Acoustic vortex beams possess helical wavefronts characterized by an orbital number n. In the presence of focusing, the toroidal vortex ring for n = 1 moves out of the focal plane z = d and toward the source with increasing n, accompanied by a departure from its toroidal shape. In this talk, ray theory is developed to explain this field transformation. An expression is derived for the radius and cross-sectional area of the annular channel formed by the family of rays emanating from a thin circular ring centered at the origin in the source plane z = 0. This expression leads to explicit results for the field amplitude and caustic coordinates due to a focused vortex source with an arbitrary axisymmetric amplitude distribution. Comparison with field calculations in which diffraction is included demonstrate that the caustics describe the redistribution of the global maximum and its shift toward the source plane with increasing n. For moderate focusing gains (of order 10 or 20), a toroidal vortex ring for n = 1 transforms with increasing n into a spheroidal surface in the prefocal region 0 < z < d having volume nλd 2/6, where λ is the wavelength, inside of which exists a shadow zone. [C.A.G. was supported by the ARL:UT McKinney Fellowship in Acoustics.]