# Available student project - Inclusion of toroidal flow into multiple relaxed region MHD

## Research fields

- Fusion and Plasma Confinement
- Clean Energy

## Project details

Controlled magnetic confinement fusion offers the possibility of an inexhaustible supply of energy with zero greenhouse gas emissions. At the very high temperatures need to initiate a fusion reaction, the fuel exists in the plasma state.

Magnetohydrodynamics (MHD) is the study of magnetised plasmas, with application ranging from solar flares through to laboratory confinement. MHD has been very successful in the description of axis-symmetric (2D) toroidal plasmas, such as tokomaks, where the field lies everywhere in toroidal surfaces. The description of the magnetic field in asymmetric (3D) plasmas is less developed, and indeed the existence of solutions where the field is confined to toroidal surfaces is not guaranteed.

Driven by the 3D existence problem, an ANU / Princeton collaboration recently proposed a stepped pressure profile model, MRXMHD. In their model, nonzero pressure gradients are restricted to toroidal surfaces, on which a sheet current balances a step function change in pressure. In general, the magnetic field only lies in toroidal surfaces at the interfaces. The model, which is mathematically well-posed, addresses the existence problem explicitly, by inferring restrictions on the field and pressure at the inerfaces.

The model has had recent succss in describing the formation of helical states in the reverse field pinch. An important but missing ingredient is the inclusion of toroidal flow into MRXMHD. Indeed, flow-shear is thought to be important in the diffusion of 3D fields into the plasma from the edge during resonant magnetic perturbation experiments. In this project extensions to MRXMHD with flow will be formulated.

## Required background

Background in vector calculus and variational methods is necessary, and experience using Mathematica desirable.

## Project suitability

- 3rd year special project
- Honours project
- Phd or Masters