The classical Poisson-Boltzmann interaction predicts that the electrostatic interaction between DNA strands is repulsive. DNA is indeed soluble in aqueous media in the presence of mono-vent salt. Small amounts of poly-valent ions produce condensation phenomena which are believed to play an important role for DNA compaction in viruses and bacteria and which violates the Poisson-Boltzmann theory. Numerical simulations will be presented which demonstrate that these condensation phenomena are due to the build of strong, short-range correlations between ions inside the Manning layer, leading to formation of a Wigner crystal.