Fast polynomial approach to calculating wake fields

摘要

In the computation of transverse wake field effects in accelerators, it is necessary to compute expressions of the form given in equations (1). It is usually desired to compute this a large number of times, the values of z(sub i) and x(sub i) being different at each iteration, other quantities remaining the same. The problem in practical applications is that the computational work grows as N(sub m)(sup 2). Even using parallel computation to achieve speedup, the elapsed time to obtain a result still increases linearly with N(sub m). The authors introduce here an approximate method of evaluating the sum in (1) whose computational work increases only as N(sub m)logN(sub m). It involves some significant initial computation which does not have to be repeated at each subsequent iteration. The basis of the approach is to replace the individual contributions of a group of distant macroparticles with a local series expansion. In this respect, it is similar to the so called fast multipole method.