Abstract
In the first part of the lectures, an introduction into the theory of magneto-hydrodynamic (MHD) stability of magnetically confined plasmas will be given, and some typical instabilities will be discussed. In the second part, a general representation of MHD in terms of stream functions and potentials will be presented. The vector equations of MHD are transformed into a system of scalar equations, which are extremely useful as they allow the physical interpretation of various terms in relation with particular instabilities. Approximations leading to simplified (“reduced”) MHD equations are discussed. In the last part of the lectures, an example of bifurcation of solutions of nonlinear reduced equations is presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Braginskii, S.I. in: Reviews of Plasma Physics, Vol.I, p.205 (Consultants bureau New York 1965 )
Grimm, R.C. and J.L. Johnson, Plasma Physics 14 (1972), 617.
Bateman, G. “MHD Instabilities”, (MIT Press, Cambridge, Mass. 1978 )
Johnson, J.L., C.R. Oberman, R.M. Kulsrud, E.A. Frieman, UN Geneva Conference 31 (1958), 198.
Bateman, G., W. Schneider, W. Grossman, Nucl.Fusion 14 (1974) 669.
Schmidt, G., “Physics of High Temperature plasmas”, Academ Press, New York 1979.
Maschke, E.K. and J. Morros Tosas, Plasma Physics and Contr. Fusion 31 (1989), 563.
Morros Tosas, J. and E.K. Maschke, Plasma Physics and Contr. Fusion 31 (1989), 549.
Maschke, E.K., J. Morros Tosas and G. Urquijo, Report EUR-CEA-FC-1495 (1993)
Bussac, M.N., D. Edery, R. Pellat and J.L. Soulé Plasma Physics and Contr. Fusion 31 (1975), 1638.
Maschke, E.K. and B. Saramito, Physica Scripta Vol. T2 /2 (1982) 410.
Gomberoff, L. and M. Hernandez, Phys.Fluids 27 (1984), 392.
Lao, L.L., S.P. Hirshman and R.M. Wieland Phys. Fluids 24 (1981), 1432.
Saramito, B. and E.K. Maschke, in: Magnetic reconnection and Turbulence (Ed. M.A. Dubois, D. Gresillon, M.N. Bussac ), Editions de Physique, Les Ulis (France), 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Wien
About this chapter
Cite this chapter
Maschke, E.K. (1994). Methods in Magneto-Hydrodynamic Stability Theory. In: Cap, F. (eds) Waves and Instabilities in Plasmas. CISM International Centre for Mechanical Sciences, vol 349. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2700-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2700-1_3
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82636-2
Online ISBN: 978-3-7091-2700-1
eBook Packages: Springer Book Archive