Exact Treatment of the Dispersion and Beam Interaction Impedance of a Thin Tape Helix Surrounded by a Radially Stratified Dielectric

An exact dispersion relation is obtained for electromagnetic waves propagating on a thin metallic tape helix of arbitrary width, supported 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, are avoided. The power flow and interaction impedance are exactly computed. The dispersion relation is solved numerically for slow waves and the resulting phase velocity and interaction impedance are compared to those computed using the frequently made assumptions of constant current along the tape and zero current across the tape. It is found that for wide tapes significant errors are made in both the phase velocity and interaction impedance when neglecting the transverse variation of the longitudinal current and neglecting the transverse current. For narrow tapes, the two approaches agree to good accuracy. Plots of the surface currents for wide and narrow tapes are presented. The longitudinal current shows a significant variation across the tape. An example is given showing the existence of an optimum tape width, at which the on-axis interaction impedance is maximized. It is separately shown how an approximate, but useful model of metallic vanes may be incorporated in the analysis by the modification of certain boundary conditions. In all cases, computations of phase velocity and impedance across a wide frequency band take well under a minute on a modern workstation.