## LSU Historical Dissertations and Theses

1990

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

W. O. Hamilton

#### Abstract

The design and development of an improved superconducting inductively modulated transducer is discussed. The transducer is designed to optimize the performance of a 2-mode, resonant bar, gravitational wave antenna. A detailed theoretical analysis which includes all relevant noise sources is described. Conditions for optimizing 2-mode detector performance are derived and design curves are presented. Based on the results of this analysis, an optimal transducer has been designed for use on the LSU gravitational wave detector. The fabrication and testing of several optimal mass 400gm transducer resonators is described. The effects of low temperature annealing on the mechanical Qs of the Nb resonators are discussed. The components of the transducer are discussed in detail. A superconducting flux transformer has been made to provide proper impedance matching to the squid amplifier. Its design achieves high coupling and low losses while a large d.c. supercurrent flows in its primary. A suspension system has been built to measure high mechanical Qs in heavy mass transducers. The suspension system did not limit Qs below $1.8\*10\sp6$. Two optimized transducers have been built and tested. Both achieved high electrical Qs of approximately 10$\sp5$. This electrical Q represents an improvement by a factor of approximately 5 over previous inductive transducers used on gravitational wave antennae. One of these transducers is mounted on the LSU gravitational wave antenna which is being cooled to 4K at the time of this writing. All the design goals for this optimized transducer have been achieved: optimal mass ($\approx$400gm), high mechanical Q ($\approx$1.8$\*10\sp6$), high electrical Q ($\approx$1$\*10\sp5$), strong coupling and optimal impedance matching to a BTI d.c. squid amplifier. The noise temperature of the LSU antenna equipped with this transducer is predicted using the theoretical analysis mentioned earlier. Based on the system's measured parameters, the detector is expected to achieve a noise temperature of $\approx$2mK. This represents a factor of 50 in improvement over its previous performance level. By coupling the optimal transducer to a squid with an energy sensitivity of 370h, an antenna noise temperature of less than 300$\mu$K can be achieved while operating at an ambient temperature of 4K. The noise analysis of a 3-mode gravitational wave detector is given. Design curves for optimizing the performance of a 3-mode system are presented. It is concluded that an optimized 3-mode system operating at 4K can achieve a noise temperature of 71$\mu$K.

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