It is known that homogeneous distribution of particles in Coulomb-like
systems can be unstable, and spatially inhomogeneous structures can be formed.
A simple method for describing such inhomogeneous systems and obtaining spacial
distributions of electron density is proposed and applied to the case of
two-dimensional electron systems on surface of liquid helium. A free energy
functional for the model in mean field approximation is obtained. Creation of
various types of structures, such as long-range periodical modulation and
multi-electron dimples, is predicted by minimizing this functional
