The potential of the EBT plasma confinement device as a fusion reactor depends critically on its ability to support a sufficiently large power density which in turn means a large enough beta defined as the ratio of the plasma pressure to magnetic field pressure. The maximum allowable beta is generally dictated by the stability of the system to hydromagnetic (MHD) modes. In this paper we examine the stability of such modes for a D-T plasma and assess the effect of the alpha particles on these instabilities. We find that the alphas have the most destabilizing effect, as reflected in the drop of the ion beta, at the instant of birth and that recovery of stability is achieved as the alphas approach equilibration with the ions of the plasma. In short, there appears to be no serious adverse effects on the reactor beta resulting from alpha-induced instabilities.