Dispersion properties of Trivelpiece-Gould waves in periodic plasma waveguides

Spectral properties of plasma waves in periodic plasma-filled waveguides are analyzed. Unusual features in the spectral behavior and field distribution of natural plasma modes are predicted. In particular, it is shown that the plasma wave spectrum has a zonal character with allowed and forbidden bands. The periodicity strongly distorts the field distribution of plasma waves at frequencies near forbidden bands. Due to the significant contribution of higher spatial harmonics, the field of the plasma wave concentrates in small regions and achieves rather large local values. However, at frequencies far from forbidden bands the influence of the periodicity on dispersion properties and field distribution of plasma waves is negligible. Possible consequences of these effects for the beam-plasma instability in periodic plasma-filled waveguides are discussed.