Because of the strong localization of the fusion-born alpha particles in velocity and configuration space and their coupling to Alfvén waves in the background plasma, the relaxation of alphas is anomalous. In a finite system, the enhanced electromagnetic fluctuations can produce rapid spatial losses of alpha population and energy. These losses prevent the alpha velocity distribution from attaining a stable collisional equilibrium, thus maintaining a steady-state turbulence level. A self-consistent numerical quasilinear calculation is performed for one of the most dominant low-frequency modes, showing the evolution of the alpha distribution and yielding the anomalous loss rates.