The ion conics provide an important mechanism for the transportation of ionospheric ions to the magnetosphere. The conics are generated by a transverse acceleration of the ions and by the subsequent upward repulsion by the magnetic mirror force. Here, the acceleration of ions by a broadband lower hybrid (LH) wave is considered. Since the broadband waves have a finite correlation time, the heating occurs even in the absence of a resonance between the ions and the waves. The LH waves excited by precipitating energetic electrons in the auroral ionosphere have characteristics such that ambient cold ions (<1 eV) cannot resonate with the waves. Thus the nonresonant heating mechanism discussed here may play a direct role in generating ion conics with energies of about a few hundred electron volts at altitudes below the auroral acceleration region where the lower hybrid waves have been observed. The nonresonant mechanism may also act to preheat the ions so that the resonant heating can follow. The extent of the energy gain of H+ ranges from a few electron volts to a few keV as the turbulence noise level varies from 10-9 to 10-6 V2 m-2 s-1. The heavy ion gains comparably less energy. The calculations were done for turbulence regions that were both extended and limited in distance, the latter being particularly relevant to the generation of conics with very sharp pitch angle distributions.