Instabilities near the lower hybrid frequency are investigated by numerically solving the linear Vlasov electromagnetic dispersion equation. The configuration is that of two unmagnetized ion components, a less dense beam and a more dense core, streaming across a uniform magnetic field with magnetized electrons in the zero momentum frame. All three components are considered to have similar temperatures. This paper studies the parametric dependences of maximum growth rate for three distinct modes: the electron/ion beam modified two-stream instability, the electron/ion core modified two-stream instability, and the ion/ion lower hybrid instability. In the electrostatic limit the electron/beam instability has a lower threshold and larger growth rate than its electron/core counterpart. Except near equal beam and core densities, our results also suggest that the electron/beam instability has a maximum growth rate that is equal to or greater than that of the ion/ion instability for all plasma beta values. Thus the electron/beam modified two-stream instability is a likely candidate to account for the presence of lower hybrid fluctuations in the foot of the earth's bow shock at low beta. ¿American Geophysical Union 1987