Indirect methods for wake potential integration.pdfVIP

Indirect methods for wake potential integration Igor Zagorodnov Deutsches Elektronen-Synchrotron (DESY), Notkestrasse 85, 22603 Hamburg, Germany May 30, 2006 The development of the modern accelerator and free-electron laser projects requires to consider wake fields of very short bunches in arbitrary three dimensional structures. To obtain the wake numerically by direct integration is difficult, since it takes a long time for the scattered fields to catch up to the bunch. On the other hand no general algorithm for indirect wake field integration is available in the literature so far. In this paper we review the known indirect methods to compute wake potentials in rotationally symmetric and cavity-like three dimensional structures. For arbitrary three dimensional geometries we introduce several new techniques and test them numerically. PACS numbers: 29.27.Bd; 02.60.Cb, 02.70.Bf Submitted to Physical Review ST AB I. INTRODUCTION The fast growth of computer power allows for direct time domain calculations of short- range wake potentials for general three dimensional accelerator elements. However, for short bunches a long-time propagation of the electromagnetic field in the outgoing vacuum chamber is required in order to take into account the scattered fields reaching the bunch later. To reduce drastically the computational time and to avoid the numerical error accumulation several indirect integration algorithms were developed for rotationally symmetric geometries [3-7]. For the general case in three dimensions such an algorithm is known only for cavity- like structures [8]. In this paper we review the known methods and introduce new techniques which allow for a treatment of arbitrary three dimensional structures. Several numerical examples are presented to illustrate the accuracy and efficiency of the described methods. II. FORMULATION OF THE PROBLEM At high energies the particle beam is rigid. To obtain the electroma