Global scattering matrix technique applied to the calculation of higher order modes for ILC superconducting cavities

A cascaded scattering matrix approach is used to determine the electromagnetic (EM) field in the main ILC cavities. This approach is used to compute higher order EM modes in the baseline configuration, and high gradient alternative configurations. We present results on three cavity designs: TESLA, Cornell University's reentrant, and KEK's "Ichiro". This approach allows realistic experimental errors to be incorporated in the studies in an efficient manner and allows several cavities to be modelled en masse. Simulations are presented on the wake-fields in super-structures and segments of entire modules. Details on trapped eigen-modes and means to avoid them are delineated.