Accurate Iterative Analysis of the K-V Equations

Those working with alternating-gradient (A-G) systems look for simple, accurate ways to analyze A-G performance for matched beams. The useful K-V equations [1] are easily solved in the smooth approximation [2], [3], [4]. This approximate solution becomes quite inaccurate for applications with large focusing fields and phase advances. Results of efforts to improve the accuracy [5], [6] have tended to be indirect or complex. Our generalizations presented previously [7] gave better accuracy in a simple explicit format. However, the method used to derive our results (expansion in powers of a small parameter) was complex and hard to follow; also, reference [7] only gave low-order correction formulas.