We propose a local, {O(N)} molecular dynamics algorithm for the simulation of charged systems. The long ranged Coulomb potential is generated by a propagating electric field that obeys modified Maxwell equations. On coupling the electrodynamic equations to an external thermostat we show that the algorithm produces an effective Coulomb potential between particles. On annealing the electrodynamic degrees of freedom the field configuration converges to a solution of the Poisson equation much like the electronic degrees of freedom approach the ground state in ab initio molecular dynamics.