  Axion clumps in an external magnetic field can emit electromagnetic radiation
which causes them to decay. In the presence of a plasma, such radiation can
become resonant if the clump frequency matches the plasma frequency. Typically,
the decay or back-reaction of the clump is ignored in the literature when
analyzing such radiation. In this paper we present a self consistent,
semi-analytic approach which captures axion back-reaction using energy
conservation. We find that inclusion of back-reaction changes the clump
frequency over time enabling clumps with a range of different initial
frequencies to become resonant at some point in their time evolution.
