Order in confined ions

The phenomena associated with the ordering in classical finite one-component plasmas are reviewed with emphasis on simulations. The inevitable surface of finite systems imposes boundary conditions that have to be satisfied. The consequence of this is shell structure in the interior, which, for sufficiently large clouds, gives way to the body-centred cubic order characteristic of infinite Coulombic matter. The density of ions is constant if the confining potential is harmonic, but for forces with different radial dependence the density is non-uniform, becoming a hollow shell for a square well. The phase transition from an ordered state to a liquid in a finite system occurs at a temperature that is lower than that for an infinite system, with an associated latent heat of melting. This lowering in temperature depends on the size (number of ions) and is associated with the surface-to-volume ratio. For time-dependent confining forces, such as are characteristic of radio-frequency quadrupole (Paul) traps, the concept of temperature is complicated by the 'micro-motion' associated with the confining field. Simulations indicate that periodic motion is coupled to the random thermal motion very weakly for 'cold' systems