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It is usually assumed that the space charge effects in relativistic beams scale with the energy of the beam as γ −2 , where γ is the relativistic factor. We show that for a beam accelerated in the longitudinal direction there is an additional space charge effect in free space that scales as E/γ, where E is the accelerating field. This field has the same origin as the "electromagnetic mass of the electron" discussed in textbooks on electrodynamics. We then consider the effect of this field on adoi:10.1103/physrevstab.11.014401 fatcat:uldxfvdoyravpi6zuhicwze27i