Effect of Resistivity on Tokamak Eigenmodes

Principal Investigator

Robin Storer

Department of Physics,

Flinders University

The aim of the project was to develop and use computational techniques to study the
magnetohydrodynamics (MHD) of fusion relevant plasmas. I intended to apply the range of programs (particularly SPECTOR) that I have developed to tokamak plasmas and also to start on the development of applications of these ideas to helical plasmas.
For tokamaks, both unstable and stable modes and the destabilisation of ideally stable modes due to resistivity are investigated. This has particular significance in developing heating methods and diagnostic techniques for toroidal plasmas. Of some interest also is an analysis of the effects of resistivity on Alfvén eigenmodes. Global Alfvén eigenmodes arise in toroidal plasmas in a variety of ways ­ due to coupling of the poloidal components because of toroidicity or the non-circular nature of the cross-section etc. They have the potential to be de-stabilising to tokamak plasmas so it is important to verify the effect of resistivity. Most previous work has concentrated on an ideal MHD analysis which determines the appropriate real values of w². A resistive analysis will lead to complex values of w² i.e. it will determine the resistive damping or destabilisation.

For helical plasmas, the effects of resistivity on the magnetohydrodynamics of the plasma has only just started to be investigated. Some of the techniques that I have developed for axi-symmetric plasmas may be able to be applied to large aspect ratio helical plasmas, of the type found in stellarators and heliacs. This will indicate if a fully three-dimensional approach is warranted.

Projects

e80 - VPP

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

In a major recent modification to SPECTOR provision has been made to determine the response of the plasma to an externally applied field. Comparisons have been made between the response as a function of frequency and poloidal structure and the complex spectral pattern. This is not as straightforward as it may seem as the density of spectral points is very large (proportional to the square root of the resistivity) and the response receives contributions from a large number of eigenmodes.

- Appendix B

What computational techniques are used?

The code uses the inverse iteration procedure to calculate the eigenvalues of a large block-tri-diagonal matrix of order about 20,000 with block matrix sizes of about 100x100. Most of the vectorization will be in the core of the program where the most time is spent inverting matrices. There are packages available for that which are vectorised.

Publications

R. G. Storer, Computational Magnetohydrodynamics, in Computational Physics, H. Gardner and C. Savage (Eds), World Scientific Pub. pp81-116 (1997).

R. G. Storer, Toroidal Effects on the Resistive Magnetohydrodynamic Spectrum, in Theory of Fusion Plasmas, Ed by J. W. Connor, E. Sindoni and J. Vaclavick; Edittrice Compositori (Bologna) pp 363-368 (1997).

S. Sen, R. G. Storer, , Theory of drift waves in the presence of parallel and perpendicular flow curvature II Toroidal model , Physics of Plasmas 4, 3113 (1997).

S. Sen, R. G. Storer, Suppression of Rayleigh-Taylor Instability by Flow Curvature , Physics of Plasmas 4, 3731 (1997).

R. G. Storer, Resistive MHD Spectra, Journal of the Korean Physical Society, 31, S177 (1997)

R. G. Storer, MHD Response of a Toroidal Resistive Plasma to External Driving Fields, Proc 21st AINSE Plasma Science and Technology Conference, Lucas Heights, NSW (Feb, 1997).

Appendix B -