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 ^ { 2 } C _ { l } / ( 2 \pi ) \simeq 0.91 \times 10 ^ { -12 } [ ( 1 + z _ { reion } ) / 10 ] ^ { 0.34 } ( l / 500 % 0 ) ^ { 0.23 - 0.015 ( z _ { reion } -9 ) } for the reionization redshift 6 < z _ { 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 _ { 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 .