Theory of the Propagation of Nonstable Waves

Laurence S. Hall

doi:10.1103/PhysRevD.1.404

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Theory of the Propagation of Nonstable Waves

Laurence S. Hall

Lawrence Radiation Laboratory, University of California, Livermore, California 94550

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Phys. Rev. D 1, 404 – Published 15 January, 1970

DOI: https://doi.org/10.1103/PhysRevD.1.404

Abstract

The general theory of the propagation of pulse disturbances in an unstable, slightly inhomogeneous, and time-dependent medium is derived in complementary fashion to the eikonal theory of the propagation of stable waves. For a dispersion $D (k, ω; a)$ , where k is the wave number and $ω$ is the (complex) frequency which is related to k for given values of the auxiliary parameters a (temperature, density, etc.) by the vanishing of $D$ , the rate of change of propagation velocity of an element of the disturbance is found to be $\frac{dV}{da} = Re (- \frac{D_{a}}{k D_{ω}})$ in one dimension. A similar equation holds in the case of a general $n$ -dimensional system. This relation makes possible the construction of the complete pulse shape in fairly simple fashion for the case of a general slowly varying medium. The theory is illustrated by application to a particular unstable dispersion.

References (17)

Max Born and Emil Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), 3rd ed., Chap. III
L. I. Schiff, Quantum Mechanics (McGraw-Hill Book Co., New York, 1968), 3rd ed
Leon Brillouin, Wave Propagation and Group Velocity (Academic Press Inc., New York, 1960)
Omitted endnote
L. S. Hall and W. Heckrotte, Phys. Rev. 166, 120 (1968)
Hall and Heckrotte, [5]
K. B. Dysthe, Nucl. Fusion 6, 215 (1966) Hall and Heckrotte, [5]
R. J. Briggs, Electron-Stream Interaction with Plasmas (M.I.T. Press, Cambridge, Mass., 1964) L. S. Hall, W. Heckrotte, and T. Kammash, Phys. Rev. 139, A1117 (1965)
R. J. Eden and J. C. Polkinghorne and their collaborators, Homology and Feynman Integrals, edited by R. C. Hwa and V. L. Teplitz (W. A. Benjamin, Inc., New York, 1966)
Omitted endnote
Omitted endnote
K. B. Dysthe, Nucl. Fusion 6, 215 (1966)
C. F. Kennel and R. Z. Sagdeev, J. Geophys. Res. 72, 3303 (1967)
E. G. Harris, Phys. Rev. Letters 2, 34 (1959) J. Nucl. Energy C2, 138 (1961) Hall et al., [8]
H. L. Berk, T. K. Fowler, L. D. Pearlstein, R. F. Post, J. D. Callen, C. W. Horton, and M. N. Rosenbluth, in Proceedings of the Conference on Plasma Physics and Controlled Nuclear Fusion, Novosibirsk, 1968 (International Atomic Energy Agency, Vienna, 1969), Vol. II, p. 151
B. Coppi, G. Laval, R. Pellat, and M. N. Rosenbluth, Nucl. Fusion 6, 261 (1966)
H. L. Berk, L. D. Pearlstein, J. D. Callen, C. W. Horton, and M. N. Rosenbluth, Phys. Rev. Letters 22, 876 (1969)

[c1] Max Born and Emil Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1965), 3rd ed., Chap. III

[c2] L. I. Schiff, Quantum Mechanics (McGraw-Hill Book Co., New York, 1968), 3rd ed

[c3] Leon Brillouin, Wave Propagation and Group Velocity (Academic Press Inc., New York, 1960)

[c4] Omitted endnote

[c5] L. S. Hall and W. Heckrotte, Phys. Rev. 166, 120 (1968)

[c6] Hall and Heckrotte, [5]

[c7] K. B. Dysthe, Nucl. Fusion 6, 215 (1966) Hall and Heckrotte, [5]

[c8] R. J. Briggs, Electron-Stream Interaction with Plasmas (M.I.T. Press, Cambridge, Mass., 1964) L. S. Hall, W. Heckrotte, and T. Kammash, Phys. Rev. 139, A1117 (1965)

[c9] R. J. Eden and J. C. Polkinghorne and their collaborators, Homology and Feynman Integrals, edited by R. C. Hwa and V. L. Teplitz (W. A. Benjamin, Inc., New York, 1966)

[c10] Omitted endnote

[c11] Omitted endnote

[c12] K. B. Dysthe, Nucl. Fusion 6, 215 (1966)

[c13] C. F. Kennel and R. Z. Sagdeev, J. Geophys. Res. 72, 3303 (1967)

[c14] E. G. Harris, Phys. Rev. Letters 2, 34 (1959) J. Nucl. Energy C2, 138 (1961) Hall et al., [8]

[c15] H. L. Berk, T. K. Fowler, L. D. Pearlstein, R. F. Post, J. D. Callen, C. W. Horton, and M. N. Rosenbluth, in Proceedings of the Conference on Plasma Physics and Controlled Nuclear Fusion, Novosibirsk, 1968 (International Atomic Energy Agency, Vienna, 1969), Vol. II, p. 151

[c16] B. Coppi, G. Laval, R. Pellat, and M. N. Rosenbluth, Nucl. Fusion 6, 261 (1966)

[c17] H. L. Berk, L. D. Pearlstein, J. D. Callen, C. W. Horton, and M. N. Rosenbluth, Phys. Rev. Letters 22, 876 (1969)

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Theory of the Propagation of Nonstable Waves

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