The effect of quasi-linear diffusion of alpha particles in an external high frequency (HF) field on the continuum Alfven wave instability driven by the pressure gradient of the alpha particles is investigated theoretically in the limit of weak 'collisions' (νQL < ωA < ωbα), where νQL, = r/R, ωA and ωbα are the characteristic frequency of the quasi-linear process, inverse aspect ratio of the tokamak, Alfven frequency and alpha particle bounce frequency, respectively. It is shown that in this limit efficient instability suppression is possible. The HF electric field strength needed for stabilization is available from modem HF power sources