Toroidal Theory of MHD Instabilities

We continue with the adventures of the Alfvén wave and its two magnetosonic companions as they travel in the curved space of magnetic surfaces and field lines (Sec. 2), find themselves trapped in singularities of an unprecedented richness (Sec. 3), decide to get themselves better maps of the landscape to do the required twisting while some of their youthful energy is leaking away (Sec. 4), cause trouble at the edge of a powerful empire (Sec. 5), and finally see the light in a distant future (Sec. 6). Needed on the trip are the evolution equations of both ideal and resistive MHD 'derived' in reference [1], the solutions to the toroidal equilibrium equations discussed in reference [2], the general background on spectral theory of inhomogeneous plasmas presented in reference [3], which is extended in the two directions of toroidal geometry and resistivity in this lecture [4]. This leads to such intricate dynamics that numerical techniques are virtually the only way to proceed. This aspect is further elaborated in reference [5] on numerical techniques.