11-1] THE MAGNETRON 585 



slowed-down electrons will eventually reach the anode. It is not 

 necessary that the conditions for synchronism be met exactly; a phase- 

 focusing mechanism holds the electrons in synchronism long enough for 

 them to be slowed down sufficiently to reach the anode. The conditions for 

 synchronism are given mathematically by 



Vh 



^I 



{rj 



•■■[ 



B 



2m irf 

 e n 



(11-2) 



where / = operating frequency 



Ta = anode radius 



Vc — cathode radius 



B = magnetic field strength 



m = mass of electron 



e = charge of an electron 



n = Hartree harmonic of the interaction field. 



Fh is called the Hartree voltage, after 

 the man who developed the theory. 

 As the anode voltage of a magnetron 

 is increased, oscillations can be ex- 

 pected when the voltage reaches the 

 Hartree voltage, provided it is below 

 the cutoff voltage. When the tube 

 breaks into oscillation, the current 

 drawn to the anode will increase 

 sharply. The relationship between 

 the Hartree voltage and the cutoff 

 voltage is shown in Fig. 11-9. In 

 practice these conditions are not met 

 exactly, because of the conditions of 

 space charge that were neglected in 

 the theory but which affect the 

 electron trajectories. 



MAGNETIC FIELD B 



Fig. 11-9 Hartree Diagram, Showing 

 Relationship Between Cutoff Voltage 

 and Hartree Voltage for Osscillation in 

 the Various Modes, for an Eight-Res- 

 onator System. 



Moding. The experimental current-voltage relationship of the static, 

 nonoscillating magnetron is shown in Fig. 11-10, along with the voltage- 

 current relationship of two of the modes of oscillation. The form of the 

 curve shown is typical of experimentally observed results. In the example 



ipor a more detailed definition of «, the reader is referred to H. D. Hagstrum, "The Gener- 

 ation of Centimeter Ways," Proc. IRE 35, 556 (1947). (In this article, the symbol k designates 

 the harmonic that we designate by «.) 



