One important issue with regard to acceleration of electrons in free s
pace using intense laser beams is the phase slippage of the electrons
relative to the electromagnetic field. This arises from a phase veloci
ty mismatch between the electron and light wave. Left uncontrolled thi
s slippage can result in degradation of the e-beam characteristics (e.
g., emittance) and dispersion of the electron bunches. By a method sim
ilar to microwave accelerators, multistaging offers a means to control
the e-beam evolution by tuning each successive stage. The phase of th
e electron bunches relative to the laser field at the entrance of each
section determines the acceleration and/or focusing that ensues in th
at section; therefore, the entrance phase is a natural tuning paramete
r. It is shown that by controlling the entrance phase it is possible t
o preserve the e-beam quality, both transverse (emittance) and longitu
dinal (bunching, energy spread). Calculations of the longitudinal and
transverse beam dynamics are performed to determine the evolution of a
finite-emittance e beam from stage to stage. By this method the condi
tions on entrance phase that allow successful e-beam trapping are foun
d. It is also shown that conditions that assure e-beam trapping automa
tically preserve the overall beam quality.