Clumping factors of HII, HeII and HeIII
  Estimating the intergalactic medium ionization level of a region needs proper
treatment of the reionization process for a large representative volume of the
universe. The clumping factor, a parameter which accounts for the effect of
recombinations in unresolved, small-scale structures, aids in achieving the
required accuracy for the reionization history even in simulations with low
spatial resolution.
  In this paper, we study for the first time the redshift evolution of clumping
factors of different ionized species of H and He in a small but very high
resolution simulation of the reionization process. We investigate the
dependence of the value and redshift evolution of clumping factors on their
definition, the ionization level of the gas, the grid resolution, box size and
mean dimensionless density of the simulations.
