  Early in the reionization process, the intergalactic medium (IGM) would have
been quite inhomogeneous on small scales, due to the low Jeans mass in the
neutral IGM and the hierarchical growth of structure in a cold dark matter
Universe. This small-scale structure acted as an important sink during the
epoch of reionization, impeding the progress of the ionization fronts that
swept out from the first sources of ionizing radiation. Here we present results
of high-resolution cosmological hydrodynamics simulations that resolve the
cosmological Jeans mass of the neutral IGM in representative volumes several
Mpc across. The adiabatic hydrodynamics we follow are appropriate in an
unheated IGM, before the gas has had a chance to respond to the photoionization
heating. Our focus is determination of the resolution required in cosmological
simulations in order to sufficiently sample and resolve small-scale structure
regulating the opacity of an unheated IGM. We find that a dark matter particle
mass of m_dm < 50 Msun and box size of L > 1 Mpc are required. With our
converged results we show how the mean free path of ionizing radiation and
clumping factor of ionized hydrogen depends upon the ultraviolet background
(UVB) flux and redshift. We find, for example at z = 10, clumping factors
typically of 10 to 20 for an ionization rate of Gamma ~ 0.3 - 3 x 1e-12 s^-1,
with corresponding mean free paths of ~ 3 - 15 Mpc, extending previous work on
the evolving mean free path to considerably smaller scales and earlier times.
