  We present a theoretical analysis of the evaporative cooling of a
magnetically guided atomic beam by means of discrete radio-frequency antennas.
First we derive the changes in flux and temperature, as well as in collision
rate and phase-space density, for a single evaporation step. Next we show how
the occurrence of collisions during the propagation between two successive
antennas can be probed. Finally, we discuss the optimization of the evaporation
ramp with several antennas to reach quantum degeneracy. We estimate the number
of antennas required to increase the phase-space density by several orders of
magnitude. We find that at least 30 antennas are needed to gain a factor $10^8$
in phase-space density.
