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Charging of a clean two-dimensional island is studied in the regime of smallconcentration of electrons when they form the Wigner crystal. Two forms ofelectron-electron interaction potential are studied: the pure Coulombinteraction and the exponential interaction corresponding to the screening by apair of close metallic gates. The electrons are assumed to reside in aparabolic external confining potential. Due to the crystalline symmetry thecenter of the confinement can be situated at distinct positions with respect tothe crystal. With the increasing number of electrons $N$ the centerperiodically hops from one such a location to another providing the lowesttotal energy. These events occur with the period $\sim N^{1/2}$. At thesemoments in the case of the pure Coulomb interaction the charging energy of theisland has a negative correction $\approx 15%$. For the case of the exponentialinteraction at the moments of switching the capacitance becomes negative and$\sim N^{1/4}$ new electrons enter the island simultaneously. Theconfigurations of disclinations and dislocations in the island are alsostudied.Comment: 18 pages, RevTeX, plenty of beautiful Postscript figure

Charging spectrum and configurations of a Wigner crystal island