  Self-propelled particles that are subject to noise are a well-established
generic model system for active matter. A homogeneous alignment field can be
used to orient the direction of the self-propulsion velocity and to model
systems like phoretic Janus particles with a magnetic dipole moment or
magnetotactic bacteria in an external magnetic field. Computer simulations are
used to predict the phase behavior and dynamics of self-propelled Brownian
particles in a homogeneous alignment field in two dimensions. Phase boundaries
of the gas-liquid coexistence region are calculated for various P\'eclet
numbers, particle densities, and alignment field strengths. Critical points and
exponents are calculated and, in agreement with previous simulations, do not
seem to belong to the universality class of the 2D Ising model. Finally, the
dynamics of spinodal decomposition for quenching the system from the one-phase
to the two-phase coexistence region by increasing P\'eclet number is
characterized. Our results may help to identify parameters for optimal
transport of active matter in complex environments.
