Revised Linac Beam Dynamics Equations

The set of equations for proton linac beam dynamics given by P. Lapostolle at the Frascati Conference (1965) is derived again by a more rigorous method and extended to include relativistic effects. This is accomplished by a systematic classical perturbation theory using expansions with respect to small perturbation parameters, one describing the influence of the field on the freeparticle motion, the other relativistic effects. This permits estimates of the accuracy.