The path‐integrated linear growth of electromagnetic ion cyclotron waves in the outer (L ≥ 7) magnetosphere is investigated using a realistic thermal plasma distribution with an additional anisotropic energetic ring current H+ to provide free energy for instability. The results provide a realistic simulation of the recent AMPTE observations. For conditions typical of the dayside magnetosphere, high plasma beta effects reduce the group velocity and significantly increase the spatial growth rates for left‐hand polarized instabilities just below the helium gyrofrequency ΩHe+, and on the unguided mode above Ω>He+ but below the cross over frequency ωcr. Relatively high densities, typical of the afternoon local time sector, favor these low group velocity effects for predominantly field‐aligned waves. Lower densities, typical of those found in the early morning local time sector, increase the group velocity but allow strong convective instabilities at high normalized frequencies well above ΩHe+. These waves are reflected in the magnetosphere and can exist for several equatorial transits without significant damping. They are left‐hand polarized only on the first equatorial crossing and become linearly polarized for the remainder of the ray path. Consequently, these waves should be observed with basically linear polarization at all frequencies and all latitudes in the early morning local time sector. Wave growth below ΩHe+ is severely limited owing to the narrow bandwidth for instability and the small resonant path lengths. In the afternoon sector, where plasma densities can exceed 107 m−3, intense convective amplification is possible both above and below ΩHe+. Waves below ΩHe+ are not subject to reflection when the O+ concentration is small and therefore should be observed with left‐hand polarization near the equator and essentially linear polarization at higher latitudes. Since the He+ concentration is usually large in the afternoon sector, guided mode waves above ΩHe+ reflect to form a background distribution with basically linear polarization. We suggest that the strong left‐hand polarized emissions observed by AMPTE in the afternoon sector near the equator are probably due to strongly growing low group velocity waves at frequencies just below ΩHe+, and on the unguided mode above ΩHe+.