  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.
