Abstract
A general Hamiltonian suitable for perturbative analysis of rapidly accelerating beams is derived from first principles. With the proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, yet is able to take into account the rapid acceleration, rf focusing, magnetic focusing, and average space-charge forces in rf photoinjectors. From the linear Hamiltonian, the beam-envelope evolution is solved and analyzed, which better illuminates the invariant-envelope solution as well as the theory of emittance compensation. The third-order nonlinear Hamiltonian is derived and analyzed to some extent. To make the analysis systematic and self-contained, alternative derivations are given for the smoothed ponderomotive rf focusing and the transfer matrix of a rf cavity.
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