An atom laser is a device which would ideally produce a coherent excit
ation of a single mode of the Bose-atom field. That is to say, an atom
laser field would have a well defined number of atoms, and a slow rat
e of phase diffusion. Here we consider an atom laser model recently pr
oposed by Holland at al, based on evaporative cooling of atoms. We ext
end their model, and give approximate analytical results for the time-
dependent intensity and phase statistics of the atom laser in differen
t regimes. Although the intensity fluctuations may be relatively small
, the laser linewidth is always in excess of the bare linewidth of the
laser mode. Nevertheless, in one regime (weak collisions), the laser
linewidth may be less than the output flux of atoms, which is a minimu
m requirement for considering the output to be coherent.