176 



BELL SYSTEM TECHNICAL JOURNAL 



It is clear from this simplified picture of the orbits in a DC cylindrical 

 magnetron without space charge, that, at a given electric field, an electron 

 orbit for a sufficiently strong magnetic field may miss the anode completely 

 and return to the cathode. The critical magnetic field at which this is just 

 possible is called the cut-off value, Be. For a given voltage between cathode 

 and anode, as the magnetic field is increased, the current normally passed 

 by the device falls rather abruptly at 5c. A current versus magnetic field 

 curve, together with electron orbits corresponding to four regions of the 



Fig. 4. — Electron paths in a cylindrical DC magnetron at several magnetic fields above 

 and below the cut-off value, Be. The electrons are assumed to be emitted from the cathode 

 with zero initial velocity. 



curve, are shown in Fig. 5. For the case of parallel plane electrodes, the 

 cut-off relation between the critical anode potential, Fc, and magnetic field. 

 Be, and the electrode separation, d, for the parallel plane case, is obtained 

 by equating the electrode separation to the diameter of the rolling circle. 

 Thus, 



d = 



\d)BV 



2 -t -f 1-, 



from which 



F. = 



eBtd' 

 2m 



