436 BELL SYSTEM TECHNICAL JOURNAL 



In Fig. 10.3, Pm and L„, are plotted vs h for no attenuation {d = 0). We 

 see that Pm becomes very small as b approaches (3/2)2' ^, the value at which 

 the increasing wave disappears. 



If space charge is to be taken into account, it should be taken into account 

 both in the drift space between anode and helix and in the helix itself. In 

 the helix we can express the effect of space-charge by means of the parameter 

 QC and boundary conditions can be fitted as in Chapter IX. The drift 

 space can be dealt with as in Section 9.7 of Chapter IX. The inclusion of 

 the effect of space-charge by this means will of course considerably com- 

 plicate the analysis, especially if 6 ?^ 0. 



While working with Field at Stanford, Dr. C. F. Quate extended the 

 theory presented here to include the effect of all three waves in the case of 

 low gain, and to include the effect of a fractional component of beam cur- 

 rent having pure shot noise, which might arise through failure of space- 

 charge reduction of noise toward the edge of the cathode. His extended 

 theory agreed to an encouraging extent with his experimental results. 

 Subsequent unpublished work carried out at these Laboratories by Cutler 

 and Quate indicates a surprisingly good agreement between calculations 

 of this sort and observed noise current, and emphasizes the importance of 

 properly including both partition noise and space charge in predicting noise 

 figure. 



10.4 Other Noise Considerations 



Space-charge reduction of noise is a cooperative phenomenon of the whole 

 electron beam. If some electrons are eliminated, as by a grid, additional 

 "partition" noise is introduced. Peterson shows how to take this into 

 account.' 



An electron may be ineffective in a traveling-wave tube not only by being 

 lost but by entering the circuit near the axis where the r-f field is weak 

 rather than near the edge where the r-f field is high. Partition noise arises 

 because sidewise components of thermal velocity cause a fluctuation in the 

 amount of current striking a grid or other intercepting circuit. If such side- 

 wise components of velocity appreciably alter electron position in the helix, 

 a noise analogous to partition noise may arise even if no electrons actually 

 strike the helix. Such a noise will also occur if the "counteracting pulses" 

 of low-charge density which are assumed to smooth out the electron flow 

 are broad transverse to the beam. 



These considerations lead to some maxims in connection with low-noise 

 traveling-wave tubes: (1) do not allow electrons to be intercepted by various 

 electrodes (2) if practical, make sure that loifir) is reasonably constant over 

 the beam, and/or (3) provide a very strong magnetic focusing field, so that 

 electrons cannot move appreciably transversely. 



