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Thermodynamic stability of a tokamak plasma

Published online by Cambridge University Press:  13 March 2009

M. Brusati
Affiliation:
JET Joint Undertaking, Abingdon, Oxfordshire OX14 3EA, U.K.
A. DiVita
Affiliation:
JET Joint Undertaking, Abingdon, Oxfordshire OX14 3EA, U.K.

Extract

A thermodynamic analysis of tokamak plasmas is developed, starting from a single-fluid model. Some general propertiesof entropy production in the plasma are discussed. An approach is employed that is more general than the one based on Onsager symmetry relationships. This choice appears to be justified by experiments. The concept of ‘thermodynamic stability’ is introduced, and a general criterion for the stability of stationary states far from thermodynamic equilibrium is assessed. An upper limit on the particle density is found to exist as a necessary condition in order to prevent disruptions. Analysis of the entropy balance shows that this limit is modified when neutral-beam heating is applied. Radial temperature profiles are shown to be stable against external heating under specific experimental conditions, inparticular when ion and electron temperatures are comparable. An offset scaling law for the energy confinement time TE = TE(Pinp) (with Pinp total input power) is obtained for stationary states when stability against additional heating is imposed.

Type
Articles
Copyright
Copyright © Cambridge University Press 1993

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References

REFERENCES

Alladio, F. 1985 Report ENEA RT/FUS/85/18, Ente Nazionale per l'Energia Nucleare e le Energie Alternative, GRE Frascati (and references therein).Google Scholar
Arunasalam, V., Bretz, N. L., Efthimion, P. C.et al. 1990 Nucl. Fusion 30, 2111.CrossRefGoogle Scholar
Balescu, R. 1987 J. Stat. Phys. 48, 1091.CrossRefGoogle Scholar
Balescu, R. 1989 Proceedings of 3rd European Conference on Fusion Theory, Oxford.Google Scholar
Balet, B., Cordey, J. G. & Stubberfield, P. M. 1990 Report JET-P(90)51, JET Joint Undertaking, Abingdon.Google Scholar
Biskamp, D., Pfirsch, D. & Pohl, F. 1986 Proceedings of 11th International Conference on Plasma Physics and Controlled Fusion, Kyoto (IAEA-CN-47).Google Scholar
Callen, J. D. 1987 Report JET-P(87)10, JET Joint Undertaking, Abingdon.Google Scholar
Campbell, D. J., Christiansen, J. P., Cordey, J. G. et al. 1986 Report JET-P(86)46, JET Joint Undertaking, Abingdon.Google Scholar
Coppi, B. 1980 Comments Plasma Phys. Contr. Fusion 5, 261.Google Scholar
DeGroot, S. R. & Mazur, P. 1984 Non-Equilibrium Thermodynamics. McGraw-Hill.Google Scholar
DiVita, A. 1991 J. Plasma Phys. 46, 423.CrossRefGoogle Scholar
Duesing, G. 1986 Plasma Phys. Contr. Fusion 28, 9A.CrossRefGoogle Scholar
Gage, D. H., Schiffer, M., Kline, S. J. & Reynolds, W. C. 1966 Non-Equilibrium Thermodynamics: Variational Techniques and Stability (ed. Donnelly, R. J., Herman, R. & Prigonine, I.), p. 283. University of Chicago Press.Google Scholar
Glansdorff, P. & Prigogine, I. 1954 Physica 20, 773.CrossRefGoogle Scholar
