Nonlinear Equations Describing 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 and space charge forces are included by calculating the field due to such a cylinder when it is placed between two perfectly conducting planes. The nonlinear equations are re-expressed in terms of normalized variables which make them suitable for machine computation. A brief discussion of the procedure for solving these equations numerically is included