  The kinetic SZ effect, which is the dominant CMB source at arc-minute scales
and $\nu \sim 217$ Ghz, probes the ionized gas peculiar momentum up to the
epoch of reionization and is a sensitive measure of the reionization history.
We ran high resolution self-similar and $\Lambda$CDM hydro simulations and
built an analytical model to study this effect. Our model reproduces the
$\Lambda$CDM simulation results to several percent accuracy, passes various
tests against self-similar simulations, and shows a wider range of
applicability than previous analytical models. Our model in its continuous
version is free of simulation limitations such as finite simulation box and
finite resolution and allows an accurate prediction of the kinetic SZ power
spectrum $C_l$. For the WMAP cosmology, we find $l^2C_l/(2\pi)\simeq 0.91
\times 10^{-12} [(1+z_{\rm reion})/10]^{0.34}(l/5000)^{0.23-0.015(z_{\rm
reion}-9)}$ for the reionization redshift $6<z_{\rm reion}<20$ and
$3000<l<9000$. The corresponding temperature fluctuation is several $\mu$K at
these ranges. The dependence of $C_l$ on the reionization history allows an
accurate measurement of the reionization epoch. For the Atacama cosmology
telescope experiment, $C_l$ can be measured with $\sim 1%$ accuracy. $C_l$
scales as $(\Omega_b h)^2 \sigma_8^{4\sim 6}$. Given cosmological parameters,
ACT would be able to constrain $z_{\rm reion}$ with several percent accuracy.
Some multi-reionization scenarios degenerate in the primary CMB temperature and
TE measurement can be distinguished with $\sim 10 \sigma$ confidence.
