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#

Data Fitting in the Time Domain

The SR data are fitted to a theoretical model of the
magnetic field *B* within a type II superconductor. The approximate
field distribution *n*(*B*) yielded by taking the real amplitude of the Fourier
transform of the measured
muon spin polarisation
is not useful for fitting, since
the inherent finite time window introduces distortions in the form of
ringing and broadening. To avoid these problems, all the results reported in
this thesis come from fits in the time domain.

Fitting the recorded muon polarisation to a function calculated from
a theoretical field *B* model forms the basis of a time domain analysis.
The polarisation function

utilised to fit the SR data consists of a contribution from the muons
that land in the superconducting sample and a term describing the
background signal created by those that miss it. The parameters *A* and
*A*_{b} reflect respectively the initial amplitudes of the superconducting and
background asymmetries, or spin polarisations. The Gaussian damping factors
and
model the field *B*inhomogeneity which is
additional to that of a regular array of vortices [49].
In the case of the superconducting signal the main sources of this
are nuclear dipolar fields and vortex lattice disorder.
The phase angles
and
account for the amount of spin
precession that occurs *before* the muons trigger the muon counter. The
vortex lattice field model described in the next section determines the
distribution *n*(*f*) of Larmor precession frequencies *f*.

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*Jess H. Brewer *

2001-10-31