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 equa tion approximates the phase, The solutions of the transport equations appro ximate the amplitude as an asymptotic series in omega(-1). Examples are pre sented to illustrate that the second term in the series grows relative to t he first term along some rays, This secular behavior is associated with the exponential decay of amplitude, which occurs along chaotic rays. The resul ts suggest that chaotic ray solutions (including ray paths, phases, and amp litudes) break down rapidly with range. Although the analysis is limited to a special case that is free of caustics, the results bring into question t he use of chaotic ray solutions for long-range propagation.