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I study electron movement in electromagnetic fields beyond the adiabatic approximation, using so-called Stormer theory. Some of the electron orbits are regular or integrable, but their measure is zero. Other orbits, called quasiperiodic, are unstable, but only for infinite times. All other orbits are chaotic or hyperchaotic, or simple scattering states. Examples for typical electron orbits are given for all these cases. An open question still is whether the spectral changes due to Stormer will translate into changes in the limits on neutrino masses and on errors in neutrino-electron correlation experiments.

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