The method for accelerating ions and electrons in the field-reversed configuration using odd-parity rotating magnetic fields (RMFs) in the ion-cyclotron range-of-frequencies (ICRF) is studied. The approach is based on long, accurate numerical integration of Hamilton’s equations for single-particle orbits. Rapid ion heating to thermonuclear conditions occurs in <0.1 ms in a modest-sized FRC. Strong variation of the magnetic-field strength over the confinement region prevents a true cyclotron resonance, resulting in stochastic though effective heating. Lyapunov exponents are computed to demonstrate chaotic orbits. Electrons are also effectively heated in this frequency range, primarily by a mechanism involving trapping in the wells of the azimuthal electric field. Odd-parity RMF promotes oppositely directed ion and electron motion near the minor axis, appropriate for supporting the plasma current.