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BELL SYSTEM TECHNICAL JOURNAL 



trons. For if the magnetron is to deliver more power at a given magnetic 

 field, the induced RF current must increase. This entails increased space 

 charge and a greater DC current flow. To maintain the increased space 

 charge additional DC voltage is required. 



4.3 The Electronic Efficiency: The performance chart also shows the 

 not too surprising fact that more power may be drawn from the magnetron 

 as the voltage and current are increased. More interesting are the increase 

 of the over-all efficiency with voltage and the maximum through which the 

 efficiency passes with increasing current. This variation of over-all effi- 

 ciency, 1), is to be attributed to changes in the electronic efficiency, r]e, since 

 the other factor involved in the over-all efficiency, the circuit efficiency, t7c, 

 is essentially constant over the diagram (77 = TjeTjc). 



VOLTAGE V ' (= 2V) 



MAGNETIC FIELD B' ^2B) 



^-o/ MAX. ELECTRONIC ^.q, 



^° EFFICIENCY (Fje) ^ 



Fig. 18. — Approximate orbits of electrons which transfer energy to the RF field, plotted 

 for operation of a plane magnetron at two different magnetic fields. It is shown how the 

 relative kinetic energy gained beyond the last cusp and dissipated at the anode de- 

 creases as the magnetic field and voltage of operation are increased, resulting in increased 

 efficiency of electronic conversion of energy from the DC field to the RF field. The 

 two illustrative cases differ by a factor two in DC voltage and hence by the same factor 

 in magnetic field and diameter of the rolhng circle. 



The increase of electronic efficiency with voltage, and hence magnetic 

 field, may be explained by the picture of electron motions in the interaction 

 space. The highest electronic efficiency is attained when the electrons 

 reaching the anode do so with least kinetic energy. For the approximate 

 orbit of Fig. 12, the energy lost at the anode per electron is that gained as 

 kinetic energy beyond the last cusp. Bringing the last cusp closer to the 

 anode, corresponding to a reduction of the ampUtude of the rotational 

 component of the electron motion, reduces the ratio of kmetic energy lost 

 at the anode to the potential energy possessed by the electron at the cathode. 

 Thus, according to equation (6) for the radius of the rolling circle, this 

 fractional energy loss should vary as V/B^ or, since V/B is approximately 

 constant, as \/B, rjg increasing with B. In terms of the approximate elec- 

 tron orbits for a plane magnetron, Fig. 18 shows how increase in voltage 



