A generalized method for calculating wake potentials

AbsttYKt tubes vanishes. One can therefore treat more general struc-We describe a generalized method to compute wake po- tures by passing underneath the lowest radius material without tcntials created in axisymmetric structures. It relies on ex- having to introduce long beam tubes. The detailed derivation pressing the wake potentials, of any multipole order, as inte- of this method is given in [2]. Its only limitation is, for m 2 grals over the e.m. fields along an arbitrary one-dimensional 1, that the two beam tubes have equal radii. contour spanning the structure longitudinally. For perfectly This method has been implemented in the computer code conducting structures, the integration along the axis can then ABC1 [3] where the integration path is made of straight line bc replaced by choosing a contour beginning and ending on segments defined by the 3 parameters ZCF, ZCT ans RWAK the beam tubes. Thus it gencralizcs the former method of cal- as shown in Figure 1. Results from this code are presented. culating the wake potentials by integrating along a straight line at the beam tube radius. Its usefulness is illustrated with the computer code ABC1 which permits calculation of wake po-tentials in structures extending to the inside of the beam tube radius, or having unequal beam tube radii at the two sides. I