## LSU Historical Dissertations and Theses

1994

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

William O. Hamilton

#### Abstract

The transducer and SQUID are two major components for a resonant-mass gravitational wave antenna. They must always have high sensitivity and low noise. In this work, a two-mode superconducting inductive transducer for a three-mode gravitational wave bar antenna is designed. The construction and tests of small mass resonators that form the transducer are described. The experiments and test results of commercial dc SQUIDs at ultra-low temperature are discussed in detail. Special problems arise when SQUIDs are tested at ultra-low temperature in vacuum. We address the problems and provide proper solutions. Our experiments show that the dc SQUID made by Quantum Design operates well at temperatures as low as 50 mK. We find that the SQUID has an energy resolution of 2600 $\hbar$. The SQUID's noise did not decrease with temperature as was expected. The possible reasons for this are discussed. The two-mode inductive transducer is designed based on a noise analysis of the complete three-mode system. A small mass of 8-9 grams is chosen for the transducer's diaphragm. The geometry of both the small mass resonator and the intermediate resonator that form the transducer is designed with the aid of finite element analysis. One of two aluminum prototype resonators reached a mechanical Q of $8.3\times10\sp6$ at 4.2 K. Among the three fabricated niobium resonators, one achieved mechanical Qs of $2.4\times10\sp7$ at 4.2 K and $3.0\times10\sp7$ at around 7 K. Another one with arms cut by Electrical Discharge Machining has reached mechanical Qs of $7.4\times10\sp6$ at 4.2 K and $1.3\times10\sp7$ at 8.3 K. Its electrical Q has been found to be $5.0\times10\sp5$ with an electromechanical coupling efficiency of 15%. This is equivalent to an average $\beta$Q of $4.7\times10\sp5.$ This resonator is suitable for use in working transducers. An effective annealing procedure was discovered and applied in the fabrication process of these niobium resonators.

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