A search for alpha driven beta-induced Alfvén eigenmodes (BAEs) was conducted in low current (1.0-1.6 MA) TFTR supershots. Stable high beta deuterium-tritium (DT) discharges were obtained with βp = 2.4 and a central alpha beta of 0.1%. Instabilities between 75 and 200 kHz were observed by magnetics probes in many DT discharges, but the activity was also present in deuterium-deuterium (DD) comparison discharges, indicating that these modes are not destabilized (principally) by the alpha particle population. Losses of fusion products are also similar in the two sets of discharges. Theoretical simulations confirm that the achieved alpha particle pressure is too small to produce instability.