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Rooms with a view: A novel approach to iterated multidimensional wave conversion |
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| Authors: | ER Tracy AJ BrizardD Johnston AN KaufmanAS Richardson N Zobin |
| Institution: | a Department of Physics, College of William and Mary, Williamsburg, VA 23187-8795, USA b Department of Chemistry and Physics, Saint Michael’s College, Box 254, One Winooski Park, Colchester, VT 05439, USA c Lawrence Berkeley National Laboratory and Physics Department, UC Berkeley, Berkeley, CA 94720, USA d T-5 Applied Mathematics and Plasma Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA e Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA |
| Abstract: | Ray tracing in the presence of linear mode conversion leads to a ‘splitting’ of an incoming ray into two outgoing rays. When the rays are confined to a cavity, the rays can re-enter the conversion region many times, leading to iterated conversion. In this paper, we present new methods for the analysis of this problem. These involve a shift from local to global methods of analysis, and a shift in emphasis from the study of ray evolution in the dispersion surface to the study of the iterated dynamics of rays crossing the conversion surface. The analytical methods are quite general and can be applied in phase spaces of arbitrary dimension. In two spatial dimensions, (x, y), i.e. with a four-dimensional ray space, (x, y, kx, ky), rays are confined to three-dimensional regions called rooms, with one room for each wave type. In these rooms the rays do not cross, but when they intersect the conversion surface a family of converted rays is produced in the other room. The use of rooms allows a full view of the phase space dynamics of the iterated conversion of ray families. A simple two-dimensional model, inspired by the Budden resonance model, is presented as an example of these ideas. |
| Keywords: | WKB Ray tracing Eikonal theory Mode conversion Cavity Visualization |
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