  We present a theoretical analysis of the evaporative cooling of an atomic
beam propagating in a magnetic guide. Cooling is provided by transverse
evaporation. The atomic dynamics inside the guide is analyzed by solving the
Boltzmann equation with two different approaches: an approximate analytical
ansatz and a Monte-Carlo simulation. Within their domain of validity, these two
methods are found to be in very good agreement with each other. They allow us
to determine how the phase-space density and the flux of the beam vary along
its direction of propagation. We find a significant increase for the
phase-space density along the guide for realistic experimental parameters. By
extrapolation, we estimate the length of the beam needed to reach quantum
degeneracy.
