Derivation of magnetic fields on a metal cylinder excited by longitudinal and transverse magnetic dipole transmitters: I. Cylinder in unbounded dissipative dielectric medium

Abstract

AbstractWe derive new and exact analytical and convergent integral representations for the frequency‐dependent complex magnetic fields Hz(a, ϕ, z) and Hϕ(a, ϕ, z) excited by oscillating point magnetic dipole transmitters on the surface of an infinitely long metal cylinder of radius a in an unbounded dissipative dielectric medium. Hz(a, ϕ, z) is calculated for a longitudinally oriented magnetic dipole parallel to the cylinder axis and Hϕ(a, ϕ, z) for a transversely oriented magnetic dipole perpendicular to the axis. The solutions are relevant to the computation of phase shifts and attenuations measured by electromagnetic propagation logging tools, which have oscillating longitudinal and transverse magnetic dipole transmitters either on a metal drill collar or on a cylindrical antenna pad. The integral representations can be readily evaluated using simple numerical integration algorithms, e.g., Simpson's rule, to accurately compute the complex magnetic fields on the cylinder surface. A second paper will address the two‐layer cylindrical media problem.