ELECTRON BALLISTICS IN HIGH-FREQUENCY FIELDS 



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Hahn's analysis starts by treating an infinitely long electron beam, using 

 cylindrical co-ordinates and is limited to a small signal theory where the a-c 

 motions are small compared to the d-c but it does not ignore the r-f effects 

 of the space charge forces. The electron beam is thought of as a moving 

 dielectric rod which is capable of propagating axial waves much as a dielec- 



OUTPUT GAP 



OUTPUT GAP 



INPUT GAP 



ACCELERATION VOLTAGE 



INPUT GAP 

 VOLTAGE 



Fig. 12 — Diagram for a cascade amplifier (Harrison). 



trie wave guide will do. He assumes an axial magnetic field and a stream of 

 positive ions having the same velocity axially and the same charge density. 

 These ions are assumed to have infinite mass. The solution is much too 

 complicated and involved to present here even in abstract. It involves the 

 complete solution of Maxwell's equations subjected to the stated assump- 



