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A fully kinetic model for the electron flow in a crossed field device

Using the kinetic description, a self-consistent model for the electron flow in the crossed electromagnetic field configuration observed in a smooth-bore magnetron was developed. Through that model, derived for both relativistic and nonrelativistic limit, it was possible to understand how the stationary states solutions for the electron flow change when the injection temperature, the charge intensity in the system, and the external electromagnetic fields were modified. Basing on the results, it was possible to characterize the regime transition (accelerating to space charge limited), the stability transition (laminar to turbulent flow) and the mode transitions (transitions between the modes: magnetic insulated, Child Langmuir, and non-cutoff). All the theoretical results were verified using self-consistent computer simulations.