During electron beam accelerator operation on Spacelab I, substantial fluxes of electrons were observed with energies greater than the initial beam energy. In this letter numerical calculations are performed for the emission of an unneutralized, one-dimensional electron beam. These calculations show clearly that space charge oscillations, which are associated with the charge buildup on the emitter, strongly modify the beam and cause the returning beam particles to have a distribution of kinetic energies ranging from half to over twice the initial energy.