PART II • — THE UHF XOISE SPECTRUM 873 



The direction of energj' transfer is reversed during the subsequent beam 

 expansion. If the ripple were perfectly symmetrical, therefore, and the 

 dc-ac energy exchange perfectlj^ reversible, the net effect of a beam ripple 

 would be zero. Neither of these conditions is quite true in actual beams. 

 Rippled flow is never truly laminar, and | Vrlr \ usually decreases with 

 drift distance as the flow loses coherence; i.e., it is greater in beam con- 

 traction than in the next expansion. This by itself would produce a net 

 gain per ripple in /« , and a net loss in // , of equal amounts. In addition, 

 however, unavoidable small non-linearities in electron motions prevent 

 all of the ac energy in a de-amplified wave from being converted back to 

 dc kinetic energj'. Thus it is possible for hoth the fast and slow waves to 

 increase in a ripple wavelength, the latter always more than the former. 

 The greater gain of the slow wave entails a loss of radial kinetic energy, 

 in agreement with the observation that the ripple amplitude always 

 decays more rapidly when rippled-beam amplification takes place. The 

 incomplete reversibility of the ac-dc energy exchange probably accounts 

 for the observed increase in /max/min for noise currents. Finally, the net 

 amplification of all of the space-charge waves, fast as well as slow, is in 

 accord with the observed near-constancy of the ratio /max/Zmin for 

 microwave-frequency noise, despite increases in the product /max/min of 

 30 db and more. 



VI ORIGIN OF THE PROPER-FREQUENCY PEAKS 



Of the various peaks in the beam's noise spectrum, described in Sec- 

 tion III and Fig. 1, those with "proper frequencies," slightly above the 

 cyclotron value, are so large in amplitude that even an approximate 

 analysis should be able to account for them. To do so, a "working model" 

 of the beam is needed, which conforms to the experimental conditions 

 which existed during the observations: 



(1) The peak intensities were greatest near the middle of each beam 

 waist, and decreased with decrease in ripple amplitude. 



(2) The focusing field was below the nominal Brillouin \-alue. The 

 field at the cathode. Be , was finite and opposed to the main field, B. 



(3) Collector-current measurements along the beam axis showed the 

 ratio of maximum to minimum current to be greater, the smaller the 

 aperture. 



(4) The gas pressure was about 10 ' mm Hg. The beam was pulsed 

 with a 1,000-cycle square wave. 



Item (3) indicates that the flow was non-laminar; and Item (4) in- 

 dicates the presence of positive ions. All the items are consistent with 

 the following picture: 



