  We present a model for a continuous atom laser in a one-dimensional
waveguide. The beam is formed by continuous Raman outcoupling of a trapped
one-dimensional (quasi-)condensate, which is created by imposing a tightly
confining transverse optical potential on a three-dimensional magnetically
trapped ultracold thermal gas. The trapped (quasi-)condensate is modelled by a
stochastic Langevin equation, in which pumping arises naturally from the
surrounding three-dimensional thermal cloud, which acts as its heat bath. When
the outcoupling is turned on, such pumping leads to continuous replenishing of
the (quasi-)condensate, and thus to a steady-state operation for the atom
laser, which is described by a nonlinear Schroedinger equation, coupled to the
Langevin equation for the (quasi-)condensate. This model is used to study the
temporal and spatial evolution of the coherence length of the
(quasi-)condensate and the atom laser over the entire system.
