We are discussing quasistatic hybrid PIC/fluid plasma simulation approach. In addition to the particle-in-cell algorithm, it uses a new symplectic numerical scheme for wake field simulations. Specially designed for the accurate simulation of very long wake fields, this scheme is capable of simulating ?1000 plasma oscillations of the wake generated by a powerful driver - a proton bunch or a laser pulse. A comprehensive description of the discretization schemes is given, and we demonstrate the code’s correctness and its order of accuracy. Also, its superior effi ciency in the plasma wake field acceleration (PWFA) regime is shown. We also discuss its implementation on massively parallel supercomputers.