Instabilities in the solar corona

Many phenomena in the solar atmospheres can be described in terms of MHD models, including solar flares and prominences. The study of the MHD stability properties of these phenomena is crucial far our understanding of them. Why do flares occur? How can the magnetic field store the necessary energy? Why do prominences form? Why do they erupt? To answer such questions requires a theoretical model for the equilibrium and then the use of MHD stability theory. The review begins with an introduction to some of the various solar phenomena that may be investigated using stability theory. The geometry of the coronal magnetic field for many models is either a loop or an arcade and it is the stability properties of these structures that are investigated. The author presents a simple physical description of the basic MHD instabilities and describes the main difference between laboratory and coronal plasmas due to the presence of an extremely dense plasma at the footpoints of the coronal magnetic fieldlines. The implications of this density interface are discussed. Linear stability theory is applied to some solar situations and some non-linear simulations are discussed. In Section 3 linear stability theory is applied to some solar situations and the more recent non-linear simulations are discussed in Section 4. For MHD instabilities, it is the presence of the cool, dense lower layers of the Sun's atmospheres that provides the main difference between laboratory and solar plasmas. By photospheric line-tying the Sun is able to stabilize the stressed coronal magnetic field in a stable configuration for periods between a day or so, to months on end.