to study the internal kinematics of stellar populations with different metallicities and light-element abundances. The main physical parameters of these two clusters, which share similar nucleosynthetic enrichment processes despite their different masses [e.g. @dacosta2011], are listed in Table \[tab:parameters\]. In particular, we note that the long half-mass relaxation time of $\omega\,$Centauri, which exceeds the Hubble time [@baumgardt2018], makes this cluster an ideal target to infer the initial configuration of multiple stellar populations. On the contrary, The half-mass relaxation time is shorter in M22 [$t_{\rm h}\sim 3$Gyr, e.g. @baumgardt2018].

The paper is organized as follows. In Section \[sec:data\] we introduce the dataset and describe the method to select stars with high-precision proper motions and in Section \[sec:cmds\] we identify multiple stellar populations along the CMDs. We discuss the properties of multiple populations with different iron content in Section \[sec:fe subpop\], such as their spatial distributions, rotation and velocity profiles. In Section \[sec:1P2P\] we extend the analysis to the stellar populations with different light-element abundances. Finally, the summary and the discussion of the results are provided in Section \[sec:summary\].

Data and data analysis {#sec:data}
======================

To investigate the kinematics and the spatial distributions of stellar populations in M22 and $\omega\,$Centauri, we combined 