Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-02T23:32:06.354Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized Budden resonance tunnelling, with application to linear conversion nearly parallel to magnetic field

Published online by Cambridge University Press:  13 March 2009

Einar Mjølhus
Einar Mjølhus
Affiliation:
Institute of Mathematical and Physical Sciences, University of Tromsø, Tromsø, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

A model of linear wave conversion problems is formulated, which forms a natural generalization of the Budden resonance tunnelling model. The structure of the model is such as to conserve energy flux, and also is such as to allow explicit solution in terms of contour integrais. An arbitrary number of wave modes may participate. Explicit expressions for the conversion coefficients in terms of quantities derivable from the dispersion relations are obtained. A standard way of extending the model, by which resonant absorption is retrieved as conversion into an additional short wave mode, is included. The formulae obtained, are shown to include a complete solution to the problem of linear conversion in a magnetized plasma when the waves are nearly parallel to the magnetic field.

Type
Research Article
Information
Journal of Plasma Physics , Volume 38 , Issue 1 , August 1987 , pp. 1 - 26
Copyright
Copyright © Cambridge University Press 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1965 Handbook of mathematical functions. Dover.Google Scholar
Barr, H. C., Boyd, T. J. M., Gardner, G. A. & Rankin, R. 1985 Phys. Fluids, 28, 16.CrossRefGoogle Scholar
Batchelor, D. B. 1980 Plasma Phys. 22, 41.CrossRefGoogle Scholar
Bennett, J. A. 1976 Math. Proc. Camb. Phil. Soc. 80, 527.CrossRefGoogle Scholar
Booker, H. G. 1938 Phil. Trans. Roy. Soc. A237, 411.Google Scholar
Budden, K. G. 1955 Physics of the Ionosphere: Report of Physical Society Conference, Cavendish Laboratory, p. 320. Physical Society, London.Google Scholar
Budden, K. G. 1979 Phil. Trans. Roy. Soc. 290, 405.Google Scholar
Budden, K. G. 1985 The propagation of radio waves. Cambridge University Press.CrossRefGoogle Scholar
Budden, K. G. & Smith, M. S. 1973 J. Atmos. Terr. Phys. 35, 1909.CrossRefGoogle Scholar
Budden, K. G. & Smith, M. S. 1974 Proc. Roy. Soc. A341, 1.Google Scholar
Burkill, J. C. 1962 The theory of ordinary differential equations. Oliver & Boyd.Google Scholar
Erokhin, N. S. & Moiseev, S. S. 1973 Soviet Phys. Usp. 16, 64.CrossRefGoogle Scholar
Gambier, D. J. D. & Schmitt, J. P. M. 1983 Phys. Fluids, 26, 2200.CrossRefGoogle Scholar
Ginzburg, V. L. 1943 J. Phys. 7, 283.Google Scholar
Ginzburg, V. L. 1970 The propagation of electromagnetic waves in plasmas, 2nd edn.Pergamon.Google Scholar
Golant, V. E. & Piliya, A. D. 1972 Soviet Phys. Usp. 14, 413.CrossRefGoogle Scholar
Grebogi, C., Liu, C. S. & Tripathi, V. K. 1977 Phys. Rev. Lett. 39, 338.CrossRefGoogle Scholar
Kruer, W. L. & Estabrook, K. 1977 Phys. Fluids, 20, 1688.CrossRefGoogle Scholar
Lang, S. 1970 Linear Algebra. Addison-Wesley.Google Scholar
Lembège, B. & Jones, D. 1982 J. Geophys. Res. 87A, 6187.CrossRefGoogle Scholar
Maggs, J. E. & Morales, G. J. 1983 J. Plasma Phys. 29, 177.CrossRefGoogle Scholar
Mjølhus, E. 1983 J. Plasma Phys. 30, 179.CrossRefGoogle Scholar
Mjølhus, E. 1984 J. Plasma Phys. 31, 7.CrossRefGoogle Scholar
MjøLhus, E. 1985 a J. Geophys. Res. 90A, 4269.CrossRefGoogle Scholar
Mjølhus, E. 1985 b Generalized Budden Resonance Tunnelling. Institute report, IMR, University of Tromsø.Google Scholar
Mjølhus, E. & Flå, T. 1984 J. Geophys. Res. 89A, 3921.CrossRefGoogle Scholar
Morales, G. J., Antani, S. N. & Fried, B. D. 1985 Phys. Fluids, 28, 3302.CrossRefGoogle Scholar
Ngan, Y. C. & Swanson, D. G. 1977 Phys. Fluids, 20, 1920.CrossRefGoogle Scholar
Piliya, A. D. 1967 Soviet Phys. Tech. Phys. 11, 609.Google Scholar
Piliya, A. D. & Fedorov, V. I. 1970 Soviet Phys. JETP, 30, 653.Google Scholar
Pontrjagin, L. 1944 Akad. nauk. SSSR Izv. Ser. mat. 8, 243. Engl. abstr. p. 275.Google Scholar
Rawer, K. & Suchy, K. 1967 Handbuch der Physik, Band XLIX/2 Geophysik III (ed. Flügge, S.). Springer.Google Scholar
Rydbeck, O. E. H. 1950 J. Appl. Phys. 21, 1205.Google Scholar
Sayashov, Y. S. & Ritz, C. P. 1983 J. Plasma Phys. 29, 299.CrossRefGoogle Scholar
Speziale, T. & Catto, P. J. 1977 Phys. Fluids, 20, 990.CrossRefGoogle Scholar
Stix, T. H. 1962 The theory of plasma waves. McGraw-Hill.Google Scholar
Stix, T. H. 1965 Phys. Rev. Lett. 15, 878.CrossRefGoogle Scholar
White, R. B. & Chen, F. F. 1974 Plasma Phys. 16, 565.CrossRefGoogle Scholar
Wong, A. Y., Santoru, T. & Sivjee, G. G. 1982 J. Geophys. Res. 86A, 7718.Google Scholar
Wright, J. W. 1960 J. Atmos. Terr. Phys. 18, 276.CrossRefGoogle Scholar