The moment approach to high-order accelerator beam optics

High-current beams must be matched to high order to minimize emittance growth and particle losses. For matching problems, the moment approach, in which we describe the particle beam by the moments of its distribution, is particularly valuable. A variety of analytical results are available for linear motion. The moment approach is also the basis of the 3-D space-charge simulation code bedlam, in which the dynamical variables are the moments. Moment simulation codes are especially useful for numerically computing beams matched to nonlinear systems. This paper reviews the moment approach, presents a few new results, describes work in progress on new space-charge models, and outlines further potential applications of and improvements to moment-method simulations.