Magnetohydrodynamics of protoplanetary discs

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