Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-31T23:00:46.434Z Has data issue: false hasContentIssue false
  • English
  • Français

A new Hamiltonian formulation for fluids and plasmas. Part 3. Multifluid electrodynamics

Published online by Cambridge University Press:  13 March 2009

Jonas Larsson
Jonas Larsson
Affiliation:
Department of Plasma Physics, Umeå University, S-90187 Umeå, Swedent† and Lawrence Berkeley Laboratory, University of California, California 94720, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The Hamiltonian structure underlying ideal multifluid electrodynamics is formulated in a way that simplifies Hamiltonian perturbation calculations. We consider linear and lowest-order nonlinear theory, and the results in Part 1 of this series of papers are generalized in a satisfactory way. Thus the Hermitian structure of linearized dynamics is derived, and we obtain the coupling coefficients for resonant three-wave interaction in symmetric form, giving the Manley–Rowe relations.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 55 , Issue 2 , April 1996 , pp. 279 - 300
Copyright
Copyright © Cambridge University Press 1996

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Cary, J. R. 1981 Phys. Rep. 79, 131.CrossRefGoogle Scholar
Cary, J. R. & Kaufman, A. N. 1981 Phys. Fluids 24, 1238.CrossRefGoogle Scholar
Cary, J. R. & Littlejohn, A. N. 1983 Ann. Phys. (NY) 151, 1.CrossRefGoogle Scholar
Dougherty, J. P. 1974 Lagrangian methods in plasma dynamics. Part 2. Construction of Lagrangians for plasma. J. Plasma Phys. 11, 331.CrossRefGoogle Scholar
Elvsén, R. & Larsson, J. 1993 Physica Scripta 47, 571.CrossRefGoogle Scholar
Kartz, S. 1961 Phys. Fluids 4, 345.CrossRefGoogle Scholar
Kaufman, A. N. 1987 Phys. Rev. 36, 982.CrossRefGoogle Scholar
Kaufman, A. N. 1991 Phase-space plasma-action principles, linear mode conversions, and the generalized Fourier transform. Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids (ed. Rozmus, W. & Tuszynski, J. A.). World Scientific, Singapore.Google Scholar
Kaufman, A. N. & Boghosian, 1984 Lie transform derivation of the gyrokinetic Hamiltonian system. Contemporary Mathematics, Vol. 28 (ed. Marsden, J. E.), p. 169. AMS, Providence, RI.Google Scholar
Larsson, J. 1992 J. Plasma Phys. 48, 13.CrossRefGoogle Scholar
Larsson, J. 1993 J. Plasma Phys. 49, 255.CrossRefGoogle Scholar
Larsson, J. 1996 a J. Plasma Phys. 55, 235.CrossRefGoogle Scholar
Larsson, J. 1996 b J. Plasma Phys. 55, 261.CrossRefGoogle Scholar
Littlejohn, R. G. 1981 Singular Poisson tensors. Mathematical Methods in Hydrodynamics and Integrability in Dynamical Systems (ed. Tabor, M. & Treve, Y. M.), p. 47. AIP Conf. Proc., Vol. 88, AIP, New York.Google Scholar
Littlejohn, R. G. 1982 J. Math. Phys. 23, 742.CrossRefGoogle Scholar
Low, F.E. 1958 Proc.R. Soc. Lond. A248, 282.Google Scholar
Marsden, J. E. & Weinstein, A. 1983 Physica D 7, 305.Google Scholar
Morrison, P. J. 1982 Poisson brackets for fluids and plasmas. Mathematical Methods in Hydrodynamics and Integrability in Dynamical Systems (ed. Tabor, M. & Treve, Y. M.), p. 13. AIP Conf. Proc., Vol. 88, AIP, New York.Google Scholar
Pfirsch, D. 1984 Z. Naturforsch. 39A, 1.CrossRefGoogle Scholar
Pfirsch, D. & Morrison, P. J. 1991 Phys. Fluids B3, 271.CrossRefGoogle Scholar
Spencer, R. G. & Kaufman, A. N. 1982 Phys. Rev. A25, 2437.CrossRefGoogle Scholar
Su, C. 1961 Phys. Fluids 4, 1376.CrossRefGoogle Scholar
Ye, H. & Kaufman, A. N. 1992 Phys. Fluids B4, 771.CrossRefGoogle Scholar
Ye, H. & Morrison, P. J. 1992 Phys. Fluids, B4, 771.CrossRefGoogle Scholar
Zakharov, V. E., Musher, S. L. & Rubenchik, A. M. 1985 Phys. Rep. 129, 285.CrossRefGoogle Scholar