A large-signal analysis of the traveling-wave amplifier: Theory and general results

Equations are derived describing the large-signal operation of the traveling-wave amplifier, including the effects of ac space charge and attenuation along the helical slow-wave structure. The equations constitute a system of nonlinear partial-differential-integral equations valid with reasonable approximations for all values of the parameters which are encountered in typical high-power traveling-wave amplifiers. The parameters which appear in the equations are the relative injection velocity b, the gain parameter C, the large-signal space-charge parameters K and B, the loss parameter d, and the input-signal level A
0
. The working equations were programmed for and solved on the Michigan Digital Automatic Computer, MIDAC, located at the University of Michigan's Willow Run Research Center. The rf voltage amplitude A(y), the phase lag of the rf wave relative to the electron stream θ(y), and the velocity deviation 2Cu(y, φ
0
) were computed and plotted for several values of C, K, b, and B at A
0
= 0.0025, and d = 0. Also, distance-phase plots are presented for each of the above cases. These flight-line diagrams for the traveling-wave amplifier are similar to the well-known "Applegate diagram" associated with klystrons. Zero-space-charge solutions are presented for C = 0.05, 0.1, and 0.2 with b as the parameter in order to determine the value of b which gives the maximum saturation gain and the optimum tube length. For C = 0.1 similar solutions are obtained for several values of the space-charge parameter K. Presented in graphical form, the results of these various solutions shed a considerable amount of light on the high-level operation of the traveling-wave amplifier.