  A mean field argument is used to derive a master equation for systems
simultaneously interacting with external fields and coupled environmental
degrees of freedom. We prove that this master equation preserves positivity of
the reduced density matrix. Solutions of the master equation are compared with
exact solutions for a system consisting of three spins which is manipulated
with a sequence of laser pulses while interacting with a spin-bath. Exact
solutions appear to converge to the master equation result as the number of
bath spins increases.
