  We studied the structural, dynamical properties and melting of a
quasi-one-dimensional system of charged particles, interacting through a
screened Coulomb potential. The ground state energy was calculated and,
depending on the density and the screening length, the system crystallizes in a
number of chains. As a function of the density (or the confining potential),
the ground state configurations and the structural transitions between them
were analyzed both by analytical and Monte Carlo calculations. The system
exhibits a rich phase diagram at zero temperature with continuous and
discontinuous structural transitions. We calculated the normal modes of the
Wigner crystal and the magneto-phonons when an external constant magnetic field
$B$ is applied. At finite temperature the melting of the system was studied via
Monte Carlo simulations using the $modified$ $Lindemann$ $criterion$ (MLC). The
melting temperature as a function of the density was obtained for different
screening parameters. Reentrant melting as a function of the density was found
as well as evidence of directional dependent melting. The single chain regime
exhibits anomalous melting temperatures according to the MLC and as a check we
study the pair correlation function at different densities and different
temperatures, formulating a different criterion. Possible connection with
recent theoretical and experimental results are discussed and experiments are
proposed.
