Stochastic electron motion in magnetically insulated diodes

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Abstract
The transition to stochasticity is investigated for electron motion in the field configuration of a magnetically insulated diode. The model system is planar and periodic. The equilibria studied are nonrelativistic with constant electron density across the sheath. This class of equilibria includes the Brillouin flow equilibrium as a limit. Action‐angle variables are introduced that facilitate the nonlinear analysis. It is found that small periodic perturbations of the equilibrium potential may lead to stochastic motion of the sheath electrons. It is shown that the critical perturbation amplitude for global stochasticity goes to zero as the Brillouin limit is approached for a variety of perturbations. A global stochasticity diagram is presented that gives a simple characterization of the electron motion in the allowed phase space of a magnetically insulated diode. A piecewise linear map is introduced that allows an efficient study of the electron dynamics in the stochastic regions.