Electrons backstreaming into Earth's foreshock generate waves near the plasma frequency fp by the beam instability. Two versions of the beam instability exist: the ''reactive'' version, in which narrow-band waves grown by bunching the electrons in space, and the ''kinetic'' version, in which broadband growth occurs by a maser mechanism. Recently, it has been suggested that (1) the backstreaming electrons have steep-sided ''cutoff'' distributions which are initially unstable to the reactive instability, (2) the back reaction to the wave growth causes the instability to pass into its kinetic phase, and (3) the kinetic instability saturates by quasi-linear relaxation. In this paper we present two-dimensional simulations of the reactive instability for Maxwellian beams and cutoff distributions. The results of the simulations are consistent with suggestions 1 and 2 above; suggestion 3 is not addressed here. We demonstrate that the reactive instability is a bunching instability and that the reactive instability saturates and passes over into the kinetic phase by particle trapping. A reactive/kinetic transition is shown to most likely occur within 1 km and 50 km of the bow shock. We suggest that the frequency of the intense narrow-band waves decrease from above fp to perhaps 0.9 fp (dependent on the beam density) with increasing penetration into the high beam speed region (vb/Ve>10) of the foreshock, before the wave frequency rises again as the waves become broadband deeper in the foreshock. Both the simulation results and numerical solutions of the dispersion equation indicate that for the observed beam parameters the center frequency of the waves near the foreshock boundary should be between 0.9 fp and 0.98 fp, rather than above fp as previously believed. The simulation results indicate that the effects of spatial inhomogeneity are vital for a quantitative understanding of the foreshock waves. ¿ American Geophysical Union 1989