Metaplectic formulation of linear mode conversion
Journal Article
·
· Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23185 (United States)
- Lawrence Berkeley Laboratory and Department of Physics, University of California, Berkeley, Berkeley, California 94720 (United States)
The metaplectic formulation of linear mode conversion is presented. We begin by discussing the connection between wave operators in weakly inhomogeneous media, their symbols, and related pseudodifferential operators. A brief summary of WKB theory and Hamiltonian ray dynamics is given. In regions where mode conversion occurs, the WKB approximation breaks down and must be replaced by an appropriate local approximation. This is done by expanding in a Taylor series about the degenerate region and keeping only the leading-order terms. At leading order a linear canonical transformation on the ray phase space can be performed which brings the system into a simpler form. This linear canonical transformation induces a unitary transformation, called a [ital metaplectic] [ital transformation], in the wave function's Hilbert space. This is a generalization of the Fourier transformation. The advantage of metaplectic techniques over Fourier techniques lies in the wider range of transformations available to simplify the problem. We show how to construct the [ital S] matrix, relating incoming and outgoing waves, and the Wigner tensor. We examine the Wigner function in detail with particular attention to its asymptotic properties.
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 6035307
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 48:3; ISSN PLEEE8; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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