NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 875 



over the trace width to account for variations in focus for different parts 

 of the pattern. Admittedly, the process is not very accurate, but it does 

 give a rough measure of current density and helps considerably in in- 

 terpreting the observed velocity patterns. 



NOMENCLATURE 



a Circuit radius 



6 Parameter relating electron velocity to that of the cold circuit 

 wave Uq — Vi/uqC = AF/2FoC 



B Magnetic field 



(8 the axial phase constant co/^i 



C The gain parameter = (E^/2l3^P) (/o/4Fo) 



7 Radial phase constant = ^ = co/^i 



8i Complex propagation constant for the increasing wave 



I E Electric field 



A'* Electric field at phase $ 



c/m Charge to mass ratio of the electron 



i h Beam current in amperes 



/„( ) Modified Bessel function 



' /,> Tien's constant k, = 2/7^0 



l.ri Circuit circumference measured in (air) wavelengths 



X Number of wavelengths 



7] Maximum efficiency 



f]' Efficiency at an intermediate power level 



^ P RF power obtainable from the circuit 



j, QC Space charge parameter 



I q Charge per unit length in the electron beam 



/■ Radial distance from the axis 



j Vq Beam radius 



t Time variable 



Electron velocity 

 DC beam velocity 



V AC velocity of the electron beam 



t\ Wave velocity 



Fo DC beam voltage 



7',„ Voltage corresponding to the wave velocity 



AF ^^oltage difference corresponding to the difference in velocity of 

 an electron and the dc beam velocity 



bV Difference between synchronous voltage and that giving the 

 Kompfner dip 



$ Relative phase 



z Distance measured along the beam 



"0 



