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Magnetohydrodynamic dynamo in disc-like astrophysical bodies has been considered for some time. Important astrophysical objects like accretion discs, protostellar and protoplanetary nebulae and galaxies are thought to regenerate a magnetic field through a dynamo mechanism. Although there is a well developed theory for describing the regeneration of magnetic field in these objects, there are not any specific methods how to calculate such magnetic fields in general case. In this work, after a description of the dynamo theory, the specific method for solving the nonspherical dynamo is introduced. The unique feature of this method is accommodation of variable magnetic diffusivity in order to model the shape of a disc-like body. The detailed construction of the method is presented, as well as description of mathematical and numerical methods used for obtaining the solution. The method of checking the model with respect to well established spherical models is also presented. Finally, some examples are calculated and discussion is given on the behaviour of calculated magnetic field and possible astrophysical implications.

Starting from the dynamic equations of electromagnetics we derive mutual impedance formulas that include the effects of induced polarization (IP) and electromagnetic (EM) coupling. The mutual impedance formulas are given for four geometries: a fullspace, a cylinder in a fullspace, a halfspace, and a layer over a halfspace. IP effects are characterized by a Cole-Cole model, the properties of which are fully investigated. From the general mutual impedance formulas specific limiting forms are defined to characterize the IP and EM effects. Using these limiting forms a framework is developed to justify the addition or multiplication of the two effects. The additive and multiplicative models are compared in the cylinder and layer geometries with the conclusion that the additive model proves to be more accurate over a wider range of frequencies than the multiplicative model. The nature of the IP and EM effects is illustrated in all four geometries showing the effects of relevant parameters. In all cases it is shown that the real part of the mutual impedance contains important IP information that is less influenced by EM effects. Finally the effects of boundaries are illustrated by the cylinder and layer geometries and a theory is developed to incorporate EM effects and IP effects from multiple regions which utilizes frequency dependent real dilution factors. We also include a brief review of some EM "removal" schemes and dilution theory approximations.

The electromagnetic response of infinitely long, thin wires over a flat earth is presented for two different applications: the shielding properties of an ensemble of parallel wires excited by a plane wave and the electromagnetic coupling of two perpendicular wires excited by a dipole. The shielding study begins with the formulation of the boundary value problem for N wires over a lossy half space. A suitable axial impedance operator is applied to obtain a system of equations whose unknowns are the currents flowing on each wire. Once the currents are determined, the aggregate field produced by the ensemble can be computed by summing N Fourier type integrals. For the specialized case of the infinite planar grid, Floquet's Theorem and Poisson's Summation Formula are invoked, transforming the linear system of equations into a closed form expression for the current flowing on each wire. We show that the electromagnetic response of the planar grid of finite extent and the grid of infinite extent are similar. For non-planar configurations, such as the semi-circular shell, shielding values of 60 dB are possible when the structure is of non-resonant dimensions; otherwise, the performance can degrade to 20 dB. In the case of the crossed wire configuration, the starting point is the development of the integral equations that govern the coupling between wires and the source; the unknowns are the spectral currents flowing in each wire. The equations are given in terms of generalized impedance functions for the situation where the wires are over a stratified earth. However, for the numerical work, only the case where the wires are in an unbounded, homogeneous medium is considered. Two numerical methods, with overlapping regions of validity, are applied: the method of moments and the method of multiple scatterers. By using the method of moments, we can obtain a matrix equation that will determine the spectral currents for any wire spacing. The multiple scatterer method leads to a more convenient matrix series solution and shows that the coupling strength is proportional to 1/d², where d is the wire separation, plus higher order inverse terms.

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