Nonlinear MHD Processes in the Sun's Atmosphere

The outer atmosphere of the Sun, the corona, is an ionised high temperature plasma that is dominated by the coronal magnetic field. There are many important coronal phenomena that may be modelled as a magnetised fluid and described by the MHD equations. In their ideal form, the MHD equations are a system of nonlinear hyperbolic equations but it is the small dissipation terms that are important in many cases. Three examples are chosen to illustrate how numerical simulations can be used to investigate how dissipation can tap the energy in the coronal magnetic field. All involve the build-up of large gradients in the magnetic field through (i) the lack of smooth equilibria, (ii) waves propagating in an inhomogeneous plasma and (iii) the nonlinear evolution of an ideal MHD instability.