Modeling fine particle (dusty) plasmas and charge-stabilized colloidal   suspensions as inhomogeneous Yukawa systems
  In order to give a basis for the structure and correlation analysis of fine particle (dusty) plasma and colloidal suspensions, thermodynamic treatment of mixtures of macroscopic and microscopic charged particles within the adiabatic response of the latter is extended to include the case where the system is finite and weakly inhomogeneous. It is shown that the effective potential for macroscopic particles is composed of two elements: mutual Yukawa repulsion and a confining (attractive) Yukawa potential from their `shadow' (the average charge density of macroscopic particles multiplied by the minus sign). The result clarifies the relation between two approaches hitherto taken where either a parabolic one-body potential is assumed or the average distribution is assumed to be flat with finite extension. Since the satisfaction of the charge neutrality is largely enhanced by the existence of macroscopic particles, the assumption of the flat electrostatic potential and therefore flat average distribution of macroscopic particles in the domain of their existence is expected to be closer to reality than the assumption of the parabolic potential in that domain. 
Hiroo Totsuji
physics.plasm-ph