The interaction between ion Bernstein waves (IBWs) and well passing ions is considered in the limit α ≡ Ω/(ωci ωt)1/2 >> 1 (here Ω is the phase oscillation frequency in the wave field, = r/R is the inverse aspect ratio, and ωci and ωt are the ion cyclotron and transit frequencies, respectively). In this case stochasticity arises due to repeated separatrix crossings, caused by successive trapping by waves, when the ions pass through a cyclotron resonance on the transit trajectory. According to general theory, changes in the adiabatic invariant do not correlate for successive resonance passages. As a result, diffusion in velocity space should arise. The calculated diffusion coefficient scales as Dμ ∝ α-4, while in the opposite limit, α<<1 and Dμ ∝ α2. A possible application of this result to the problem of alpha channelling is discussed.