Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

The electron optical limits of performance of single-polepiece magnetic electron lenses

The thesis is concerned with the electron properties of single-polepiece magnetic electron lenses especially under conditions of extreme polepiece saturation. The electron optical properties are first analysed under conditions of high polepiece permeability. From this analysis, a general idea can be obtained of the important parameters that affect ultimate lens performance. In addition, useful information is obtained concerning the design of improved lenses operating under conditions of extreme polepiece saturation, for example at flux densities of the order of 10 Tesla. It is shown that in a single-polepiece lens , the position and shape of the lens exciting coil plays an important role. In particular, the maximum permissible current density in the windings,rather than the properties of the iron, can set a limit to lens performance. This factor was therefore investigated in some detail. The axial field distribution of a single-polepiece lens, unlike that of a conventional lens, is highly asymmetrical. There are therefore two possible physical arrangements of the lens with respect to the incoming electron beam. In general these two orientations will result in different aberration coefficients. This feature has also been investigated in some detail. Single-pole piece lenses are thus considerably more complicated electron- optically than conventional double polepiece lenses. In particular, the absence of the usual second polepiece causes most of the axial magnetic flux density distribution to lie outside the body of the lens. This can have many advantages in electron microscopy but it creates problems in calculating the magnetic field distribution. In particular, presently available computer programs are liable to be considerably in error when applied to such structures. It was therefore necessary to find independent ways of checking the field calculations. Furthermore, if the polepiece is allowed to saturate, much more calculation is involved since the field distribution becomes a non-linear function of the lens excitation. In searching for optimum lens designs, care was therefore taken to ensure that the coil was placed in the optimum position. If this condition is satisfied there seems to be no theoretical limit to the maximum flux density that can be attained at the polepiece tip. However , under iron saturation condition, some broadening of the axial field distribution will take place, thereby changing the lens aberrations . Extensive calculations were therefore made to find the minimum spherical and chromatic aberration coefficients . The focal properties of such lens designs are presented and compared with the best conventional double-polepiece lenses presently available.

Fabrication of magnetic drug-loaded polymeric composite nanofibres and their drug release characteristics

Magnetic polymer nanofibres intended for drug delivery have been designed and fabricated by electrospinning. Magnetite (Fe3O4) nanoparticles were successfully incorporated into electrospun nanofibre composites of two cellulose derivatives, dehydroxypropyl methyl cellulose phthalate (HPMCP) and cellulose acetate (CA), while indomethacin (IDN) and aspirin have been used as model drugs. The morphology of the neat and magnetic drug-loaded electrospun fibres and the release characteristics of the drugs in artificial intestinal juice were investigated. It was found that both types of electrospun composite nanofibres containing magnetite nanoparticles showed superparamagnetism at room temperature, and their saturation magnetisation and morphology depend on the Fe3O4 nanoparticle content. Furthermore, the presence of the magnetite nanoparticles did not affect the drug release profiles of the nanofibrous devices. The feasibility of controlled drug release to a target area of treatment under the guidance of an external magnetic field has also been demonstrated, showing the viability of the concept of magnetic drug-loaded polymeric composite nanofibres for magneto-chemotherapy.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.