Excess energy of cylindrical Coulomb crystals

Excess energies are calculated for cylindrical Coulomb crystals at very low temperature and various densities as an approximation of a cooled ion beam in a storage ring or of cold trapped ions. Even for the large six-shell structures it is found that the plane hexagonal lattice on the surface is still dominating--with an excess (Madelung) energy of -0.892 28--over the expected infinite bcc structure. The results of molecular-dynamics computer simulations are compared with results of a classical shell model which takes into account the constant intershell distances and hexagonal surface occupation.