland (1979). [Google Scholar]
  40. Z. Yoshida, S.M. Mahajan, S. Ohsaki, M. Iqbal and N. Shatashvili, Beltrami fields in plasmas : High-confinement mode boundary layers and high beta equilibria. Phys. Plasmas 8 (2001) 2125. [CrossRef] [Google Scholar]
  41. Z. Yoshida et al., Potential Control and Flow Generation in a Toroidal Internal-Coil System – a New Approach to High-beta Equilibrium, in 20th IAEA Fusion Energy Conference. Online at http://www-naweb.iaea.org/napc/physics/fec/fec2004/papers/icp6-16.pdf (2004). [Google Scholar]

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