Grad, H. 1961 Commun. Pure Appl. Maths. 14, 234.CrossRefGoogle Scholar
Hinton, F. L. & Hazeltine, R. D. 1976 Rev. Mod. Phys. 48, 239.CrossRefGoogle Scholar
Kadomtsev, B. 1976 Phénomànes collectives dans les plasmas. Mir.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1980 Statistical Physics, part 1, 3rd edn. Pergamon.Google Scholar
Martinell, J. J., Almaguer, J. A. & Herrera, J. J. E. 1992 Plasma Phys. Contr. Fusion 34, 977.CrossRefGoogle Scholar
Mazur, P. 1952 Bull. Acad. Roy, Belgique Cl. Sci. 38, 182.Google Scholar
Minardi, E. 1988 Proceedings of 15th EPS Conference on Plasma Physics, Dubrovnik.Google Scholar
Minardi, E. 1989 a Report JET-R(89)10, JET Joint Undertaking, Abingdon.Google Scholar
Minardi, E. 1989 b Report Jet-P(89)50, JET Joint Undertaking, Abingdon.Google Scholar
Minardi, E. 1990 Report JET-P(90)71, JET Joint Undertaking, Abingdon.Google Scholar
Minardi, E. 1991 Report JET-P(91)62, JET Joint Undertaking, Abingdon.Google Scholar
Minardi, E. & Lampis, G. 1990 Plasma Phys. Contr. Fusion 32, 819.CrossRefGoogle Scholar
Niedermeyer, H. 1985 Proceedings of 12th EPS Conference on Controlled Fusion and Plasma Physics, Budapest.Google Scholar
Onsager, L. 1931 Phys. Rev. 37, 405.CrossRefGoogle Scholar
O'Rourke, J. 1986 Report JET-P(86)13, JET Joint Undertaking, Abingdon.Google Scholar
Pfirsch, D. & Pohl, F. 1986 Plasma Phys. Contr. Fusion 29, 697.CrossRefGoogle Scholar
Prigogine, I. 1947 étude thermodyamique des phénomànes irréversibles. Desoer.Google Scholar
Peigogine, I. & Nicolis, G. 1977 Self-Organization in Non-Equilibrium Systems. Wiley.Google Scholar
Rebhan, E. 1985 Phys. Rev. A 32, 581.CrossRefGoogle Scholar
Rebhan, E. & Grauer, R. 1987 Proceedings of 12th International Conference on Plasma Physics Controlled Fusion, Madrid (IAEA-CN-48).Google Scholar
Rebut, P. H. & Brusati, M. 1986 Plasma Phys. Contr. Fusion 28, 1A.CrossRefGoogle Scholar
Rebut, P. H., Lallia, P. P. & Watkins, M. L. 1988 Proceedings of 15th International Conference on Plasma Physics and Controlled Fusion, Nice (IAEA-CN-49) (and references therein).Google Scholar
Schloegl, F. 1971 Z. Phys. 243, 203.Google Scholar
Sips, A. C. C., Hogeweij, G. M. D., Costley, A. E. et al. 1991 Report JET-P(91)01, JET Joint Undertaking, Abingdon.Google Scholar
Stacey, W. M. 1981 Fusion Plasma Analysis. Wiley.Google Scholar
Tang, W. M. 1986 Nucl. Fusion 26, 1605.CrossRefGoogle Scholar
Truesdell, C. 1968 Rational Thermodynamics. McGraw-Hill.Google Scholar
Ward, D. J. & Wesson, J. A. 1992 Nucl. Fusion 32, 1777.Google Scholar
Wesson, J. A. 1978 Nucl. Fusion 18, 87.CrossRefGoogle Scholar
Wesson, J. A. & Hender, T. C. 1992 Report JET-P(92)12, JET Joint Undertaking, Abingdon.Google Scholar
Woods, L. C. 1972 The time variable in thermodynamics. Lecture at Cornell University.Google Scholar
Woods, L. C. 1975 The Thermodynamics of Fluid Systems. Oxford University Press.Google Scholar
Woods, L. C. 1982 IMA J. Appl. Maths 29, 221.CrossRefGoogle Scholar
Yamagishi, T. 1986 J. Plasma Phys. 36, 281.CrossRefGoogle Scholar
Zemanski, M. W. 1968 Heat and Thermodynamics. McGraw-Hill.Google Scholar