Relativistic Hartree condition for magnetrons: Theory and comparison with experiments

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