MAGNETRON AS GENERATOR OF CENTIMETER WAVES 173 



amplitude of oscillation, Vrf, as well as of other parameters governing the 

 electronic behavior of the oscillator, such as voltage and magnetic field. 

 It is not known a priori but may be deduced from measurements on the op- 

 erating oscillator and its circuit. 



A necessary condition for oscillation, applicable to the magnetron as to 

 any oscillator, is that, on breaking the circuit at any point, the sum of the 

 admittances looking in the two directions is zero. Thus, if the circuit is 

 broken at the junction of electrons and resonator, as is convenient, the elec- 

 tronic admittance, Yg, looking from the circuit into the electron stream, 

 must be the negative of the circuit admittance, F„ looking from the electron 

 stream into the circuit. 



With these remarks, of general applicability to all types of electromagnetic 

 oscillators, the discussion will be continued for the centimeter wave mag- 

 netron oscillator in particular. As far as is possible, the electronic inter- 

 action space, resonator system, and output circuit of the device will be taken 

 up in that order. The function and operation of each part will be described ; 

 then the principles of its design, and its relation to previous magnetron 

 development will be indicated. 



1 .4 Electron Motions in Electric and Magnetic Fields— The DC Magnetron: 

 Before beginning the discussion of the electronics of the magnetron oscillator, 

 it would be well to review briefly electron motions in various types and com- 

 binations of electric and magnetic fields, and the operation of the DC 

 magnetron.' 



An electron, of charge e and mass m, moving in an electric field of strength 

 £, is acted upon by a force, independent of the electron's velocity, of strength 

 eE, directed oppositely to the conventional direction of the field. If the 

 field is constant and uniform, the motion of the electron is identical to 

 that of a body moving in a uniform gravitational field. 



An electron moving in a magnetic field of strength B, however, is acted 

 upon by a force which depends on the magnitude of the electron's velocity, v, 

 on the strength of the field, and on how the direction of motion is oriented 

 with respect to the direction of the field. The force is directed normal to 

 the plane of the velocity and magnetic field vectors and is of magnitude 

 proportional to the velocity, the magnetic field, and the sine of the angle, 6, 



between them. Thus the force is the cross or vector product of v and 7^, 



"? = e[vX B], F = Bev sin d. 



An electron moving parallel to a magnetic field (sin 6 = 0) feels no force. 

 One moving perpendicular to a uniform magnetic field (sin d = 1) is con- 



iThe cylindrical DC magnetron was reported by A. W. Hull. Phys. Rev. 18, 31 

 (1921). 



