Theory of the Magnetron. I

Abstract

A complete calculation of space charge and field repartition is given for a magnetron working under steady conditions. Electrons leaving the filament gradually acquire an angular velocity, and for distances greater than a certain length $L$, these electrons describe spirals around the filament. This very important length $L$ is defined by $L^2=-\frac{\mathrm{eI}}{m{{\omega }_H}^3}.$ $I$=current per unit of length of the filament, ${\omega }_H$=Larmor's angular velocity. Under critical conditions, that is, when the magnetic field is just high enough to cut the anodic current $I$, the electron cloud rotates about the filament almost as a solid body with an angular velocity ${\omega }_H$. A study of small oscillations with cylindrical symmetry shows that these oscillations have a proper frequency $\sqrt{2}{\omega }_H$, and that the magnetron is able to yield an internal negative resistance for certain frequency bands near $\sqrt{2}{\omega }_H$; this explains how a magnetron with one cylindrical anode can sustain continuous oscillations in an electric circuit.