The computer time allocated to calculating
of Eq. (3.9), is significant enough that it is
practical to avoid the large sum over reciprocal lattice vectors
for each iteration in the -minimization
procedure. Consequently, a Taylor series expansion around an initial
value of the magnetic penetration depth
was employed in the actual
fitting program:

so that, is determined by expanding about the initial point . In this way, is calculated by summing over the reciprocal lattice vectors [in Eq. (3.9)], only once for an initial set of parameters and , where is the initial value of the average field. It is not necessary to expand about . This is because changes in the average field merely shift the field distribution along the field (or frequency) axis. In the fitting process, field shifts in excess of a conservative value of T were not permitted before the program was stopped, the initial parameters changed, and the data refitted.

Table A.1 shows the accuracy of the Taylor series assuming an average magnetic field 0.5T and . The error in using Eq. (A.1), expressed as a percentage of the exact calculation of using Eq. (3.9), is shown for calculated at the vortex core and at a saddle point. The results show that even large changes in give a good approximation for . In a typical fit, is calculated in excess of 150,000times, so that using a Taylor series greatly diminishes the time required to fit.

2001-09-28