NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 871 



from (16) and (17) we can write: 



y m 



^FoC2 



= 2 



Yo - F, 

 . 2Fo(7 



)*(. 



AF^ 

 2FoC, 



- F. + AF ^ 

 2FoC 



AF ^ 



2FoC, 



. (18) 



(19) 



;8, Fo and C are constants of the tube, the first inner parenthesis may 

 be calculated from the tube constants and is shown in the curves. 

 AF/FoC and its differential are the value and the slope of the velocity- 

 curve in question. 



The important approximations here are that the velocity-phase curves 

 are representative of velocity-distance characteristics, which is true for 

 small values of C, and that the electrons move roughly tangent to the 

 given velocity pattern. By comparing several patterns at different signal 

 levels it is observed that this is true to a fair accuracy over most of the 

 curve. Also it is assumed that the wave velocity at large amplitudes is 

 the same as that for small signals, which is not quite true. The resulting 

 curves give at least a qualitative picture of the field distribution within 

 a traveling wave tube, and serve to emphasize the importance of space 

 charge fields in determining the non-linear characteristics. 



ELECTRIC FIELD OF THE HELIX WAVE 



In order to see what part of the field is due to space charge we must 

 evaluate the corresponding helix fields. A value for this can be derived 

 from the basic traveling wave tube equations assuming the helix fields to 

 be sinusoidal and not seriously affected in impedance by the beam (small 

 C again) . By definition 



E"- h 



2jS2P 4Fo 



= C' 



(18) 



and 



1 

 C 



/oFoC 



(19) 



where 77' is normalized power level, i.e., efficiency corresponding to the 

 signal level E of interest. From this we deduce for the normalized circuit 



