### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4pPA2. Computation of beam diffraction using a non-asymptotic ray theory.

**Ronald A. Roberts
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*Ctr. for Non-Destructive Evaluation ASCII, Iowa State Univ., Ames, IA
50011
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A technique for numerical computation of acoustic beam propagation is
presented based on a nonasymptotic ray theory. Similar to conventional ray
theory, an ansatz of the form (phi)(x)=A(x)e[sup if(x)] is used to transform
the Helmholtz equation for time harmonic waves. Imposing A(x) and f(x) are both
real leads to two coupled nonlinear PDEs for A(x) and f(x). Conventional ray
methods employ an expansion in frequency to decouple one of these equations
(eikonal equation) which is solved by ray tracing (method of characteristics).
Solution of the remaining transport equation then follows. In the present
method, the two coupled nonlinear PDEs are solved self-consistently without an
expansion in frequency, resulting in a ray tracing procedure which
automatically diffracts at caustics, etc., producing exact field results.
Discussion will focus on procedures to insure numerical stability. Application
to beam diffraction problems (focusing, beam spreading) will be demonstrated.