Laser excited pulsed, electron beam systems that operate at energies from 1 MeV up to 5 MeV and pulse width from 0.1 to 100 ps are described. The systems consist of a high voltage pulser and a coaxial laser triggered gas or liquid spark gap. The spark gap discharges into a pulse forming line designed to produce and maintain a flat voltage pulse for 1 ns duration on the cathode of a photodiode. A synchronized laser is used to illuminate the photocathode with a laser pulse to produce an electron beam with very high brightness, short duration and current at or near the space charge limit. Operation of the system is described and preliminary test measurements of voltages, synchronization and jitter are presented for a 5 MeV system. Applications in chemistry, and accelerator research are briefly discussed