Comparative Study of Guided Electromagnetic Wave Propagation for Two Models of an Open Tape Helix

Abstract

Rigorous methods to solve the homogeneous boundary value problems and the techniques to resolve illposed mathematical issues arising in the problem formulation of electromagnetic wave propagation of an Open tape helix slow wave structure with anisotropically conducting and completely conducting model is presented. The dispersion equation of both the models require convergent coeefficients of the infinte linear homogeneous equations whose determinant of the coefficent matrix is zero. The coefficient matrix of the anisotropically conducting model is rapidly convergent, while in the case of completely conducting model, the matrix entries which are infinite summation series representations turns out to be divergent, the not so well-posed boundary value problem is regularised with the method of mollification functions. The dispersion characteristics are plotted after truncating the infinite series expansions to adequate number of terms and summing the terms of converging series expansions(after regularization in the case of the completely conducting tape-helix model) in dispersion equations. The tape-current distribution for both models are estimated from the null-space vector of the truncated coefficient matrix corresponding to a particular (β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) root of the dispersion equation. A comparison of the numerical results for both models show that the neglect of the perpendicular tape-current density component entails a substantial modification of the dispersion characteristics of guided waves supported by an open tape helix.