Theory of the Magnetron. I

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 L²=-eImωH³. I=current per unit of length of the filament, ωH=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 ωH. A study of small oscillations with cylindrical symmetry shows that these oscillations have a proper frequency √2ωH, and that the magnetron is able to yield an internal negative resistance for certain frequency bands near √2ωH; this explains how a magnetron with one cylindrical anode can sustain continuous oscillations in an electric circuit.