Semi-analytical computations of coupled electromagnetic fields in cylindrical geometries under translational and time-harmonic excitation

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This paper examines electromagnetic fields arising in the vicinity of a cylindrical tube due to a coil carrying a time-harmonic alternating current (AC) while translating axially at constant speed along the tube bore. The probe-conductor geometry is non-axisymmetric, necessitating a three-dimensional field treatment. To treat the resulting electromagnetic fields, the second-order vector potential (SOVP) formalism is adopted, wherein both the transverse electric (TE) and transverse magnetic (TM) scalar potentials satisfy the diffusion equation in the conducting domain and the Laplace equation in air. Assuming constant translation speed and time-harmonic excitation and invoking the quasi-static approximation, the governing time-dependent PDE reduces to the stationary convection-diffusion-reaction equation -a purely spatial form. This allows the TE and TM potentials to be expanded as Fourier modes, continuous along the axial (z) and discrete along azimuthal (φ) directions. The corresponding modal coefficients are determined numerically by enforcing discretized magnetic field boundary conditions at the air-conductor interfaces. The model predicted electromagnetic fields are corroborated against TEAM benchmark problem 9 and independent finite element method (FEM) simulations, yielding excellent agreement.