Plasma Turbulence in 3-Dimensional 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 non-equilibrium situation where various self-organisation 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 H-1 Heliac (now upgraded to a national facility, H-1NF, 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 three-dimensional 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 low-magnetic-shear, strongly three-dimensional toroidal plasma containment devices such as the H-1NF Heliac.

Principal Investigator

Robert Dewar
Theoretical Physics



Facilities Used



Paul Cuthbert
Theoretical Physics

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 H-1NF 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 low-shear 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 3-D 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, one-dimensional boundary-value 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 cpu-seconds.

The supercomputing needs come from computing sufficient of these localised one-dimensional eigensolutions to construct a three-dimensional 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 0256-307X, 2000, 33–35

P. Cuthbert, Ballooning Instabilities in Three-Dimensional Toroidal Plasmas, PhD Thesis, ANU, 2000

P. Cuthbert and R. L. Dewar, Anderson-localized ballooning modes in general toroidal plasmas, Phys. Plasmas 7, 2000, 2302-2305

R. L. Dewar, P. Cuthbert and R. Ball, Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas,  Phys. Rev. Letters 86, 2001, 2321-2324