Some of my main research interests are listed below – click on the titles for more information. While I’ve vaguely grouped these by topic, many of these areas are interlinked.

*Dust dynamics and instabilities*

Many astrophysical fluids and plasmas are filled with macroscopic particles, or dust. The gas and the dust is often not perfectly coupled together, allowing for a variety of interesting dynamics. We have shown that when the dust and the gas phases are not perfectly stationary with respect to each other, the system is usually unstable. We termed these instabilities “Resonant Drag Instabilities” (RDIs). They may be important in a variety of systems, from planet-forming disks, to winds from stars or AGN.

**Turbulence and Dynamo**

**Turbulence and Dynamo**

Plasma turbulence has a puzzling tendency to create highly correlated magnetic fields. The best known example is the solar field, which changes sign every 11 years and is spatially correlated over large scales, despite the relatively small-scale turbulent convection driving the field turbulence in the first place. Despite many years of detailed observation and much theoretical effort, the processes that underlie such phenomena are still not well understood. As well as this practical importance, the nonlinear dynamics associated with how large-scale order arises from the chaos of small-scale turbulence is fascinating, and there are many interesting problems to explore. Recently I’ve been particularly interested by in collisionless fluids, where the particle distribution function can be non-Maxwellian. This creates a whole host of interesting effects, and the plasma dynamics can differ from standard fluids on macroscopic scales due to the generation of anisotropic pressures. One surprising result we found shows that even the simplest low-frequency plasma wave, the shear-Alfvén wave, can be strongly modified and is subject to a very restrictive amplitude limit.

**Accretion disks and the magnetorotational instability**

**Accretion disks and the magnetorotational instability**

Accretion disks form ubiquitously in astrophysics due to conservation of angular momentum. A big puzzle — how is the angular momentum transported outwards so that matter can fall inwards — was answered by Balbus and Hawley with the magnetorotational instability (MRI). There are still lots of fascinating questions to consider however. I’ve been particularly interested by the turbulence and dynamo caused by the saturation of the MRI, whether purely hydrodynamic turbulence might be possible, and what other effects arise in a weakly collisional system.

**Hamiltonian mechanics, gyrokinetics, and numerical methods**

**Hamiltonian mechanics, gyrokinetics, and numerical methods**

I have also worked on geometric methods in plasma physics. Here the idea is to understand the underlying mathematical structure in terms of Lagrangian and Hamiltonian dynamics. As well as being generally interesting, this can allow better design of numerical methods that respect the geometric properties of the physical system. These theories also allow very clean derivations of the guiding center equations (the basis for the theory of gyrokinetics), which describe the motion of particles in a magnetic field, without having to resolve their fast motion around field lines.