398	NONNEUTRAL PLASMAS

γ = 1.00	γ = 0.75	γ = 0.60	γ = 0.50
	γ = 0.35	γ = 0.20

γ= 0.05

γ= 0.01

Fig. 10.23. Configurations of a two–dimensional cluster containing 37 ions for di erent

values of the anisotropy parameter γ (Lozovik and Rakoch 1999).

The two–dimensional confinement can be anisotropic as well. Figure 10.23 shows di erent configurations of a two–dimensional Coulomb cluster of 37 ions, corresponding to di erent values of the anisotropy parameter (Lozovik and Rakoch 1998, 1999). Here, the parameter γ determines the anisotropy of the trap,

Uext = γ	xi2 + (2 − γ) yi2,	(10.11)
i	i

so that γ = 1 corresponds to circular symmetry. As γ increases the number of rings decreases and finally the cluster is stretched into a one–dimensional string with inhomogeneous interparticle distance.

As the temperature increases, the ion oscillations around the equilibrium increase as well and eventually the cluster melts (Lozovik 1987; Bedanov and Peeters 1994; Lozovik and Rakoch 1998, 1999). The melting occurs in two stages, both in two– and three–dimensional cases. At the first stage, when the temperature is relatively low, the orientational melting starts – the transition from the steady configuration to the state with enhanced rotational oscillations of the neighboring (rings) shells, yet the ions within each shell remain stable. At the second stage the radial order disappears as well. As the number of ions in a cluster increases, the first stage becomes less pronounced and the orientational melting can only be observed in a few shells near the surface.

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