A large-signal analysis of beam-type crossed-field traveling-wave tubes
The equations governing the behavior of beam-type, crossed-field, traveling-wave tubes are formulated and presented. The geometry is assumed to be two-dimensional. The electron beam is treated as a number of cylinders of charge (it can be regarded as a number of layers of pencils the axes of which a...
| Summary: | The equations governing the behavior of beam-type, crossed-field, traveling-wave tubes are formulated and presented. The geometry is assumed to be two-dimensional. The electron beam is treated as a number of cylinders of charge (it can be regarded as a number of layers of pencils the axes of which are parallel; these pencils can move in the two dimensions perpendicular to their axes) and space-charge forces are included by calculating the field due to these cylinders when they are placed between two perfectly conducting planes. The nonlinear equations are re-expressed in terms of normalized variables suitable for machine computation, and the procedure for solving these equations numerically is discussed. The equations are solved for a number of thin-beam, small-signal cases and the results are compared with previous analytical work. Numerical difficulties are encountered because the electric field approaches infinity in the neighborhood of a line charge. These difficulties are circumvented by a modification of the electric field in the vicinity of a line charge. Large-signal calculations are carried out for the special case of a thin sheet beam which would travel in a straight line in the absence of r-f effects. The computations are carried out for both forward- and backward-wave interaction by using several values of a space-charge parameter that cover typical operating conditions. |
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