Simulation of HOM wakefields in the main linacs of ILC

We investigate the electromagnetic field (e.m.) excited by a train of multiple bunches in the main superconducting linacs of the ILC. These e.m. fields are represented as a wake-field. Detailed simulations are made for the modes which constitute the long-range wake-field in new high gradient cavities. In particular, we focus our study on the modes in re-entrant cavities. Modes trapped within a limited number of cells can give rise to a significant diminution in the emittance of the beam and we pay particular attention to these modes.