Considerations of the effect of space-charge in the magnetron

Abstract

When a diode thermionic tube, having cylindrical symmetry, is placed in a magnetic field parallel to its axis it is commonly called a magnetron. If there is a given potential difference between the anode and cathode of the tube, and if the magnetic field is steadily increased, a sharp and pronounced decrease of anode current occurs when the field reaches a certain value. It is easy to show that, if electrons leave without velocity from a cathode of radius b, they will just graze a concentric anode of radius a at potential V when the magnetic field H has the value given by