ELECTRON BALLISTICS IN HIGH-FREQUENCY FIELDS 329 



cyclotron both employ a combination of sorting and bunching. A peculiar 

 property of the motion of an electron in a magnetic field lies in the existence 

 of the so called Larmor frequency. You will recall that the angular velocity 

 of an electron in a magnetic field depends only upon the field-strength and 

 not at all upon the electron's linear velocity. This time in seconds is 

 given by 



0.357 X 10"' 

 ^ H ' 



or in radians 



10600 



= 2 



TT 



XH 



Electrons of widely differing velocity can thus revolve together in spoke- 

 like bunches with the faster electrons going around larger circles than the 

 slow ones, but just enough larger to keep them together. This, then, is 

 one kind of bunching, which for simplicity we shall call magnetic bunching. 

 It is used in the magnetron and in the cyclotron. We will have more to say 

 on this subject a little later. 



A second kind of bunching was used in some of the early Barkhausen 

 tubes wdiere the plate electrode was operated at a fairly high negative poten- 

 tial so that none of the electrons were able to reach it. Under such condi- 

 tions a uniformly spaced stream of electrons with varying velocities is re- 

 flected as a bunched stream, the slower electrons being reflected almost at 

 once and the faster electrons penetrating the retarding field for a greater 

 distance and hence taking longer to return. This same type of bunching is 

 used in a newer form of oscillator, commonly referred to as a reflex tube 

 which was suggested by Hahn and Metcalf in 1939, and by others at about 

 the same time. The reflex tube differs from the Barkhausen tube, not in 

 the basic mechanisms so much as in the fact that the conversion mechanism 

 occurs in a different region in the tube from the region devoted to velocity 

 modulation and to energy abstraction. A second kind of bunching is then 

 reflex bunching. 



A third type of bunching was used in the diode oscillators of Muller and 

 of Llewellyn. The mathematical research done by W. E. Benham may be 

 mentioned as of interest in this connection. In these tubes a uniform stream 

 of electrons becomes bunched simply through the fact that faster moving 

 electrons overtake slower ones which precede them. In these earlier forms 

 of tubes we again have the case where this conversion is performed simul- 

 taneously with one or more of the other processes so that it is very difficult 

 to separate them. However, in 1935 Heil and Heil proposed a tube in 

 which the conversion region was separated from the other regions of the 



