The evolution of the lunar wake in simplified geometry can be simulated via a 1½D electromagnetic particle-in-cell code. By using a sufficient number of particles per cell, we are able, for the first time, to resolve the full phase space dynamics of both electrons and ions. This simulation begins immediately downstream of the moon, before the solar wind has infilled the wake region, then evolves in the solar wind rest frame. The electrons immediately begin to move into the void but are trapped by two potential wells, thus generating vortices in phase space on both sides of the wake, between which counter-streaming electron beams interact. Ion beams are generated after the lighter electrons have moved into the void, creating a two-stream distribution which mixes in phase space due to the potentials created by the electron two-stream instability. Other structures are also evident. The simulations are consistent with both WIND observations and the results of earlier electrostatic simulations which focus only on the ion dynamics.