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Dirac-bracket structure in multidimensional mode conversion |
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| Authors: | AJ Brizard ER TracyAN Kaufman D JohnstonN Zobin |
| Institution: | a Department of Chemistry and Physics, Saint Michael’s College, Box 254, One Winooski Park, Colchester, VT 05439, USA b Department of Physics, College of William and Mary, Williamsburg, VA 23187-8795, USA c Lawrence Berkeley National Laboratory and Physics Department, UC Berkeley, Berkeley, CA 94720, USA d Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA |
| Abstract: | The intersection of two (2n − 1)-dimensional dispersion manifolds Da and Db in the 2n-dimensional ray phase space P yields a (2n − 2)-dimensional conversion manifold M≡Da∩Db that naturally possesses a Dirac-bracket structure that is inherited from the canonical Poisson bracket on ray phase space. The canonical symplectic two-form Ω ≡ Ω∥ + Ω⊥, defined on the 2n-dimensional tangent plane Tz0P≡Tz0M⊕(Tz0M)⊥, can thus be decomposed into the Dirac two-form Ω∥ on the (2n − 2)-dimensional tangent plane Tz0M at a conversion point z0∈M, and the symplectic two-form Ω⊥ on its orthogonal 2-dimensional complement (Tz0M)⊥. These two symplectic two-forms are introduced in our analysis of multidimensional mode conversion, where their respective geometrical roles are defined. We note that since the Dirac-bracket structure Ω∥ vanishes identically when n = 1, it represents a new structure in multidimensional (n > 1) mode conversion theory. |
| Keywords: | Dirac-bracket structure Mode conversion |
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