Mode Conversion at the Junction of Helix Waveguide and Copper Pipe

1317 1318 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1 9 5 9 paper the representations of the fields associated with the natural modes of propagation in helix waveguide and copper pipe are given. Useful properties of these representations arc also given. In Section III the equations relating mode voltages and currents imposed by boundary conditions at the helix-waveguide-copper-pipe junction are derived. In Section IV these equations are solved. The author is indebted to H. G. Unger and J. A. Young of Bell Telephone Laboratories for their patient assistance in the preparation of this paper. The criticism of Z. Szekely is also appreciated. GLOSSARY OF SYMBOLS USED Ej = transverse electric field, ei, e2 = scale factors associated with the cylindrical coordinates wi and h = propagation constant of a mode H = transverse magnetic field, i!, i = transverse unit vectors associated with Ui and u2, I = current associated with a mode, t 2 u, 2 j ; 2 Ic = a scattering coefficient for a helix waveguide and copper pipe junction, T = a solution of the scalar wave equation, Ui, ii = generalized cylindrical coordinates, V = voltage associated with a mode, Y = wave admittance of a mode, z = unit vector pointed in axial direction of a cylindrical coordinate system, ii d i d 2 0 2