Design and construction of an ultrasonic probe for use in a Cryo-Magnet NMR Spectrometer

SINNMR (Sonically Induced Narrowing of the Nuclear Magnetic Resonance spectra of solids), is a novel technique that is being developed to enable the routine study of solids by nuclear magnetic resonance spectroscopy. SINNMR aims to narrow the broad resonances that are characteristic of solid state NMR by inducing rapid incoherent motion of solid particles suspended in a support medium, using high frequency ultrasound in the range 2-10 MHz. The width of the normal broad resonances from solids are due to incomplete averaging of several components of the total spin Hamiltonian caused by restrictions placed on molecular motion within a solid. At present Magic Angle Spinning (MAS) NMR is the classical solid state technique used to reduce line broadening, but: this has associated problems, not least of which is the appearance of many spinning side bands which confuse the spectra. It is hoped that SlNNMR will offer a simple alternative, particularly as it does not reveal spinning sidebands The fundamental question concerning whether the use of ultrasound within a cryo-magnet will cause quenching has been investigated with success, as even under the most extreme conditions of power, frequency and irradiator time, the magnet does not quench. The objective of this work is to design and construct a SINNMR probe for use in a super conducting cryo-magnet NMR spectrometer. A cell for such a probe has been constructed and incorporated into an adapted high resolution broadband probe. It has been proved that the cell is capable of causing cavitation, up to 10 MHz, by running a series of ultrasonic reactions within it and observing the reaction products. It was found that the ultrasound was causing the sample to be heated to unacceptable temperatures and this necessitated the incorporation of temperature stabilisation devices. Work has been performed on the investigation of the narrowing of the solid state 23Na spectrum of tri-sodium phosphate using high frequency ultrasound. Work has also been completed on the signal enhancement and T1 reduction of a liquid mixture and a pure compound using ultrasound. Some preliminary "bench" experiments have been completed on a novel ultrasonic device designed to help minimise sample heating. The concept involves passing the ultrasound through a temperature stabilised, liquid filled funnel that has a drum skin on the end that will enable the passage of ultrasound into the sample. Bench experiments have proved that acoustic attenuation is low and that cavitation in the liquid beyond the device is still possible.

Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.