Plasma dynamos and flow-driven magnetic instabilities
Major Goals

Essentially Non-Linear Dynamos
Dynamos seem to exist in systems that are not linearly unstable to magnetic energy growth and exhibit subcritical transitions. If magnetic fields are present to help organize the flow, dynamos can be sustained. Accretion disks are probably dynamos of this sort: a finite magnetic field is necessary to create Magneto-rotational instability drive turbulence that in turn acts as a dynamo to seed the MRI while facilitating accretion.

Plasma Dynamos and Dissipation
Build a code that integrates multiple physical processes in spherical and cylindrical geometry. Focus understanding origin of the large-scale magnetic field. Compare with solar observations, and with available liquid metal experiments.
In collisionless plasma dynamos (like hot accretion disks or galaxy cluster plasmas), how does magnetic field generation differ from the MHD models.

Large-Scale Fast Dynamos
How does small scale magnetic turbulence self-organize to develop net magnetic flux at very large magnetic Reynolds number?