Flux Trapping Effect: Magnetic Suspension & Levitation

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Magnetic suspension and levitation in superconductors result from the flux trapping effect, where magnetic flux becomes confined within the material. When a magnet is brought close to a superconductor, it can attract and repel, but if the magnet's field strength exceeds the superconductor's critical field, the superconductor loses its superconducting properties. Type II superconductors have two critical field strengths; below the lower threshold, the superconductor becomes normal, while above it, only certain regions transition to normal. These normal state channels allow magnetic flux to penetrate, leading to trapped flux within the superconductor. This phenomenon is essential for understanding magnetic levitation and suspension in superconductors.
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Magnetic suspension and levitation is the caused by the flux trapping effect in superconductors.How does this flux get "trapped"?

Another quick question-
We link a magnet to a superconductor by bringing it very close to one ,until both of them start attracting and repelling. My question is, if the magnetic field strength of this magnet is greater than the critical field of the superconductor,the superconductor will lose its properties and become normal, instead of demonstrating magnetic levitation and suspension ,right ?
 
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Without getting into details, Type II superconductor effectively has two critical field strengths. While there still exists the critical field under which the entire superconductor becomes normal conductor, above the lower of the thresholds, only small regions become normal. These regions form channels through the superconductor. Since the surface current can now exist in boundaries around these channels, magnetic flux can penetrate superconductor through these normal state channels. The magnetic flux in these channels becomes trapped.
 
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I was using the Smith chart to determine the input impedance of a transmission line that has a reflection from the load. One can do this if one knows the characteristic impedance Zo, the degree of mismatch of the load ZL and the length of the transmission line in wavelengths. However, my question is: Consider the input impedance of a wave which appears back at the source after reflection from the load and has traveled for some fraction of a wavelength. The impedance of this wave as it...
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