Secular behavior and breakdown of chaotic ray solutions

Solutions of the eikonal equation and the first two transport equations are derived for problems involving ray chaos. The solution of the eikonal equation approximates the phase. The solutions of the transport equations approximate the amplitude as an asymptotic series in /spl omega//sup -1/. Examples are presented to illustrate that the second term in the series grows relative to the first term along some rags. This secular behavior is associated with the exponential decay of amplitude, which occurs along chaotic rays. The results suggest that chaotic ray solutions (including ray paths, phases, and amplitudes) break down rapidly with range. Although the analysis is limited to a special case that is free of caustics, the results bring into question the use of chaotic ray solutions for long-range propagation.