Methods in Magneto-Hydrodynamic Stability Theory
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.
KeywordsRayleigh Number Scalar Representation Kink Mode Kink Instability Toroidal Plasma
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