  The motion of ions in the fields B = B_0 zhat and E = E_0 yhat cos(k_perp y -
omega t) is considered. When omega >> Omega_i and v_perp > omega/k_perp, the
equations of motion may be reduced to a set of difference equations. These
equations exhibit stochastic behavior when E_0 exceeds a threshold. The
diffusion coefficient above the threshold is determined. Far above the
threshold, ion Landau damping is recovered. Extension of the method to include
parallel propagation is outlined.
