  Inspired by the recent considerations of parton momentum broadening in the
glasma phase, we study the medium-induced soft gluon radiation of jet partons
at early times in heavy-ion collisions. The glasma state is assumed to be
comprised of independent color domains with homogenous longitudinal fields that
vary event by event, and we further complete this model with an event-averaging
procedure accounting for the finite correlation length. Using this description,
we evaluate the rate of medium-induced radiation from an energetic parton at
midrapidity in the glasma phase. We mainly focus on SU(2) color fields for
simplicity, also referring to the U(1) case and comparing with the BDMPS-Z rate
to gain further insight. Our results show that there is an intricate interplay
of the synchrotron-like radiation in a single color domain with the destructive
interference between different color domains, after the medium averaging is
performed. Thus, we find that the emission rate is sensitive to the matter
structure, decreasing for a glasma state populated by smaller color domains,
i.e. for a glasma with a larger characteristic saturation scale. Our approach
can be applied to more realistic backgrounds, and sets the stage for the
modelling of jet evolution in the early stages of heavy-ion collisions.
