We forecast the prospective constraints on the ionized gas model f_ gas(z) at different evolutionary epochs via the tomographic cross-correlation between kinetic Sunyaev-Zeldovich (kSZ) effect and the reconstructed momentum field at different redshifts. The experiments we consider are the Planck and CMB Stage-4 survey for CMB and the SDSS-III for the galaxy spectroscopic survey. We calculate the tomographic cross-correlation power spectrum, and use the Fisher matrix to forecast the

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... of different f_ gas(z) models. We find that for constant f_ gas model, Planck can constrain the error of f_ gas (σ_f_ gas) at each redshift bin to ∼ 0.2, whereas four cases of CMB-S4 can achieve σ_f_ gas∼ 10^-3. For f_ gas(z)=f_ gas,0/(1+z) model the error budget will be slightly broadened. We also investigate the model f_ gas(z)=f_ gas,0/(1+z)^α. Planck is unable to constrain the index of redshift evolution, but the CMB-S4 experiments can constrain the index α to the level of σ_α∼ 0.01--0.1. The tomographic cross-correlation method will provide an accurate measurement of the ionized gas evolution at different epochs of the Universe.