Why is the Dipole a better trap than Accelerator?

• Three “adiabatic invariants” (, J, L) w/characteristic times of 1ms, 1s, 1000s

• KAM theorem: the 3 adiabatic invariants are separated by factors of 1000 in time, and therefore do not “mix”. So dynamical evolution, or diffusive/stochastic “acceleration” is not fast.

• Arnol’d diffusion, or chaotic motion in the Poincaré section, can lead to rapid diffusion if these “basins” are connected to each other--“Arnol’d web”