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Using archival {\it Fermi}-LAT data with a time span of $\sim12$ years, westudy the population of Millisecond Pulsars (MSPs) in Globular Clusters (GlCs)and investigate their dependence on cluster dynamical evolution in the MilkyWay Galaxy. We show that the $\gamma$-ray luminosity ($L_{\gamma}$) andemissivity ($\epsilon_{\gamma}=L_{\gamma}/M$) are good indicators of thepopulation and abundance of MSPs in GlCs, and they are highly dependent on thedynamical evolution history of the host clusters. Specifically speaking, thedynamically older GlCs with more compact structures are more likely to havelarger $L_{\gamma}$ and $\epsilon_{\gamma}$, and these trends can be summarizedas strong correlations with cluster stellar encounter rate $\Gamma$ and thespecific encounter rate ($\Lambda=\Gamma/M$), with $L_{\gamma}\propto\Gamma^{0.70\pm0.11}$ and $\epsilon_{\gamma}\propto \Lambda^{0.73\pm0.13}$ fordynamically normal GlCs. However, as GlCs evolve into deep core collapse, thesetrends are found to be reversed, implying that strong encounters may have leadto the ejection of MSPs from core-collapsed Systems. Besides, the GlCs arefound to exhibit larger $\epsilon_{\gamma}$ with increasing stellar massfunction slope, decreasing tidal radius and distances from the Galactic Center(GC). These correlations indicate that, as GlCs losing kinetic energy andspiral in towards GC, tidal stripping and mass segregation have a preference inleading to the loss of normal stars from GlCs, while MSPs are more likely toconcentrate to cluster center and be deposited into the GC. Moreover, we gauge$\epsilon_{\gamma}$ of GlCs is $\sim10-1000$ times larger than the Galacticbulge, the latter is thought to reside thousands of unresolved MSPs and mayresponsible for the GC $\gamma$-ray excess, which support that GlCs aregenerous contributors to the population of MSPs in the GC.

A Fermi-LAT Study of Globular Cluster Dynamical Evolution in Milky Way Galaxy: Millisecond Pulsars as the Probe