The Wave Picture of Microwave Tubes 



By J. R. PIERCE 



(Manuscript received March 12, 1954) 



Many microwave tubes make use of a long electron beam. The radio fre- 

 quency excitation on such a beam can be expressed in terms of two space- 

 charge waves, one of which has negative energy and negative power flow. 

 The electron beam may pass through resonators, through lossy surroundings, 

 through slow-wave circuits. In this paper the low-level operation of klystrons, 

 resistive-wall amplifiers, easitrons, space-charge-wave amplifiers, traveling- 

 wave tubes and double-stream amplifiers is explained in terms of waves on 

 electron beams and on circuits. Noise is discussed in terms of such waves. 



INTRODUCTION 



There are many different ways in which one can make a valid analysis 

 of the low-level or small-signal behavior of the many types of microwave 

 tubes which use long electron beams. Which way one should choose de- 

 pends partly on one's purpose in making the analysis, and partly on the 

 particular problem to be solved. 



All of these analyses lead at some point to waves or modes of propaga- 

 tion: waves which travel along an electron stream, along a circuit, or 

 along the two together; waves which are unattenuated or which increase 

 or decrease with distance. Sometimes, the analysis starts out with elec- 

 tron current, electron velocity and circuit dimensions as the fundamental 

 physical ciuantities, just as network analysis can start out with induc- 

 tance, capacitance and resistance. However, an analysis can start out 

 instead with waves, their propagation constants and their characteristic 

 impedances as the fundamental physical bases of the analysis. We might 

 argue that as w^e are to end with waves, we may well start with waves. 

 As it turns out, the picture of the operation of various tubes in terms of 

 waves is simple and pleasing. 



It is the purpose of this paper to present a picture of the operation of 

 microwave tubes in terms of waves. This may be of some interest to 

 those outside of the tube field, in that it gives an account of many recent 

 devices. For experts in the field it can serve as an introduction to a 

 method of analysis which is fairly recent and which may be unfamiliar. 



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