  The kSZ effect has been detected at z<1 using various techniques and data
sets. The ongoing and upcoming spectroscopic galaxy surveys such as DESI and
PFS will push the detection beyond z = 1, and therefore map the baryon
distribution at high redshifts. Such detection can be achieved by both the kSZ
stacking and tomography methods. While the two methods are theoretically
equivalent, they differ significantly in the probed physics and scales, and
required data sets. Taking the combination of PFS and ACT as an example, we
build mocks of kSZ and galaxies, quantify the kSZ detection S/N, and compare
between the two methods. We segment the PFS galaxies into three redshift bins:
0.6 < z < 1.0, 1.0 < z < 1.6, and 1.6 < z < 2.4. For tomography method, our
analysis reveals that the two higher redshift bins exhibit higher S/N, with
values of 32 and 28, respectively, compared to the first redshift bin (S/N =
8). This is attributed to not only the increasing of electron density with
redshifts, but also the larger survey volume and the reduced non-linearity,
facilitating velocity reconstruction at higher redshifts. Therefore, the
capability of the PFS survey to measure high redshift kSZ effect stands as a
substantial advantage over other spectroscopic surveys at lower redshift. The
S/N of kSZ stacking largely depends on the number of clusters/groups available
from another photometric survey. But in general, its S/N is lower than that of
kSZ tomography. Incorporating next-generation CMB surveys like CMB-S4,
characterized by significantly reduced instrument noise and improved angular
resolution, is expected to enhance tomographic detection by a factor of ten and
stacking detection by five. This future high S/N detection holds the promise of
not only providing precise constraints on the overall baryon abundance but also
initiating a new insight into baryon distribution.
