MAGNETRON AS GENERATOR OF CENTIMETER WAVES 197 



electron must have to maintain proper phase with the total RF fields existing 

 across the anode gaps. 



Posthumus'^ derived an expression, assuming negligible cathode diameter, 

 which is similar to equation (14). By the same method as that used above. 

 Slater has derived an expression diflfering from (14) by a term which results 

 from the use of a more accurate value for the electron's translational velocity 

 at the midpoint between cathode and anode in cylindrical geometry. 

 Slater's expression is: 



\k\ 



•4'-fey]-^'Kf0['-t:y 



(15) 



Hartree has derived an expression from a consideration of the conditions 

 under which electrons are just able to reach the anode with infinitesimal 

 amplitude of RF voltage in the ^"' harmonic. It is: 



In a sense this condition represents a cut-off relation for the oscillating 

 magnetron analogous to Hull's cut-off relation for the DC magnetron [equa- 

 tion (8)]. 



Plotted on a V-B graph, the expressions (14), (15), and (16) represent 

 parallel straight Hues. The line of equation (14) passes through the origin; 

 the so-called Hartree Une of (16) is tangent to the DC cut-off parabola; the 

 so-called Slater Une of (15) lies above the Hartree line but below the line of 

 expression (14). Each of the above expressions indicates that the electrons 

 will drive a given harmonic of the RF interaction field in a type III magne- 

 tron oscillator only at values of DC voltage and magnetic field which bear 

 a definite relation. This relation expresses the fact that V/B is very nearly 

 constant [equation (14)]. 



In Fig. 16 are plotted as an illustration, the Hartree hnes for the funda- 

 mentals (/> = 0) of the n = 1, 2, 3, and 4 m.odes and for the ^ = -5 harmonic 

 (p = — 1) of the « = 3 mode of a 10 cm. magnetron with eight resonators.^ ^ 



1^ This magnetron, used as an illustrative example in Part I, has the following char- 

 acteristics: 



Number of resonators, N = 8. 



Cathode radius, ro = 0.3 cm. 



Anode radius, ra = 0.8 cm. 



Anode length, h = 2.0 cm. 



Anode to end cover distance = 0.6 cm. 



Frequency (tt mode), f = 2800 mc/s. 



Wavelength (ir mode), X = 10.7 cm. 



DC operating voltage, V = 16 kv. 



Operating magnetic field, B = 1600 gauss. 



Typical operating peak current, I = 20 amps. 



Over-all efficiency, ij = 42%. 



Peak power output, Pq = 135 kw. 



Pulse duration, t = 1 microsecond. 



Pulse repetition frequency = 1000 pps. 



