  We examine the stability of ringlike configurations of N charges on a plane
interacting through the potential $V(z_1,...,z_N)=\sum_i |z_i|^2-\sum_{i<j}
ln|z_i-z_j|^2$. We interpret the equilibrium distributions in terms of a shell
model and compare predictions of the model with the results of numerical
simulations for systems with up to 100 particles.
