8 BELL SYSTEM TECHNICAL JOURNAL 



speed of light, the wire in the helix will be about thirteen times as long as the 

 axial length of the helix, giving a wave velocity of about iV the speed of 

 light along the axis of the helix. A longitudinal magnetic focusing field of a 

 few hundred gauss may be used to confine the electron beam and enable it 

 to pass completely through the helix, which for 4000 megacycle operation 

 may be around a foot long. 



Fig. 2.1 — Schematic of the traveUng-wave amplifier. 



ELECTRON 

 BEAM 



it 



ELECTROMAGNETIC WAVE TRAVELS 

 FROM LEFT TO RIGHT ALONG HELIX 



li 



¥'\g. 2.2 — Portion of the traveling-wave amplifier pertaining to electronic interaction 

 with radio-frequency fields and radio-frequency gain. 



In analyzing the operation of the traveling-wave tube, it is necessary to 

 focus our attention merely on the two essential parts shown in Fig. 2.2, the 

 circuit (helix) and the electron stream. 



2.2 'Vnv. 'Iypk of Analysis Used 



A mathematical treatment of the traveling-wave tube is very important, 

 not so much to give an exact numerical prediction of operation as to give a 

 picture of the operation and to enable one to predict at least qualitatively 

 the effect of various ])hysical variations or features. It is unlikely that all of 



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