General Steady-state Theory of Linear Magnetrons. I†

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Abstract
This paper presents a general steady-state theory of linear magnetrons. Space charge and the Maxwellian velocity distribution of the emitted electrons are taken into account, but the collisions between individual electrons are neglected. Part I of the paper explains the mathematical basis of the calculations and gives expressions for the volume density of the electrons and for the two components of the electron current density. A detailed analysis of these expressions is provided in Part It of the paper, No calculations of the actual potential distribution are given. However, for a certain range of such distributions, the following general conclusions concerning the steady-state theory of a linear magnetron can be drawn. ( 1 ) Brillouin's single-stream flow is not possible when the omission velocities of the electrons are taken into account. ( 2 ) In a well ‘ cut-off ’ magnetron the tangential component of the current density may be several hundred times larger than the perpendicular component. Thus, even slight imperfections in the geometry of the valve may cause large contributions to the anode current from those electrons which nominally should only graze the anode. ( 3 ) When the tangential component of the current density is relatively high, the conditions inside the magnetron may approach those given by the single-stream flow, although now the perpendicular component of the current density is still present, oven if it is rather small. This resolves the difficulty of establishing a pure single-stream flow. ( 4 ) The appearance of a potential minimum between the electrodes does not necessarily limit the amount of the current drawn to the anode.