Full wave analysis of beam instability of dense plasma wave spectrum in plasma filled periodic waveguide

Summary form only given. The influence of plasma on dispersion properties of periodic waveguides is under extensive experimental, theoretical and numerical investigations (Nusinovich et al., 1998). Nevertheless, one of the major theoretical problems, namely, a rigorous analysis of the beam instability of plasma waves which originate the so-called "dense" spectrum, (Lou et al., 1991) is left open. Such spectral behaviour can hardly be treated by the conventional approach based on the expansion of the fields into the spatial harmonic series, since the resulting dispersion relation in the form of an infinite determinant diverges when the number of spatial harmonics is increased (Ogura, 1992). To clarify this issue, a new approach, based on an integral equation (IE) method, has been developed. For planar periodic waveguide filled with homogeneous longitudinally magnetized plasma and driven by a thin electron beam, an IE with a singular kernel has been obtained for the field on the waveguide axis. It has been regularized by extracting the static part of the kernel. Spectral properties of the resulting Volterra integral equation of the first type were analysed in the quasistatic approximation. The periodical "cold" solutions for the fields have been obtained in closed analytical form. The periodicity of the "cold" dispersion relation with respect to the wavenumber is qualitatively satisfied over several periods. The dispersion relation with the beam has unstable solutions, which can be interpreted as Cherenkov instabilities of the spatial plasma harmonics. For low plasma densities, the spatial growth rate of the first backward harmonic of the plasma wave is shown to be remarkably larger compared with that obtained by the conventional technique which consists in truncating an infinite matrix (Kurilko et al., 1981). This discrepancy can be attributed to the principal role of the interaction between highest plasma and beam spatial harmonics which form the quasistatic part o- the fields. The relative estimations for plasma wave energy in the saturation regime predict a beam-wave energy transfer much more efficient compared with the conventional ones.