Plasma Turbulence in 3-dimensional Magnetically Confined Plasmas


Principal Investigator

Robert L Dewar

Dept of Theoretical Physics & Plasma Research Lab.

Research School of Physical Sciences and Engineering


D B Singleton

ANU Supercomputer Facility

V Lewandowski

Dept of Theoretical Physics

Research School of Physical Sciences and Engineering

M Persson

Chalmers Univ. of Technology

Gothenburg, Sweden


s55 - VPP, PC, VizLab

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 (to be 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 consists of three basic phases linear stability analysis, weakly nonlinear evolution of coupled modes, and simulation of developed turbulence. In each of these there is a choice of plasma model whether to use a simple magnetohydrodynamic (MHD) fluid model, a more sophisticated fluid model or a full particle (gyrokinetic) model. The aim is to develop efficient computational models, verifying at each step that they can produce a converged result for the heliac geometry when the spatial resolution is increased.



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

A standard high beta (plasma pressure/magnetic pressure) configuration of the H-1NF heliac has been examined in close detail to investigate the phase-space dependence of the local ballooning eigenvalue for ideal MHD ballooning modes. These modes are known to limit the maximum pressure which can be obtained in a confinement device, and as such are an important

- Appendix A



consideration for the development of future fusion devices. With the use of the VPP, the parametric structure of the local eigenvalue has been revealed, and the role of the magnetic shear investigated. A greater understanding of the effects of the low magnetic shear in devices such as H-1 has been gained, with the next step being the construction of global modes from these local solutions.

Further work was done on scans of parameters (including ) affecting the linear stability of drift waves in H-1NF, using both resistive and cold-ion models in the ballooning representation. The hybrid gyrokinetic-fluid code previously developed has been used to simulate ion drift waves in H-1NF.

What computational techniques are 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

Title: Contour plot of local ballooning mode growth rates on different magnetic surfaces s and field lines a in the H-1NF Heliac. The surface parameter q on the right axis measures the average twist of the field lines. Stable regions are indicated by S.
Appendix A -



(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.


P. Cuthbert, J. L. V. Lewandowski, H. J. Gardner, M. Persson, D. B. Singleton, R. L. Dewar, N. Nakajima and W. A. Cooper, Toroidally localized and nonlocalized ballooning instabilities in a stellarator, Phys. Plasmas, 5, 1998, 2921-2931.

R.L. Dewar, P. Cuthbert, J.L.V. Lewandowski, H.J. Gardner, D.B. Singleton, N. Nakajima, M. Persson and W.A. Cooper, Discrete and Continuum Ballooning Modes in a Stellarator, J. Plasma Fusion Res. SERIES, 1, 1998, 108-110.

R.L. Dewar, P. Cuthbert, J.L.V. Lewandowski, H.J. Gardner, D.B. Singleton, N. Nakajima, M. Persson and W.A. Cooper, Quasi-two-dimensional waves in three-dimensional magnetic confinement systems, Physica Scripta T75, 1998, 134-137.

J. L. V. Lewandowski, A Simple Model for Collisional Drift Waves, Canadian Journal of Physics, 75, 1998, 891-906.

J. L. V. Lewandowski and M. Persson, Localization of Drift Waves in a Helically Symmetric Stellarator Model, Plasma Physics & Controlled Fusion, 39, 1998, 1941-1946.

J. L. V. Lewandowski, Resistive Drift Waves in a Toroidal Heliac, Journal of the Physical Society of Japan, 66, 1998, 3831-3841.

J. L. V. Lewandowski, Local Stability Analysis of Low-Shear Stellarators, Journal of the Korean Physical Society, 33, 1998, 143-153.

J. L. V. Lewandowski, Collisional Drift Waves in 3-Dimensional Plasmas, Journal of the Korean Physical Society, 33, 1998, 414-427.

J. L. V. Lewandowski, Fluid/gyro-kinetic simulations in a stellarator, Nuovo Cimento della Societa Italiana di Fisica D 20, 1998, 1493-1512.

- Appendix A