For certain initial conditions, the motion of charged particles in a magnetic dipole field is well described by the hierarchy of adiabatic invariants: the magnetic moment &mgr;, the longitudinal invariant J, and the magnetic flux &psgr;. Electrostatic waves that break the axisymmetry of the dipole field and resonate with the drift motion can generate large-scale or so-called thick-layer chaos in &psgr;. This chaos will drive Arnol'd diffusion in &mgr; and J, making the motion asymptotically unstable. Previous studies involving mappings [Tennyson et al., 1980; Kook and Meiss, 1989> have found the thick-layer Arnol'd diffusion rate to be proportional to the square of the perturbation amplitude, consistent with quasilinear theory. Here we present numerical evidence that for many cases of physical interest, such as particle motion in a perturbed dipole field, the thick-layer diffusion rate is greatly attenuated from the quasilinear results. ¿ American Geophysical Union 1992