A two-parameter accelerating FODO cell

A beamline containing accelerating cavities sandwiched between focusing and defocusing quadrupoles is made periodic by (a) postulating the simplest effect of cavities on transverse dynamics and (b) adopting a fiction that the ratio of initial to final momenta, (p_i/p _f) - not the difference in energies, (E_f - E_i ) - is the same for all cavities. While not realistic, the optics of such a linac can be expressed without reference to initial beam parameters, using methods devised for storage rings. We will derive results for a simple two-parameter thin lens model, the parameters being p_i/p_f and the ratio of quadrupole spacing to focal length