**Richards Joe Stanislaus, Ph.D. Scholar, Department of Electrical Engineering, SoE; Faculty Advisor – Dr. G. Naveen Babu**

The homogeneous boundary value problem existing in the electromagnetic wave propagation in a dielectric-loaded perfectly conducting tape helix with infinitesimal tape thickness is investigated in this paper. The ill-posed boundary value problem is regularized using the mollification method. The homogeneous boundary value problem is solved for the dielectric loaded perfectly conducting tape helix taking into account the exact boundary conditions for the perfectly conducting dielectric loaded tape helix. The solved approximate dispersion equation takes the form of the solvability condition for an infinite system of linear homogeneous equations viz., the determinant of the infinite order coefficient matrix is zero. For the numerical computation of the dispersion equation, all the entries of the symmetrically truncated version of the coefficient matrix are estimated by summing an adequate number of the rapidly converging series for them. The tape-current distribution is estimated from the null-space vector of the truncated coefficient matrix corresponding to a specified root of the dispersion equation. The numerical results suggest that the propagation characteristic computed by the anisotropically conducting model (that neglects the component of the tape-current density perpendicular to the winding direction) is only an abstinent approximation to consider for moderately wide tapes. This work is extended to the large signal field analysis of the tape helix slow wave structures.

At microwave frequencies, linear beam travelling wave tube (TWT) amplifier holds a significant place in high power amplification. The TWT amplifiers used are predominantly a helix slow wave structure (SWS). Modeling of such SWS’s are complex unless the structure is considered to be infinitesimally thin and possess infinite tape material conductivity. The model is often simplified by employing the anisotropically conducting tape helix material in which the surface tape current density component perpendicular to the winding direction is neglected. Travelling wave tubes operate on the principle of electron beam-wave interaction process. The radio frequency signal is passed through a slow-wave structure in which the r.f. phase speed is reduced close to the velocity of the electron beam. The electron beams interact with the axial component of the r.f. electric field and a net transfer of kinetic energy from the electron beam takes place to the r.f. wave. In this interaction process the electrons are accelerated and decelerated to for electron bunches as they move across the interaction of the slow wave structure. The electron bunches then transfer the energy and amplifies the r.f. wave.

The method of analyzing the perfectly conducting model of the open tape helix is applied to the practically relevant case of a tape helix supported inside by a coaxial perfectly conducting cylindrical shell by symmetrically disposed bars of rectangular cross-section. The placement of rectangular support rods at regular angular displacement around the helix generates azimuthal harmonics. Considering the effect of azimuthal harmonics, the region between the helix and the outer conducting envelope is divided into n number of cylindrical tubes coaxial with the helix. The discrete support rods occupied in each dielectric tube are azimuthally averaged out into a continuous dielectric tube of an effective permittivity. The presumable error due to the short edge sides of the rectangular bars are neglected assuming that, while azimuthal averaging of the rectangular support structure, the effect due to the short-side walls results in a negligible effect within the acceptable limits.

The characteristic equation is presented for the electromagnetic wave propagation through dielectric loaded perfectly conducting tape helix model. This equation was numerically computed to produce the dispersion graph plotted between the normalized free space number and the normalized guided wave propagation constant. The solutions were then compared with the dispersion curve of sheath helix model and the HFSS Eigen mode simulation results of a unit cell of one pitch width. This graph supports the fact that the perfectly conducting tape helix model is the most reliable approach towards the practical model.

This small signal analysis of the dielectric loaded perfectly conducting tape helix model will be applied to the large signal analysis of the slow wave structure. The analysis would incorporate the modelling of the hot wave problem of the slow wave structure parameters, namely, electron arrival time, electron speed, the field components, the induced current density, power gain and the efficiency of the hot wave structure.