A convergent kinetic theory of collisional star clusters (i) a
  self-consistent 'truncated' mean-field acceleration of stars
  Fundamental relaxation processes in the secular evolution of a collisional
star cluster of $N$-'point' stars have been conventionally discussed based on
either of collision kinetic theory (for strong two-body encounters) and wave
one (for statistical acceleration and gravitational polarization). If combining
the 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 the
gravitational constant and $m$ the mass of stars. The lower limit $\triangle$
of the distance between two stars is order of the Landau distance. The
truncated m.f. acceleration is a necessary consequence due to the strong
encounters and m.f. acceleration being not able to 'coexist' at specific
distance between stars.
  The present paper aims at initiating a star-cluster convergent kinetic theory
to self-consistently derive kinetic equations of star clusters, mathematically
non-divergent in distance- and wavenumber- spaces based on the truncated m.f.
acceleration, correct at time scales of the secular evolution. This will be
achieved by focusing on mathematical formulations of the Kandrup's
generalised-Landau equation including the effect of the strong encounters and
by extending the Grad's truncated distribution function and Klimontovich's
theory of non-ideal systems.
