  We study the minimizers of an energy functional with a self-consistent
magnetic field, which describes a quantum gas of almost-bosonic anyons in the
average-field approximation. For the homogeneous gas we prove the existence of
the thermodynamic limit of the energy at fixed effective statistics parameter,
and the independence of such a limit from the shape of the domain. This result
is then used in a local density approximation to derive an effective
Thomas--Fermi-like model for the trapped anyon gas in the limit of a large
effective statistics parameter (i.e., "less-bosonic" anyons).
