Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy and the kinetic theory of dusty plasmas

We consider the modern state of a consistent kinetic theory of dusty plasmas. We present the derivation of equations for microscopic phase densities of plasma particles and grains. Such equations are suitable for extending the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy to the case of dusty plasmas and for deriving the kinetic equations with regard for both elastic and inelastic particle collisions. Moreover, we describe the effective grain–grain potentials kinetically.