Analytic solutions to Maxwell–London equations and levitationforce for a general magnetic source in the presence of a long type-IIsuperconducting cylinder |
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Authors: | Qiong-Gui Lin |
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Affiliation: | (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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