High-energy accretion discs around black holes or compact stars are composed of a fully ionized plasma and are highly electrically conducting. In these situations the magnetic field can play a significant role in the dynamics of the disc. This is described by the theory of magnetohydrodynamics, which is a fusion of fluid dynamics and electromagnetism.

The magnetorotational instability (MRI) is a powerful linear instability of an electrically conducting accretion disc in the presence of a magnetic field. Its nonlinear development typically results in magnetic turbulence in the disc. This transports angular momentum outwards, allowing the disc to develop an accretion flow, and dissipates energy, allowing the disc to shine. A particularly interesting question is whether the MRI can act as a nonlinear dynamo, meaning that the turbulence sustains the magnetic field against dissipation.

Magnetic fields also assist in the production of jets and winds from discs. If the disc is threaded by a magnetic field, electrically conducting gas above the disc tends to be forced into corotation with the point on the disc at which the field is anchored. If the field is inclined at more than thirty degrees to the vertical direction, gas can be flung outwards.

Since the intensity of turbulence in the disc and the efficiency with which outflows are launched depend sensitively on the strength of the magnetic field, the transport of magnetic flux through the disc by laminar and turbulent advection or diffusion is an important issue.

Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?

Magnetorotationally driven wind cycles in local disc models

Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow

Global evolution of the magnetic field in a thin disc and its consequences for protoplanetary systems

Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Transport of magnetic flux and the vertical structure of accretion discs - II. Vertical profile of the diffusion coefficients

Local outflows from turbulent accretion disks

The magnetorotational instability as a jet launching mechanism

Transport of magnetic flux and the vertical structure of accretion discs - I. Uniform diffusion coefficients

Jet launching from accretion discs in the local approximation

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows

Localized magnetorotational instability and its role in the accretion disc dynamo

Subcritical dynamos in shear flows

On self-sustained dynamo cycles in accretion discs

Magnetorotational-type Instability in Couette-Taylor Flow of a Viscoelastic Polymer Liquid

Self-Sustaining Nonlinear Dynamo Process in Keplerian Shear Flows

Global Magnetorotational Instability with Inflow. II. The Nonlinear Development of Axisymmetric Wall Modes

Global Magnetorotational Instability with Inflow. I. Linear Theory and the Role of Boundary Conditions

On the dynamics of magnetorotational turbulent stresses

On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities

Launching of Jets and the Vertical Structure of Accretion Disks

The response of a turbulent accretion disc to an imposed epicyclic shearing motion

Extracting Energy from Black Holes: The Relative Importance of the Blandford-Znajek Mechanism

Waves and instabilities in a differentially rotating disc containing a poloidal magnetic field

The equilibrium of a differentially rotating disc containing a poloidal magnetic field

The non-axisymmetric instability of a cylindrical shear flow containing an azimuthal magnetic field