Effect of correlations on the thermal equilibrium and normal modes of a non-neutral plasma

Recent experiments have trapped small spheroidal clouds of like charges, and have cooled them to cryogenic temperatures where strong correlation effects, such as transitions to crystalline states, have been observed. The experiments have also excited normal modes of oscillation in the charge clouds. The normal modes have previously been considered theoretically using a cold-fluid model that neglects correlations. This paper examines the effect bf strong correlation on the equilibrium and on the modes. Two correlation effects are predicted to cause frequency shifts in the modes: correlation pressure changes the shape and density of the equilibrium, and bulk and shear moduli introduce restoring forces neglected in the fluid theory. A viscoelastic model of the plasma incorporating these effects is solved perturbatively to obtain formulas for the frequency shifts.