Relativistic Hartree condition for magnetrons: Theory and comparison with experiments

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Abstract
The Hartree voltage UH is derived for a cylindrical magnetron in the relativistic limit with and without an axial current. This voltage corresponds to the breakdown voltage of the magnetron in the presence of a rotating perturbation field. In general, UH is less than the cutoff voltage UI for magnetic insulation in the absence of a perturbation field. Comparisons with a number of different experiments at zero axial current indicate that the maximum microwave power occurs for voltages slightly larger than UH, but well below UI. With axial current, two different Hartree voltages are derived, UHA and UHB<UHA, based on different assumptions. Recent experiments at Physics International show little microwave power for voltages less than UHB and high power for voltages at or slightly larger than UHA. The absence of large microwave power outputs at large axial currents may be caused by the finite axial length of the magnetron.

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