The effect of triplet production on pair-Compton cascades in thermal   radiation
  We calculate the spectrum of photons resulting from electromagnetic cascades through thermal radiation, and examine the consequences of including triplet production in these cascades. We assume that the cascade is one-dimensional, and we find that this approximation is justified in the present work for thermal radiation with temperature less than $10^{-3} mc^2$. Results are obtained for both monoenergetic and power-law primary spectra, and for a variety of path lengths. We find that triplet production is particularly important in electron--photon cascades through thermal radiation when the primary energy exceeds $10^5 m^2c^4/kT$ for propagation over small path lengths. The importance of triplet production decreases as the path length increases, and it has no effect on saturated cascades. 
A. Mastichiadis, R.J. Protheroe and A.P. Szabo