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Non-ideal stability: variational method for the determination of the outer-region matching data

Published online by Cambridge University Press:  13 March 2009

A. Pletzer  and
R. L. Dewar
A. Pletzer
Affiliation:
Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physical Sciences and Engineering, The Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia
R. L. Dewar
Affiliation:
Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physical Sciences and Engineering, The Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia
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Abstract

Within the framework of studies of the stability of magneto-plasmas to non-ideal modes, such as resistive modes, the problem of determining the asymptotic matching data arising from the outer (ideal) region is considered. Modes possessing both tearing and interchange (ballooning) parity are considered in finite-pressure plasmas. The matching data, which form a matrix whose elements represent the small solution response to forcing by a big solution, are shown to derive from a variational (energy) principle. The variational principle, as presented, applies to both cylindrical and two-dimensional (toroidal) geometries. Allowing for the presence of multiple rational surfaces, a reciprocity relation between off-diagonal elements of the matching data matrix is obtained. The variational principle is suitable for numerical approximation, and, in particular, for the finite-element method, for which convergence rates are estimated. By packing nodes near the rational surface, maximum convergence, proportional to the inverse square of the number of mesh nodes for tent functions, is achieved.

Type
Research Article
Information
Journal of Plasma Physics , Volume 45 , Issue 3 , June 1991 , pp. 427 - 451
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

Bineau, M. 1966 Nucl. Fusion, 2, 130.CrossRefGoogle Scholar
Chu, M. S., Greene, J. M., Klasky, M. & Chance, M. S. 1990 Numerical study of a singular differential equation relevant for the finite beta tearing mode in a toroidal plasma. Technical Report GA-A20135, General Atomics, San Diego. J. Comp. Phys. (to be published.)Google Scholar
Connor, J. W., Cowley, S. C., Hastie, R. J., Hender, T. C., Hood, A. & Martin, T. J. 1988 Phys. Fluids, 31, 577.CrossRefGoogle Scholar
Coppi, B., Greene, J. M. & Johnson, J. L. 1966 Nucl. Fusion, 6, 101.CrossRefGoogle Scholar
Dewar, R. L. & Grimm, R. G. 1984 Computational Techniques and Applications: CTAC-83 (ed. Noye, B. J. & Fletcher, C.), p. 730. North-Holland.Google Scholar
Dewar, R. L. & Pletzer, A. 1990 J. Plasma Phys. 43, 291.CrossRefGoogle Scholar
Dobrott, D., Prager, S. C. & Taylor, J. B. 1977 Phys. Fluids, 20, 1850.CrossRefGoogle Scholar
Freidberg, J. P. 1987 Ideal Magnetohydrodynamics, pp. 289–293. Plenum.CrossRefGoogle Scholar
Furth, H. P., Killeen, J. & Rosenbluth, M. N. 1963 Phys. Fluids, 6, 459.CrossRefGoogle Scholar
Furth, H. P., Rutherford, P. H. & Selberg, H. 1973 Phys. Fluids, 16, 1054.CrossRefGoogle Scholar
Gel'fand, I. M. & Shilov, G. E. 1964 Generalized Functions, vol. 1, chap. 1, pp. 48–52. Academic.Google Scholar
Glasser, A. H., Greene, J. M. & Johnson, J. L. 1975 Phys. Fluids, 18, 875.CrossRefGoogle Scholar
Glasser, A. H., Jardin, S. C. & Tesauro, G. 1984 Phys. Fluids, 27, 1225.CrossRefGoogle Scholar
Grimm, R. C., Dewar, R. L. & Manickam, J. 1983 J. Comp. Phys. 49, 94.CrossRefGoogle Scholar
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics. Springer.CrossRefGoogle Scholar
Manickam, J., Grimm, R. C. & Dewar, R. L. 1983 Energy Modeling and Simulation (ed. Kydes, A. S., Agrawal, A. K., Rahman, S., Vichnevetsky, R. & Ames, W. F.), p. 355. North-Holland.Google Scholar
Miller, A. D. & Dewar, R. L. 1986 J. Comp. Phys. 66, 356.CrossRefGoogle Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, vol. 1, pp. 527–528. McGraw-Hill.Google Scholar
Morton, K. W. 1987 Finite Elements in Physics (ed. Gruber, R.), p. 1. North-Holland.Google Scholar
Newcomb, W. A. 1960 Ann. Phys. (NY), 10, 232.CrossRefGoogle Scholar
Pletzer, A. & Dewar, R. L. 1990 Computational Techniques and Applications: CTAC-89 (ed. Hogarth, W. L. & Noye, B. J.), p. 429. Hemisphere.Google Scholar
Wilson, H. R. 1990 Plasma Phys. Contr. Fusion, 32, 443.CrossRefGoogle Scholar