Abstract
In this article the review of interaction potentials for compound particles (i.e. atoms, clusters etc.) ofcomplex plasmas that have been derived and developed by academician Fazylkhan Baimbetov and hisstudents over the past 25 years is given. Complex plasmas such us dense non-ideal plasmas, partiallyionized plasmas, dusty plasmas are considered. We consider effective interaction potentials for classicalnon-ideal plasmas, semiclassical weakly coupled plasmas, and quantum plasmas. The effective potentialsinclude relevant effects of non-idelaity and quantum degeneracy. These effective potentials are forequilibrium and stationary out-of equilibrium state of plasmas. In the latter case, the effect of dynamicalscreening resulting in oscillatory pattern of the potential due to formation of the wakefield considered inboth classical and quantum plasmas is taken into account. There appears anomalous behavior of thewakefield in quantum plasmas. Atoms and dust particles are considered to be compound particles withallowance for polarization, i.e acquiring a dipole moment. The screening of the field of such dipoles areconsidered making use the multipole expansion of the screened Coulomb potential. Additionally, thediscussion of these results comparing to works of researchers from elsewhere is presented. The furtherdevelopment of the effective potential theory should determine what effect the plasma streaming willhave on transport properties such as viscosity and diffusion of non-ideal plasmas.