Plasma Turbulence in 3Dimensional Magnetically Confined Plasmas
The goal of nuclear fusion power research is to use strong magnetic fields to insulate a plasma (hot gas) of hydrogen isotopes, at a temperature of hundreds of millions of degrees, from walls near room temperature. The enormous temperature gradient creates a highly nonequilibrium situation where various selforganisation phenomena tend to occur, destroying smooth density and temperature distributions and instead creating turbulent structures that allow heat and particles to escape faster than desired ("anomalous transport").
The aim of advanced magnetic confinement designs, such as the H1 Heliac (now upgraded to a national facility, H1NF, in which temperatures up to ten million degrees will be obtained), is to thwart this tendency towards formation of turbulence by designing twisted magnetic field configurations that make instability energetically unfavourable. The simulation of such a device forms a grand challenge to theory and computation because the full threedimensional geometry, both of the equilibrium and the perturbation, must be accurately taken into account.
The project has concentrated on the first phase of a turbulence study  linear stability analysis using a simple magnetohydrodynamic (MHD) fluid model  to understand the unusual geometric effects that arise in lowmagneticshear, strongly threedimensional toroidal plasma containment devices such as the H1NF Heliac.
Principal Investigator Robert Dewar 
Project s55 Facilities Used VPP, MDSS, VizLab 
CoInvestigator Paul CuthbertTheoretical Physics RSPhysSE ANU

RFCD Codes 240303, 240201 
Significant Achievements, Anticipated Outcomes and Future Work
The analysis of a high beta (beta = plasma pressure/magnetic pressure) configuration of the H1NF heliac to determine the nature of the local ballooning eigenvalue for ideal MHD ballooning modes has led to the successful completion of a PhD thesis and several papers in prestigious journals. Ballooning modes are known to limit the maximum pressure which can be obtained in a confinement device, and as such are an important consideration for the development of future fusion devices.
With the use of the VPP, the parametric structure of the local ballooning eigenvalue was revealed, and the role of the magnetic shear investigated. The major outcomes of the work were a) establishing the importance of Anderson localization in lowshear systems, b) showing that the complex structure of the branches of the ballooning mode eigenvalue could be understood using symmetry operations and a perturbation expansion in magnetic shear, and c) showing that the rays of a regularized version of 3D ballooning WKB are chaotic, so that understanding the global spectrum will require a "quantum chaos" analysis.
Computational Techniques Used
The fundamental computation in the "WKB ballooning method" consists of solving a linear 2nd order, onedimensional boundaryvalue eigenproblem on a magnetic field line; a simple exercise in principle, at least when a simple fluid model is used. However the ODE coefficients (derived from an equilibrium configuration also calculated on a supercomputer) must be calculated at up to 30,000 points on a field line. Each point requires summing between 600 and 1,100 Fourier components and calculation of coefficients on the full set of points takes tens of cpuseconds.
The supercomputing needs come from computing sufficient of these localised onedimensional eigensolutions to construct a threedimensional array from which global eigenmodes and their growth rates can be constructed.
Publications, Awards and External Funding
R.L. Dewar and P. Cuthbert, Anderson Localization and Ballooning Eigenfunctions, Chinese Physics Letters ISSN 0256307X, 2000, 33–35
P. Cuthbert, Ballooning Instabilities in ThreeDimensional Toroidal Plasmas, PhD Thesis, ANU, 2000
P. Cuthbert and R. L. Dewar, Andersonlocalized ballooning modes in general toroidal plasmas, Phys. Plasmas 7, 2000, 23022305
R. L. Dewar, P. Cuthbert and R. Ball, Strong "quantum" chaos in the global ballooning mode spectrum of threedimensional plasmas, Phys. Rev. Letters 86, 2001, 23212324