REFLEX OSCILLATORS 629 



making resonator calculations. These can be profitably combined with 

 disk transmission line formulae. ' " 



The writers would like to point out that in the present state of the art 

 the testing of resonator calculations by models is important. Models 

 need not be made of the size finally desired. If all dimensions are made A^ 

 times as large, the wavelength will be A^ times as great. The characteristic 

 admittance M will be unchanged. If the material is the same, and the 

 surface is smooth and homogeneous, Q and \/Gr , the shunt resonant 

 resistance, will be \/7V^ times as great. 



It is perhaps a needless caution to say that the accuracy of a metliod of 

 resonator calculation cannot be judged by its mathematical complexity or 

 the difl&culty of using it. Methods of calculation which are simple and 

 may seem to make unduly broad approximations are sometimes better 

 founded than appears on the surface, and complicated methods, exact if 

 carried far enough, may be so unsuited to the problem as to give very bad 

 answers if used in obtaining approximate values. 



APPENDIX II 



Modulation Coefficient 



In this appendix the effects of space charge are neglected. 



The modulation coeflficient /3 is defined as the peak energy in electron volts 

 an electron can gain in passing through the field of a gap divided by the 

 peak r-f voltage across the gap. If an electron were transported across the 

 gap very quickly when the r-f voltage was at a maximum the energy in 

 electron volts gained by the electron would be equal to the peak r-f voltage. 

 Thus, the modulation coeflficient can also be defined as the ratio of the peak 

 energy actually gained to the energy which would be gained in a very quick 

 transit at the time of maximum voltage. 



In this appendix modulation coefficient will be considered only for r-f 

 voltages small compared with the d-c accelerating voltage. 



If an electron gains an energy /3 times the r-J voltage V across the gap, 

 the work done on it is ^eV electron volts. By the conservation of energy, 

 an induced current must flow between the electrodes of the gap, transferring 

 a charge-|8e against the voltage V and hence taking an amount of energy 

 ^eV from the circuit. Pursuing this argument we see that the modulation 

 coefficient /3 times the electron convection current in the beam, q, gives the 

 current induced in the gap by electron flow. In a circuit sense, there is fed 

 into the gap, as from an infinite impedance source, an induced current 



We will assume that the gap involves a region in which the field along the 

 electron path rises from zero and falls to zero again. This region is assumed 



