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A technique for the collective acceleration of an intense electron beam to very high energies is presented. A long pulse electron beam (800 ns) with a linear current rise is used to load a set of N cavities with magnetic field energy. At a time T the beam current is dropped and the stored energy in the cavities is transferred to a small portion of the following beam. Very efficient energy transfer is possible in this system, and the possibility of generating beams with energy in excess of 1 GEV exists. Verification of the acceleration mechanism in one and two cavity systems is presented. The autoacceleration process is a collective acceleration mechanism that redistributes the energy within an electron beam such that the majority of the electrons transfer their energy to only a small portion of the beam.