An analytical investigation is made of the development of the thermonuclear magneto‐acoustic cone instability in a tokamak reactor. The excitation mechanism for the instability is the anisotropy in the &agr;‐particle distribution function resulting from either direct orbit losses or ripple losses. Explicit expressions are obtained describing the time evolution of the magneto‐acoustic wave energy density as well as the distribution function, the anomalous particle loss, and the density of the &agr; particles. The results show that the quasilinear evolution of the instability causes rapid and severe &agr;‐particle losses and saturates at a high level of turbulence for the magneto‐acoustic waves. It is also shown that the quasilinear diffusion of the &agr; particles caused by the cone instabilities may result in the generation of a significant toroidal current in the plasma.