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The impedance and electromagnetic field of a circularly cylindrical coil at an arbitrary position and orientation inside a cylindrical conductor, such as a borehole or tube, has been evaluated using analytical expressions. Previously, such expressions were available for two specific cases: one where the axis of the coil is parallel to the axis of the conductor and the other where the axes of the coil and conductor are perpendicular. In this paper, we consider the general case accounting for an arbitrary coil position and orientation. The analytical solution is made possible by successive transformations of the expressions for the coil field between spherical and cylindrical coordinate systems. The extended model is valuable for simulating eddy current inspections of boreholes and tubes with internal probes accounting for lateral movement and tilt. [ABSTRACT FROM AUTHOR]

A fundamental problem in eddy-current nondestructive evaluation is one of finding the quasi-static electromagnetic field of a cylindrical coil in the vicinity of the edge of a metal block. Although the field can be calculated numerically, an effective analytical approach can potentially provide a better understanding of the edge fields and form the basis of a procedure for solving a whole class of related edge problems including edge structures that contain corner cracks. One can represent the metal block as a conductive quarter space in an unbounded region. However, it has been found that the analysis is more straightforward if the problem domain is truncated in two dimensions. With the domain boundaries far from both the coil and the corner, the truncation has a negligible effect on the solution near the edge but the field calculation becomes much easier. A double Fourier series representation of the field is used, as in the case of a rectangular waveguide problem. The field in the conductor is then matched at the interfaces with that in air to determine the expansion coefficients that are used to represent the field in different parts of the domain. In this way we have derived expressions for the magnetic field, the induced eddy-current density and the coil impedance at arbitrary position and orientation of the coil. [ABSTRACT FROM AUTHOR]

Electromagnetic fields due to excitation coils in boreholes containing cracks have been calculated using a boundary element method formulated in terms of a scalar decomposition of the field. By using a Green's kernel that ensures continuity of the tangential electric and magnetic field at the cylindrical surface, it is only necessary to render the flaw region in a discrete form. The effect of an ideal crack, one with zero opening but acting as a perfect barrier to eddy currents, is here represented by a current dipole layer orientated normal to the crack surface. An integral equation determines the source density on the crack and a numerical solution is found using boundary elements. The coil impedance change due to the crack is then computed using an expression based on a reciprocity principle. [ABSTRACT FROM AUTHOR]

We describe the calculation of eddy currents in a two-layer conducting rod of finite length excited by a coaxial circular coil carrying an alternating current. The calculation uses the truncated region eigenfunction expansion (TREE) method. By truncating the solution region to a finite length in the axial direction, we can express the magnetic vector potential as a series expansion of orthogonal eigen-functions instead of as a Fourier integral. The restricted domain can be arbitrarily large to yield results that are as close to the infinite domain results as desired. Integral form solutions for an infinite rod are well known and relatively simple. For a finite length cylindrical conductor, however, additional boundary conditions must be satisfied at the ends. We do this by comparing series expansions term by term to match the solutions across the end of the cylinder. We derive closed-form expressions for the electromagnetic field in the presence of a finite two-layer rod. A special case of the solution is that for a conductive tube. We illustrate the end effect by calculating the coil impedance variation with respect to the axial location of the coil. The results are in very good agreement with those obtained by using a two-dimensional finite-element code. [ABSTRACT FROM AUTHOR]