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The possibility of using space-charge waves on an ion beam or column as a wakefield accelerator is discussed. The primary advantages of using ion plasma waves over electron plasma waves are that the kinetic energy and fall-time requirements on the driving beam are reduced. One disadvantage in using a lower plasma frequency is that a larger current is required to achieve the same accelerating gradient. The basic aspects of wakefield accelerators are reviewed and this concept is analyzed in this context. Particle-in-cell simulations show that wakefields utilizing ion waves, although more complicated than plasma wakefields, can produce acceleration.