Wakefield of two counter-rotating beams

This paper deals with the problem of defining the wakefunction for two counter-moving charges, i.e. two charges moving in opposite direction. In this case, the distance between the charges cannot be considered constant. From the counter-moving wakefunction the counter-moving wakepotential is derived. An example of this kind of wakepotential for a lossless pill-box cavity is obtained analitically and compared with numerical simulations.