[en] Extensive analytical studies suggest that significant currents of high energy ions can be obtained by collective acceleration via large amplitude cyclotron waves in a non-neutral intense relativistic electron beam. This acceleration mechanism was previously demonstrated in fully self-consistent two-dimensional computer simulations for low ion current and energy. However, the simulations employed a packet of cyclotron waves created ad hoc upstream of the acceleration region. Acceleration was limited by phase-mixing and damping of the packet. Results are presented of an ongoing effort to simulate, first, realistic growth of large amplitude, single frequency cyclotron waves in the relativistic electron beam and, second, acceleration of various ion currents with those waves