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Analysis of a generalized nonlinear diffusion equation in fusion plasma physics

Published online by Cambridge University Press:  13 March 2009

D. Anderson  and
M. Lisak
D. Anderson
Affiliation:
Institute for Electromagnetic Field Theory and EURATOM-FUSION Research (EUR-NE), Chalmers University of Technology, S-412 96 Göteborg, Sweden
M. Lisak
Affiliation:
Institute for Electromagnetic Field Theory and EURATOM-FUSION Research (EUR-NE), Chalmers University of Technology, S-412 96 Göteborg, Sweden
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Extract

Using similarity methods, an investigation is made of a generalized nonlinear diffusion equation arising in plasma physics in connexion with several recently proposed models for turbulent plasma energy transport and particle diffusion.

In almost every field of physics, diffusion or transport equations of the form Ψt = Δ. (DΔΨ) play an important role. The theory of linear diffusion equations, where the diffusion constant D is independent of Ψ, has been developed to a high degree of sophistication (e.g. Carsiaw & Jaeger 1959).

Type
Articles
Information
Journal of Plasma Physics , Volume 27 , Issue 1 , February 1982 , pp. 149 - 156
Copyright
Copyright © Cambridge University Press 1982

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References

REFERENCES

Ahmadi, G. & Hirose, A. 1981 IEEE Trans. Plasma Sci., PS-9, 21.CrossRefGoogle Scholar
Ames, W. F. 1965 Nonlinear Partial Differential Equations in Engineering, vol. 1. Academic.Google Scholar
Anderson, D. & Lisak, M. 1979 Nucl. Fusion, 19, 1521.CrossRefGoogle Scholar
Anderson, D. & Lisak, M. 1980 Phys. Rev. A 22, 2761.CrossRefGoogle Scholar
Anderson, D., Gustavsson, H.-G. & Lisak, M. 1981 Physica Scripta, 23, 781.CrossRefGoogle Scholar
Bhadra, D. K. & Gross, L. 1977 Nucl. Fusion, 17, 622.CrossRefGoogle Scholar
Carslaw, H. S., Jaeger, J. C. 1959 Conduction of Heat in Solids. Oxford University Press.Google Scholar
Chen, F. F. 1974 Introduction to Plasma Physics. Plenum.Google Scholar
Crank, J. 1979 The Mathematics of Diffusion. Oxford University Press.Google Scholar
Gary, S. P. & Schmidt, J. 1974 Phys. Lett., 48 A, 23.CrossRefGoogle Scholar
Goodman, T. R. 1964 Advances in Heat Transfer vol. 1 (ed. Irvine, T. F. & Harnett, J. P.). Academic.Google Scholar
Gradshteyn, I. S. & Ryhzik, I. M. 1980 Table of Integrals, Series, and Products. Academic.Google Scholar
Horton, W. 1972 Phys. Rev. Lett. 28, 1506.CrossRefGoogle Scholar
Kadomtsev, B. B. & Pogutse, O. P. 1970 Reviews of Plasma Physics, vol. 5 (ed. Leontovich, M. A.). Consultants Bureau.Google Scholar
Lönngren, K. E. 1977 Recent Advances in Plasma Science (ed. Buti, B.). Indian Academy of Sciences, Bangalore.Google Scholar
Lonngren, K. E. & Reddy, S. M. 1978 J. Appl. Phys., 49, 4500.CrossRefGoogle Scholar
Stott, P. E. 1976 Plasma Phys., 18, 251.CrossRefGoogle Scholar