An Instability in the Radiative Ionization of Atomic Hydrogen/Helium Gas
  We show that the process of photoionizing a gas of atomic hydrogen and helium by line radiation whose energy is slightly above the helium single-ionization threshold is unstable if the helium fraction by number is less than approximately one half. However, in the two scenarios we consider here, based on the Decaying Dark Matter (DDM) model of cosmological reionization, there is no significant growth. In the first scenario we consider ionization and recombination to be approximately in equilibrium. This is relevant to high photon flux rates and early reionization, but in that case the heating is balanced by Compton cooling, which is very stabilizing. In the second scenario we ignore recombination. This is relevant to low photon flux rates or to the last stage of the reionization. In that case there is too little growth on a cosmological time scale to be significant. 
Ethan Bradford and Craig Hogan