Pragmatic Method of Deducing a Wake Function for a General 3D Structure

Abstract

We present a practical and self-consistent approach to obtaining a wake function to be used in beam instability simulations from a numerical wake potential computed with an electromagnetic (EM) field solver for a finite length test bunch. The wake potential is processed to a numerical impedance by Fourier transforming (FT) it to the frequency domain and deconvoluting the bunch spectrum. We then decompose it into a set of well-known analytical functions that satisfy the causality and Maxwell’s equations, eliminating the unphysical artifacts possibly contained in numerical solutions. Additional inverse FT of the decomposed impedance function into time domain allows retrieving an effective wake function. Relatively long bunches can be used for the numerical wake potential calculations, significantly reducing the computation time. We show that the method can be applied to a general 3D structure, which opens up the possibility of finding effective wake functions of complicated realistic vacuum chambers.