Electromagnetic theory

This study is performed as a partial aid to a larger study that aims to determine if
electromagnetic fields produced by underwater power cables have any effect on marine
species. In this study, a new numerical method for calculating magnetic fields around
subsea power cables is presented and tested. The numerical method is derived from
electromagnetic theory, and the program, Matlab, is implemented in order to run the
simulations. The Matlab code is validated by performing a series of tests in which the
theoretical code is compared with other previously validated magnetic field solvers. Three
main tests are carried out; two of these tests are physical and involve the use of a
magnetometer, and the third is numerical and compares the code with another numerical
model known as Ansys. The data produced by the Matlab code remains consistent with
the measured values from both the magnetometer and the Ansys program; thus, the code is
considered valid. The validated Matlab code can then be implemented into other parts of
the study in order to plot the magnetic field around a specific power cable.

Computational accuracy is widely recognized as a critical issue in applied electromagnetics. Increasing computational power is being applied to solve more complex electromagnetic systems with an emphasis on computational accuracy. The work of this thesis is focused on the implementation of Method of Moments (MoM) to integral equation formulations. The goal of this effort is to use what is known as condition number, and, a heuristic rule-of-thumb is applied to investigate the computational accuracy of MoM in numerical electromagnetics. Other possible applications of condition number of the MoM matrix are also indicated.

A method for estimating the size distribution of magnetite nanoparticles from their magnetic properties is presented. The 10 nm diameter particles were coated with poly(acrylic) acid and prepared as a water-based suspension. A vacuum-dried sample was placed in a transmission electron microscope (TEM) so that the physical sizes of the particles could be estimated. The particle magnetization was measured by a superconducting quantum interference device (SQUID) in magnetic fields up to 25 kiloOersted and temperatures ranging from 5 to 370 Kelvin. The magnetic moments in the sample were estimated by fitting those measurements to a Langevin magnetization model, weighted by a log-normal distribution with unknown parameters.The best-fit procedure yielded particle volumes smaller than those observed by transmission electron microscopy, suggesting the existence of a magnetically inactive layer of atoms. In addition, our particles exhibited stronger spin-wave behavior than expected for particles of similar size, as evidenced by the lower saturation magnetization and higher Bloch coefficient.