Development of effective potentials for complex plasmas

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