Convective growth of slow and fast beam acoustic waves in the plasma sheet boundary layer (PSBL) is investigated. It has been shown previously that a cold ion population must be present in order to excite beam acoustic waves in the PSBL. However, growth rates are significantly enhanced when warm plasma sheet boundary layer ions are prent. Net wave growth along a ray path is determined by convective growth. This quantity is calculated for particle distribution models consistent with the PSBL where the intensity of broadband turbulence is observed to peak. Total number density dependence on beam acoustic convective growth is evaluated, and it is found that even for low density conditions of ~0.01 cm-3, a measurable level of broadband turbulence is expected. Relative drift effects between cold and warm ion populations are also considered. In particular, it is found that slow mode convective growth can be enhanced when slowly streaming cold ions are present, compared to fast ion streams. ¿American Geophysical Union 1987