Publisher's Synopsis
Excerpt from Propagation Constants of Traveling Waves
The usual technique employed in the analysis of a structure for possible use as a traveling-wave tube amplifier reduces to the problem of solving an equation the roots of which are the propagation constants of the possible modes of the system. Then one seeks to determine whether any of the roots correspond to an exponentially increasing wave, that is, to an amplifying wave. In general this propagation equation may be transcendental and rather difficult to solve. It would therefore be advantageous to have rules which would limit the portion of the complex plane which has to be examined for possible roots. One might expect that the law of conservation of energy would impose such a limitation. Pierce and Fieldlil give a physical argument for be lieving that such a restriction does indeed exist, but their argument is not proven rigorously. In the present paper, Since we Wish to make extensive use of a restriction of this type, we shall give a mathematically rigorous proof. We show that a restriction exists for the case of circular cylindrical symmetry involving perfect conductors and dielectrics and a uniform velocity beam; this restriction is in fact that the propagation constant of an amplifying wave must be such that the wave travels more slowly than the electron velo City. (note that nothing is asserted about the unperturbed wave Speed, that is, the speed of propagation of a traveling wave in the absence of the electron beam.) About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
