Time-Harmonic Electromagnetic Fields Excited By An Arbitrary Current Dipole In Spherical Conductor

In this thesis, studies are made on the problem of time-harmonic electromagnetic fields excited by an arbitrary current dipole in spherical conductor. The problem is presented in eddy-current nondestructive test and geophysical prospecting. Under the condition of magnetic quasi-static state, the boundary-value problem about modified magnetic vector potential is solved and the analytical solution is obtained. The analytical solution is compared with numerical solution gotten utilizing general finite element analysis software. This thesis consists of main items as follows:1. The fundamental theories needed in the thesis are introduced briefly and some of them are enriched. The addition formula of spherical harmonics function of degree n and order 1 is derived using the relations between coordinate varieties after coordinate rotating and the property of the associated Legendre polynomial. The relations among the magnetic vector potential, the modified magnetic vector potential and the second-order vector potential (SOVP) are shown going forward one by one. It is explained that the solutions of electromagnetic fields in different coordinate systems can be transformed and an example having analytical solution is given. Two kinds of vector functions are introduced in spherical coordinate system. The vector functions are orthogonal over spheres and more universal than spherical vector wave functions.2. The analytical solution of time-harmonic electromagnetic fields excited by an arbitrary current dipole in spherical conductor is obtained. Firstly, in spherical coordinate system, the SOVP formulation for the time-harmonic electromagnetic fields of the current dipole in conductive infinite-space is derived, using reciprocity theorem and transforming relations between special functions. Then, selecting appropriate coordinate system, using superposition principle, the boundary-value problem of modified magnetic vector potential on the problem of a time-harmonic current dipole in spherical conductor is solved and analytical solution is obtained. Finally, by means of the addition formulas of Legendrepolynomial and spherical harmonics function of degree n and order 1, the analytical solution in spherical coordinate system specially located is transformed into that in spherical coordinate system arbitrarily located. The electric dyadic Green's function inside the sphere and the magnetic dyad outside the sphere are given. In addition, spherically multilayered conductor is discussed and the dyadic Green's functions are given for a two-layer conductive sphere.3. To verify analytical solutions, the numerical solution is computed for the problem that an arbitrary time-harmonic current dipole is in a conductive sphere utilizing finite element method and the analytical solution is compared with the numerical solution. Before giving the numerical solution, the finite element method and how to make the finite element analysis for 3D time-harmonic electromagnetic fields and 3D eddy-current fields are introduced in detail.