3D MHD Equilibrium and Stability


Principal Investigator

Henry Gardner

Department of Computer Science,

Faculty of Engineering and Information Technology

For some decades there has been an international scientific and engineering program to study the
containment of plasma (ionised matter) by toroidal magnetic fields in order to develop a fusion power reactor. Australia presently makes a major contribution to this program through the H-1NF Heliac. The H-1NF is a machine of the "stellarator" type which is located at ANU and is partly funded through the Major National Research Facility Program. Stellarators are an alternative to tokamaks for candidate fusion reactors. They do not need to have large currents inside the plasma in order to generate the helical magnetic field lines necessary for confinement and should be easier to maintain in a steady state and less prone to instabilities. On the debit side, the lack of axial symmetry of stellarators makes their theory more complicated and simulation more computationally expensive than for other devices. In particular the simply nested magnetic surfaces found in tokamaks can be broken and can give rise to magnetic islands and regions of chaotic magnetic field lines.
This project aims to simulate plasma equilibrium within H-1NF. The simulation treats the plasma as a single conducting fluid which is a sufficiently accurate approximation to find reasonable equilibrium solutions. A major part of the study concentrates on the growth of magnetic islands with plasma pressure and methods to reduce or control this. The presence of large magnetic islands can be the main limit to plasma confinement at high pressure.


Sally Lloyd

Department of Theoretical Physics

Robert Dewar

Department of Theoretical Physics,

Research School of Physical Sciences and Engineering

David Singleton




k12 - VPP



What are the results to date and the future of the work?

A major part of the code consists of making the pressure constant on a magnetic surface. This is done by following field-lines and averaging the pressure along them. The development of a new algorithm for this part of the code has increased the speed of the code 30 times. Simulations have been run for a variety of initial conditions showing magnetic islands which grow and islands which shrink and change phase. The development and interaction of double island chains has also been observed. Further work will ensure that

Appendix A -


these are stable solutions to the plasma equilibrium and determine which factors control the development of these different types of magnetic island.

What computational techniques are used?

We are using a code developed in Japan by T. Hayashi. This solves the time-dependent, inviscid, MHD equations on a specially shaped three dimensional grid using a two-step Lax-Wendroff scheme. Relaxation along field lines is much slower than perpendicular to them and is treated in a special way when magnetic islands are present. Pressure is averaged along field- lines and interpolated back onto the grid. The magnetic field is then relaxed on the spatial grid using a small value of the plasma resistivity and the entire procedure is repeated until a steady state is obtained.


S. S. Lloyd, H. J. Gardner, T. Hayashi, An Improved HINT Code for Low Shear Stellarators, to appear in Proceedings of 2nd Asia Pacific Plasma Theory Conference, National Institute for Fusion Science, Toki, Japan, 24-26 Sept 1997.

S. S. Lloyd, H. J. Gardner, T. Hayashi, S. R. Hudson, Self-Healing of Magnetic Islands in a Heliac, to appear in Journal of Plasma and Fusion Research (JPFR Series Vol.1).

- Appendix A