Analytic solutions to Maxwell–London equations and levitation
force for a general magnetic source in the presence of a long type-II
superconducting cylinder |
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Authors: | Qiong-Gui Lin |
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Institution: | (1) P.R. China and Department of Physics, Sun Yat-Sen University, China Center of Advanced Science and Technology (World Laboratory), P.O. Box 8730, Beijing 100080, Guangzhou, 510275, P.R. China |
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Abstract: | The interaction between a general magnetic source and a
long type-II superconducting cylinder in the Meissner or mixed state
is studied within the London theory. We first study the Meissner
state and solve the Maxwell–London equations when the source is a
magnetic monopole located at an arbitrary position. Then the field
and supercurrent for a more complicated magnetic charge distribution
can be obtained by superposition. A magnetic point dipole with
arbitrary direction is studied in detail. It turns out that the
levitation force on the dipole contains in general an angular as well
as a radial component. By integration we obtain the field and
supercurrent when the source is a two-dimensional monopole (a
magnetically charged long thread along the axial direction), from
which the results for a two-dimensional point dipole easily follow.
In the latter case the levitation force points in the radial
direction regardless of the orientation of the dipole. The case for a
current carrying long straight wire parallel to the cylindrical axis
is solved separately. The limit of ideal Meissner state is discussed
in most cases. The case of mixed state is discussed briefly. It turns
out that vortex lines along the axial direction and vortex rings
concentric with the cylinder have no effect outside the cylinder and
the levitation forces remain the same as in the case of the Meissner
state. |
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Keywords: | 74 20 De Phenomenological theories 41 20 Gz Magnetostatics magnetic shielding magnetic induction boundary-value problems 74 25 Ha Magnetic properties 74 25 Op Mixed states critical fields and surface sheaths |
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