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Fundamental relaxation processes in the secular evolution of a collisionalstar cluster of $N$-'point' stars have been conventionally discussed based oneither of collision kinetic theory (for strong two-body encounters) and waveone (for statistical acceleration and gravitational polarization). If combiningthe both theories together, one must introduce a self-consistent 'truncated'Newtonian mean-field (m.f.) acceleration of star at position $r$ and time $t$due to a phase-space distribution function $f\left(r', p',t\right)$ for stars$A^{\triangle}(r,t)=-Gm\left(1-\frac{1}{N}\right)\int_{\mid r-r' \mid >\triangle}\frac{r-r'}{\mid r-r' \mid^{3}}f\left(r',p',t\right)\text{d}^{3}{r'}\text{d}^{3}{p'},$ where $G$ is thegravitational constant and $m$ the mass of stars. The lower limit $\triangle$of the distance between two stars is order of the Landau distance. Thetruncated m.f. acceleration is a necessary consequence due to the strongencounters and m.f. acceleration being not able to 'coexist' at specificdistance between stars.  The present paper aims at initiating a star-cluster convergent kinetic theoryto self-consistently derive kinetic equations of star clusters, mathematicallynon-divergent in distance- and wavenumber- spaces based on the truncated m.f.acceleration, correct at time scales of the secular evolution. This will beachieved by focusing on mathematical formulations of the Kandrup'sgeneralised-Landau equation including the effect of the strong encounters andby extending the Grad's truncated distribution function and Klimontovich'stheory of non-ideal systems.

A convergent kinetic theory of collisional star clusters (i) a self-consistent 'truncated' mean-field acceleration of stars