  Linear accelerators containing the sequence of independently phased cavities
with constant geometrical velocity along each structure are widely used in
practice. The chain of cavities with identical cell lengths is utilized within
a certain beam velocity range, with subsequent transformation to the next chain
with higher cavity velocity. Design and analysis of beam dynamics in this type
of accelerator are usually performed using numerical simulations. A full
theoretical description of particle acceleration in an array of independent
phased cavities has not been developed. In the present paper, we provide an
analytical treatment of beam dynamics in such linacs employing Hamiltonian
formalism. We begin our analysis with an examination of beam dynamics in an
equivalent traveling wave of a single cavity, propagating within accelerating
section with constant phase velocity. We then consider beam dynamics in arrays
of cavities, utilizing an effective traveling wave propagating along with the
whole accelerator with the velocity of synchronous (reference) particle. The
analysis concluded with the determination of the matched beam conditions.
Finally, we present a beam dynamics study in 805 MHz Coupled Cavity Linac of
the LANSCE accelerator facility.
