  Vortex fluctuations in the $La_{2-x}Sr_{x}CuO_{4+\delta}$ system have been
studied as a function of magnetic field, temperature and carrier concentration
in order to determine the dimensionality of the fluctuations. For a $x=0.10$
sample, there is a unique crossing-temperature on the magnetization vs.
temperature plots for all magnetic fields up to 7 T, and the data scale very
well with 2D fluctuation theory. At lower x-values where $H_{c2}$ is much
smaller, there are two well defined crossing points, one at low fields
(typically less than 1 T) and another at high fields (typically 3-7 T). A fit
of the data to fluctuation theory shows that the low field crossing data scale
as 2D fluctuations and the high field crossing data scale as 3D fluctuations.
It would appear that as the magnetic field approaches $H_{c2}$, there is a 2D
to 3D cross-over where the low field 2D pancake vortex structure transforms
into a 3D vortex structure.
