Hostname: page-component-848d4c4894-89wxm Total loading time: 0 Render date: 2024-07-07T21:44:40.707Z Has data issue: false hasContentIssue false
  • English
  • Français

A Fourier-space description of oscillations in an inhomogeneous plasma. Part 1. Continuous Fourier transformation

Published online by Cambridge University Press:  13 March 2009

Z. Sedláček  and
P. S. Cally
Z. Sedláček
Affiliation:
Institute of Plasma Physics, Academy of Sciences of the Czech Republic, P.O. Box 17, Za Slovankou 3, 182 00 Prague 8, Czech Republic
P. S. Cally
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

Oscillations in inhomogeneous cold plasmas or inhomogeneous magnetofluids are interpreted in terms of the dynamics of their spectra in wavenumber space. By Fourier transforming the basic integro-differential equation of the problem, a generalized wave equation in wavenumber space is derived, thus converting the oscillation and phase-mixing processes in the original χ space into processes of dispersive propagation and scattering of the spectrum in wavenumber space. The Barston singular continuum eigenmodes correspond to stationary scattering states of a monochromatic wave in wavenumber space, whereas the damping phenomena in χ space correspond to transient ‘leaking’ phenomena accompanying scattering and dispersive propagation of a wave packet in wavenumber space.

Type
Research Article
Information
Journal of Plasma Physics , Volume 52 , Issue 2 , October 1994 , pp. 245 - 264
Copyright
Copyright © Cambridge University Press 1994

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

Adam, J. A. 1986 Phys. Rep. 142, 263.CrossRefGoogle Scholar
Barston, E. M. 1964 Ann. Phys. (NY) 29, 282.CrossRefGoogle Scholar
Bondeson, A. 1985 Phys. Fluids 28, 2406.CrossRefGoogle Scholar
Bremermann, H. 1965 Distributions, Complex Variables and Fourier Transforms. Addison-Wesley.Google Scholar
Cally, P. S. 1991 J. Plasma Phys. 45, 453.CrossRefGoogle Scholar
Cally, P. S. & Sedláček, Z. 1992 J. Plasma Phys. 48, 145.CrossRefGoogle Scholar
Cally, P. S. & Sedláčelk, Z. 1994 J. Plasma Phys. 52, 265.Google Scholar
Case, K. M. 1959 Ann. Phys. (NY) 7, 349.Google Scholar
Friedman, B. 1956 Principles and Techniques of Applied Mathematics. Wiley.Google Scholar
Friedrichs, K. O. 1948 Commun. Pure Appl. Phys. 1, 361.Google Scholar
Kamp, L. P. J. 1991 J. Phys A: Math. Gen. 24, 2029.Google Scholar
Kamp, L. P. J. 1992 Europhys. Lett. 20, 217.CrossRefGoogle Scholar
Lighthill, M. J. 1958 An Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press.CrossRefGoogle Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Livshits, M. S. 1973 Operators, Oscillations, Waves. Open Systems. American Mathematical Society.Google Scholar
Nussenzveig, H. M. 1972 Casuality and Dispersion Relations. Academic.Google Scholar
Rosencrans, S. I. & Sattinger, D. H. 1966 J. Maths and Phys. 45, 289.CrossRefGoogle Scholar
Sattinger, D. H. 1966 a J. Math. Anal. Appl. 15, 497.Google Scholar
Sattinger, D. H. 1966 b J. Maths and Phys. 45, 188.Google Scholar
Sedláček, Z. 1971 a J. Plasma Phys. 5, 239.Google Scholar
Sedláček, Z. 1971 b J. Plasma Phys. 6, 187.Google Scholar
Sedláček, Z. 1972 Czech. J. Phys. B 22, 439.CrossRefGoogle Scholar
Sedláček, Z. 1973 Czech. J. Phys. B 23, 892.Google Scholar
Sedláček, Z., Adam, J. A. & Roberts, B. 1986 Initial-value problem for the 1-D wave equation in an inhomogeneous medium. Institute of Plasma Physics, Czechoslovak Academy of Sciences, Report IPPCZ-268.Google Scholar
Sedláček, Z. & Nocera, L. 1992 J. Plasma Phys. 48, 367.Google Scholar
Uberoi, C. & Sedláček, Z. 1992 Phys. Fluids B 4, 6.CrossRefGoogle Scholar
van, Kampen N. G. 1955 Physica 21, 949.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.Google Scholar
Ye, H. C., Sedláček, Z. & Mahajan, S. M. 1993 Phys. Fluids B 5, 2999.CrossRefGoogle Scholar