  Spontaneous radiation plays an important role in SASE FELs and storage ring
FELs operating in giant pulse mode. It defines the correlation function of the
FEL radiation as well as its many spectral features. Simulations of these
systems using randomly distributed macro-particles with charge much higher that
of a single electron create the problem of anomalously strong spontaneous
radiation, limiting the capabilities of many FEL codes. In this paper we
present a self-consistent macro-particle model which provided statistically
exact simulation of multi-mode, multi-harmonic and multi-frequency
short-wavelength 3-D FELs including the high power and saturation effects. The
use of macro-particle clones allows both spontaneous and induced radiation to
be treated in the same fashion. Simulations using this model do not require a
seed and provide complete temporal and spatial structure of the FEL optical
field.
