The longitudinal high-frequency impedance of a periodic accelerating structure

In many future collider and FEL designs intense, short bunches are accelerated in a linear accelerator. For example, in parts of the Linac Coherent Light Source (LCLS) a bunch with a peak current of 3.4 kA and an RMS length of 30 microns will be accelerated in the SLAC linac. In such machines, in order to predict the beam quality at the end of acceleration it is essential to know the short range wakefields or, equivalently, the high frequency impedance of the accelerating structure. R. Gluckstern has derived the longitudinal, high-frequency impedance of a periodic structure, a solution which is valid for a structure with a small gap-to-period ratio. We use his approach to derive a more general result, one that is not limited to small gaps. In addition, we compare our results with numerical results obtained using a field matching computer program.