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abrupt transition amplitude analytic approximately beam direction calculated cn CN compensation theorem complex reflection coefficient complex transmission coefficient constant DOUBLE PRECISION field H finite Fredholm integral equation free space FRESNEL INTEGRAL gives GO TO 50 Green's theorem groundwave Hankel function impedance plane impedance profile IMPLICIT COMPLEX incident surface wave inductive integrand Irikov Jl+X k+m-l Kay's linear taper magnetic field magnetic line source mathematical and numerical monotonically decreasing nonlinear regression nonuniform surface numerical procedures numerical results numerical solution obtained Open Waveguides perfect conductor perturbed fields phase delay Power balance R. J. King radiation field radiation pattern reactive surface reflected surface wave second term shown in Fig solved SUBROUTINE surface reactance surface wave antennas surface wave propagating taper T T tion TM surface wave total radiation transition region transmitted surface wave trapezoidal rule unperturbed Volterra integral equation zero