  The evolution of two colliding beams in a linear accelerator can be described
by two coupled Vlasov equations. In PEP-NOTE-325 by S. Kheifets and A. W. Chao
the case without external focusing was considered. In this paper we derive the
equilibrium distribution and the tune shift in the presence of external
focusing. Motion is considered only in the vertical direction and the beams are
presumed to be one-dimensional.
