Techniques in Machine Function Integral Calculations

摘要

This note is a summary of machine function integral expressions the author has accumulated in several years' work on accelerator physics. It is not of theoretical importance, but it can help much in practical calculation. Many accelerator physicists have noticed that to express such integrals by functions at some special points and parameters of the magnet in question has an advantage over step-by-step summation, owing to less time elapsed and better accuracy obtained. However, most of the formulae they present in papers or programs still have much room for simplification. To express the integrals as simply as possible saves time, and it can help set some parameters as function of goodness or fit function in searching for an ideal lattice configuration, though the parameters are usually considered too complicated. (ERA citation 09:012569)