Space-charge waves in partially depleted negative-mobility media

Space-charge waves in a two-dimensional negative-mobility medium are described by a relatively simple and easy-touse expression for the complex propagation constant. Attention is focused on the dominant mode in the most important limit of low growth rate. Diffusion is included in the analysis. Whereas most previous workers imposed a stiff lateral-motion constraint at the surfaces of the drifting electron stream, we allow the electrons to move freely in the transverse direction at the lateral boundaries of the stream. This free-surface assumption corresponds to the partially depleted condition which prevails in many experiments. It has the effect of reducing diffusion damping and hence enhancing the growth of space-charge waves at high frequencies. The enhanced high-frequency growth rate makes the free-surface theory agree better with experimental data on thin-layer reflection and traveling-wave amplifiers than the stiff-surface theory does. Our results are cast in a form which allows heterogeneous dielectric media to be characterized by a single "effective dielectric constant." Dielectric configurations considered include symmetrical and unsymmetrical combinations of simple dielectric media, multilayered dielectric media, and simple or multilayered dielectric media with metal backing.