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Description:
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In part I , a numerical study of the mixed states in a mesoscopic type -II superconducting
cylinder is described . Steady -state configurations and transient behavior of
the magnetic vortices for various values of the applied magnetic field H are presented .
Transitions between different multi -vortex states as H is changed is demonstrated by
abrupt changes in vortex configurations and jumps in the B vs H plot . An efficient
scheme to determine the equilibrium vortex configuration in a mesoscopic system at
any given applied field , not limited to the symmetry of the system , is devised and
demonstrated .
In part II , a superconducting thin film is subject to a non -uniform magnetic field
from a vertical magnetic dipole , consisting of two magnetic monopoles of opposite
charges . For a film with constant thickness and with no pins , it has been found that
the film carries two pairs of vortex -antivortex in the steady state in the imposed
flux range of 2 .15 < (Phi )+ < 2 .90 (in units of flux quantum ) and no vortex at all for
(Phi )+ <= 2 .15 . Transitions from a superconducting state with 3 pairs of vortex -antivortex
to one with 2 pairs , where a pair of vortex -antivortex annihilates , have been observed
in the pseudo -time sequence . With a perturbation with antidots (holes ) , vortexantivortex
pair has been created for lower magnetic fluxes down to (Phi )+ = 1 .3 .
In the sample of size 16 (Xi ) x 16 (Xi ) , the attraction force between the vortex and
antivortex always dominates over the pinning force , so that they eventually come out
of pins , move toward each other , and annihilate each other . The annihilation rate ,
measured with time taken for the annihilation , is reduced noticeably by the increase
of the distance between pins , or the increase in the pin size . A simulation of the
magnetic vortex pinning in the sample of size 32 (Xi ) x 32 (Xi ) suggests we are likely to
achieve pinning of the vortex -antivortex pair with the sample size around this and
vortex -antivortex separation of 22 (Xi ) . Using this sample as a template , the maximum
density of pinned vortices achievable is calculates to be about 7 .6 x 10^14 vortices /m2
for (Xi ) = ~ 1 .6A° . |