Reentrant Electron Beam Effects In A Circular Crossed-field Amplifier - Experiments And Numerical Simulations

Abstract

lossy dielectric material, a conducting shell and vanes for dispersion modification. The model is further divided into axial regions which may include severs, lossy materials, or circuit velocity steps, with the helix geometry varied arbitrarily in each region. The backward-wave root of the coupled dispersion equation is discarded and the sum of the fields for the three forward waves (two waves in a sever or high-loss region) is followed to the circuit output. The dispersion equations are expressed in terms of equating admittance functions at radial boundaries. This formulation provides programming flexibility where a variety of beam and circuit configurations are permitted. The hot dispersion equation is obtained by equating the beam admittance to the circuit admittance, both determined at the beam outer radius.The original field analysis was limited to the symmetric mode of the sheath h e l i and by the assumption of zero transverse beam velocity (strong focusing). The model and computer code are currently being extended to replace the sheath helix by a thin tape helix to improve the accuracy for tape helii circuits; this adds considerably to the complexity of obtaining numerical solutions to the dispersion equations, which now involve an infinite sum of space harmonics.The numdrical procedures to solve the dispersion equations will be described. Results obtained using the field analysis will be compared with those from the conventional coupled-mode Pierce theory for the same geometry. The issue of weak (Brillouin) vs. strong focusing will be discussed and recent refinements to the field theory will be described. The authors are continuing to extend the theory and numerical procedures in order to expand it's utility as an accurate design tool over the wide range of design parameters encountered in modem TWTs.A nonlinear formulation of the interaction in a helix traveling wave tube (TWT) is presented. The formulation is intended to treat a wide class of helix TWTs including both emission-gated and multi-tone operation. The essential feature of each of these configurations is that multiple waves must be included in the formulation. As a result, a fully time-dependent analysis is required. The numerical procedure for this in a helix TWT is complicated by the fact that the radial profile of the field varies with frequency. This contrasts, for example, with the case of a smooth bore waveguide in which the radial profile for each TEl, or TMln mode is invariant in frequency. Because of this, a complete self-consistent particle-in-cell (PIC) formulation must be three-dimensional. Azimuthally symmetric two-dimensional PIC simulations which employ equivalent circuit models for the helix can provide reasonably good approximations for wave dispersion but fail to account for the frequency variation in the transverse mode structure. In view of this, in oder to circumvent the computational expense of a 3D PIC formulation, we adopt an approach in which the electromagnetic field is represented as a superposition of azimuthally ...