ELECTRON BALLISTICS IN II I Gil -FREQUENCY FIELDS 345 



electron paths within the magnetron and having determined these paths (2) 

 that of getting an understanding of the mechanism whereby electrons in 

 traversing these paths are able to deliver energy to the connected high- 

 frequency circuits. One might think that the first problem w-ould be a 

 relatively easy job. As a matter of fact the literature is surfeited with 

 papers purporting to give the answer. Unfortunately almost all of the 

 jniblished work ignores the effect of space charge. A few moments' thought 

 will suggest that space charge may be a controlling factor because of the 

 long electron paths which are sure to result in crossed electric and magnetic 

 fields, and indeed more detailed computations bear this out. Nevertheless 

 the neglect of space charge greatly simplihes the problem. There are those 

 who believe that the no-space-charge theories have no bearing on the way 

 actual magnetrons work and that any correspondence between the predic- 

 tions of such theories and the actual behavior of magnetrons is simply the 

 result of an unfortunate coincidence. In fact Brillouin points out that 

 the simplified form in which the Larmor theorem is applied by many, is in 

 itself an approximation which was perfectly valid as originally applied by 

 Larmor to the electronic orbits within the atom but which does not apply 

 to conditions as they exist in the magnetron. 



A number of recent workers have attempted to include the effects of 

 space charge but have unfortunately largely restricted themselves to small 

 signal theories while the magnetron is seldom operated under small signal 

 conditions, at least not intentionally. Most theories are further restricted 

 to a consideration either of the coaxial case where the cathode radius is 

 small compared to the anode radius or of the plane case. Most practical 

 structures are intermediate between these extremes. 



As an example of the difficulties involved, Fig. 13, reproduced from a 

 paper by Kilgore, shows the electron paths as computed neglecting space 

 charge and also show's experimental proof that these paths actually exist. 

 This illustration has been frequently reproduced and widely accepted. 

 The experimental picture was obtained in the presence of gas, to make 

 the electron beam path visible, and unfortunately the ionization which 

 makes the beam visible also tends to neutralize space charge effects. The 

 experimental arrangement departs still further from reality in that the 

 electron emission from the cathode was restricted to a limited region so 

 that the space charge forces were still further reduced. Now it is probably 

 true that some magnetrons operate with electron paths as shown; still it is 

 not true that all magnetrons operate in this way. 



Contrasting with this picture which was until recently commonly ac- 

 cepted, Brillouin, Blewett and Ramo, and others have shown that stable 

 distributions are possible in which a space charge of almost uniform density 

 rotates with a uniform angular velocity about the axis. Brillouin goes so 



