  We explore a Boltzmann scheme for studying the evolution of compact binary
populations of globular clusters. We include processes of compact-binary
formation by tidal capture and exchange encounters, binary destruction by
dissociation and other mechanisms, and binary hardening by encounters,
gravitational radiation and magnetic braking, as also the orbital evolution
during mass transfer, following Roche lobe contact. For the encounter processes
which are stochastic in nature, we study the probabilistic, continuous limit in
this introductory work, deferring the specific handling of the stochastic terms
to the next step. We focus on the evolution of (a) the number of X-ray sources
N_{XB} in globular clusters, and (b) the orbital-period distribution of the
X-ray binaries, as a result of the above processes. We investigate the
dependence of N_{XB} on two essential cluster properties, namely, the star-star
and star-binary encounter-rate parameters 'Gamma' and 'gamma', which we call
Verbunt parameters. We compare our model results with observation, showing that
the model values of N_{XB} and their expected scaling with the Verbunt
parameters are in good agreement with results from recent X-ray observations of
Galactic globular clusters, encouraging us to build more detailed models.
