Exact treatment of the dispersion and beam interaction impedance of a thin tape helix surrounded by a radially stratified dielectric

Summary form only given. An exact dispersion relation has been obtained for electromagnetic waves propagating on a thin metallic tape helix of arbitrary width, surrounded by a radially stratified dielectric layer and enclosed by a metallic shell. By expanding the surface currents on the tape in a series of Chebyshev polynomials, the unquantifiable assumptions made in all previously published analyses of the tape helix regarding the forms of the surface current on the tape, or the electric fields at the radius of the tape, have been avoided. The power flow and interaction impedance have also been exactly computed. This new formulation of tape helix dispersion and impedance has been included in the CHRISTINE large signal, multi-frequency TWT simulation code. Examples will be presented in which the dispersion relation is solved numerically for slow waves and the resulting phase velocity and interaction impedance are compared to those computed using (1) the frequently made analytical assumptions of constant current along the tape and zero current across the tape and (2) results from a finite difference, frequency domain EM code.