Magnetohydrodynamics of protoplanetary discs

Protoplanetary discs are made of gas and dust orbiting a young star. They are also the birth place of planetary systems, which motivates a large amount of observational and theoretical research. In these lecture notes, I present a review of the magnetic mechanisms applied to the outer regions R>1 AU of these discs, which are the planet-formation regions. In contrast to usual astrophysical plasmas, the gas in these regions is noticeably cold (T<300 K) and dense, which implies a very low ionisation fraction close to the disc midplane. In these notes, I deliberately ignore the innermost R~0.1 AU region which is influenced by the star-disk interaction and various radiative effects. I start by presenting a short overview of the observational evidence for the dynamics of these objects. I then introduce the methods and approximations used to model these plasmas, including non-ideal MHD, and the uncertainties associated with this approach. In this framework, I explain how the global dynamics of these discs is modelled, and I present a stability analysis of this plasma in the local approximation, introducing the non-ideal magneto-rotational instability. Following this mostly analytical part, I discuss numerical models which have been used to describe the saturation mechanisms of this instability, and the formation of large-scale structures by various saturation mechanisms. Finally, I show that local numerical models are insufficient since magnetised winds are also emitted from the surface of these objects. After a short introduction on winds physics, I present global models of protoplanetary discs, including both a large-scale wind and the non-ideal dynamics of the disc.