A map model has been developed for studying the nonlinear interaction of alpha particles with the toroidal Alfve´n eigenmodes. The map is constructed by assuming a linear interaction during a single poloidal transit, which allows the study of the nonlinear interaction over many transits. By using this map, analytic expressions are obtained for the particle nonlinear bounce frequency, and the wave amplitude threshold for the onset of particle orbit stochasticity. The map model can also facilitate self‐consistent simulations which incorporate the time variation of the waves.