New modes in a plasma with periodic boundaries: The origin of the dense spectrum

We analyze the new features of the low-frequency (ω<${\mathrm{\omega }}_{\mathit{p}}$) modes of wave propagation in a plasma-filled, spatially periodic structure. The spectrum of these modes is drastically modified by the periodic boundaries in a way that produces a fundamentally new kind of spectral behavior, a ‘‘dense spectrum.’’ The interaction of ballistic electron beam modes with the dense spectrum of plasma modes is shown to be unstable. These modes may play an important role in the area of plasma microwave electronics.