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BELL SYSTEM TECHNICAL JOURNAL 



strained to move in a circle by the magnetic force at right angles to its path. 

 Since this force is balanced by the centrifugal force, the radius, p, of the 

 circular path depends on the electron's momentum and the strength of the 

 field; that is, 



Bev = — 'j 

 P 



yielding 



P = 



mv 

 'eB' 



(1) 



Fig. 3. — The cycloidal path of an electron which started from rest at the cathode in 

 crossed electric and magnetic fields for the case of parallel plane electrodes. The mecha- 

 nism of generation of the orbit by a point on the periphery of a rolling circle is depicted. 



The time, Tc, required to traverse the circle is independent of the radius 

 and hence of the velocity of the electron; Tc = 2Trp/v = lirm/eB. Thus, 

 the angular frequency of traversing the circular path, the so-called cyclo- 

 tron frequency, depends on the magnetic field alone and is given by, 



lirfc = 2tt = B. 

 ■^ Tc m 



(2) 



In the magnetron, electron motion in crossed electric and magnetic fields 

 is involved. Consider first such motion between two parallel plane elec- 

 trodes, neglecting space charge. If, as in Fig. 3, the electric field is directed 

 in the negative y direction and the magnetic field in the negative s direction, 

 the equations of motion of the electron are : 



