Any process that is slow compared to the bounce- and gyro- timescales but comparable to the drift timescale can conserve the first two invariants but breaks the third invariant (given by the total magnetic flux enclosed by the trapped particle due to its gradient-curvature drift motion across field lines around the magnetized body). Such processes (in Earth's magnetosphere) include the arrival of an interplanetary shock, storm-time compression of the magnetosphere, and also sub-storm dipolarization events on the night-side. MHD waves generated by these processes can also interact with particles on the drift timescale, causing drift-resonances and radial transport (or diffusion in the case of multiple waves).
Alex
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