Wave dynamics of regular and chaotic rays

Technical Report · Thu Sep 01 04:00:00 EDT 1983

DOI:https://doi.org/10.2172/5373229· OSTI ID:5373229

McDonald, S W

In order to investigate general relationships between waves and rays in chaotic systems, I study the eigenfunctions and spectrum of a simple model, the two-dimensional Helmholtz equation in a stadium boundary, for which the rays are ergodic. Statistical measurements are performed so that the apparent randomness of the stadium modes can be quantitatively contrasted with the familiar regularities observed for the modes in a circular boundary (with integrable rays). The local spatial autocorrelation of the eigenfunctions is constructed in order to indirectly test theoretical predictions for the nature of the Wigner distribution corresponding to chaotic waves. A portion of the large-eigenvalue spectrum is computed and reported in an appendix; the probability distribution of successive level spacings is analyzed and compared with theoretical predictions. The two principal conclusions are: 1) waves associated with chaotic rays may exhibit randomly situated localized regions of high intensity; 2) the Wigner function for these waves may depart significantly from being uniformly distributed over the surface of constant frequency in the ray phase space.

• Research Organization: California Univ., Berkeley (USA). Dept. of Physics; Lawrence Berkeley Lab., CA (USA)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5373229
• Report Number(s): LBL-14837; ON: DE84006061
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700108* -- Fusion Energy-- Plasma Research-- Wave Phenomena
EIGENFUNCTIONS
EIKONAL APPROXIMATION
ELECTROMAGNETIC RADIATION
FUNCTIONS
HEATING
HIGH-FREQUENCY HEATING
MATHEMATICAL MODELS
PLASMA
PLASMA HEATING
PLASMA WAVES
RADIATIONS
WAVE PROPAGATION