Traveling-wave tube propagation constants for finite values of gain per wavelength

The propagation constants of a traveling-wave tube can be normalized in such a way that curves of a quantity proportional to gain per wavelength, vs a parameter proportional to electron velocity, approach a single curve at large values of a space-charge parameter. The usual Pierce normalization yields analogous curves that approach an asymptotic curve for zero space charge. Suitable curves for calculation of traveling-wave tube gain, based on this large space-charge normalization, have been computed and are presented for a wide range of values of the relevant parameters. It is found that, even for very large values of the gain parameter, corresponding to values of C of the order of 0.3, these curves do not depart substantially from the asymptotic curve.