SELF-CONSISTENT FIELD-THEORY OF A HELIX TRAVELING-WAVE TUBE AMPLIFIER

A self-consistent relativistic field theory of a helix traveling wave tube (TWT) is presented for a configuration in which a thin annular beam propagates through a sheath helix enclosed within a loss-free wall. A linear analysis of the interaction is solved subject to the boundary conditions imposed by the beam, helix, and wall. A determinantal dispersion equation is obtained which implicitly includes beam space-charge effects without recourse to a heuristic model of the space-charge field. This dispersion equation is valid for arbitrary azimuthal mode number, and is solved numerically for the azimuthally symmetric case. The coupled-wave Pierce theory is recovered in the near-resonant limit. Numerical comparisons between the complete dispersion equation and the Pierce model are described. The ballistic and space-charge dominated regimes of the Pierce analysis, in which the gain scales as the cube and fourth root of the current respectively, are addressed explicitly. A discrepancy is found between the Pierce and the field theory even for low currents in the nominally ballistic regime. This arises from the dielectric effect of the beam on the helix modes, which can result in the gain increasing faster than the cube root of the current.