  A 1D, steady-state model for Brillouin and Raman backscatter from an
inhomogeneous plasma is presented. The daughter plasma waves are treated in the
strong damping limit, and have amplitudes given by the (linear) kinetic
response to the ponderomotive drive. Pump depletion, inverse-bremsstrahlung
damping, bremsstrahlung emission, Thomson scattering off density fluctuations,
and whole-beam focusing are included. The numerical code DEPLETE, which
implements this model, is described. The model is compared with traditional
linear gain calculations, as well as "plane-wave" simulations with the paraxial
propagation code pF3D. Comparisons with Brillouin-scattering experiments at the
OMEGA Laser Facility [T. R. Boehly et al., Opt. Commun. 133, p. 495 (1997)]
show that laser speckles greatly enhance the reflectivity over the DEPLETE
results. An approximate upper bound on this enhancement, motivated by phase
conjugation, is given by doubling the DEPLETE coupling coefficient. Analysis
with DEPLETE of an ignition design for the National Ignition Facility (NIF) [J.
A. Paisner, E. M. Campbell, and W. J. Hogan, Fusion Technol. 26, p. 755
(1994)], with a peak radiation temperature of 285 eV, shows encouragingly low
reflectivity. Re-absorption of Raman light is seen to be significant in this
design.
