IXTERACTIOX BETWERX ELECT ROX STREAMS ,55 



is required, therefore, for this helix that one of the streams travel at a 

 velocity corresponding to a potential in the neighborhood of 54 volts. 

 Useful interaction occurs from 50 to 60 volts. The inner stream is adjusted 

 for helix interaction in this amplifier, and the outer stream travels at a lower 

 velocity to bring about the interaction between the two streams. Operation 

 about a mean voltage of about 50 volts was planned in designing the ampli- 

 fier, and in estimating its expected performance. The amplifier is 16 wave- 

 lengths long in terms of the wavelength associated with a mean voltage of 

 50 volts and a frequency of 200 Mc. Eleven of these wavelengths are in the 

 center portion between the helices. 



The conditions in the amplifier tube differ from those assumed in the 

 derivation of the theory of the double-stream interaction in the following 

 significant ways: 



1. The beams are separated in space and not completely intermingled. 

 Calculations on the effect of this separation have been made. Numeri- 

 cal examples of the calculated magnitude of the effect on gain will be 

 given below. 



2. Hollow tubular beams are used, instead of "solid" beams of uniform 

 current density over their cross-sectional area. The theory indicates 

 that, for the beam dimensions and currents used here, the parameters 

 which depend upon beam radius and total current in the beam are 

 nearly the same whether the current is concentrated in an infinitely 

 thin cylindrical shell or uniformly distributed over the cross-section of a 

 cylinder of the same radius. 



3. The metal wall surrounding the beams is not infinitely remote. Its 

 diameter was chosen as a compromise between the requirements of 

 preventing serious d-c. space charge depression of potential in the 

 beam and of being far enough removed from the beam to prevent a large 

 effect on the interaction due to its presence. Its proximity tends to 

 increase the minimum current required for producing gain, and there- 

 fore to reduce the ratio of actual to critical current on which the gain 

 depends. 



4. The beams are not perfectly confined to hollow cylinders of the dimen- 

 sions given. There is evidence that some spreading outside of these 

 dimensions occurs. The currents reaching the collector can be meas- 

 ured and these are used as "beam currents" in the discussion to follow 

 and in comparisons between theory and experiment. Somewhat larger 

 currents than these were initially launched, and the lost fraction may 

 have contributed to the interaction before striking the walls. 



Although the assumptions of the theory are not fulfilled in the actual 

 amplilier, estimates of its performance were first made without correction 

 for the discrepancies. With voltages of 40 and 60 volts on the outer and 



