Propagation of a Magnetic Field into a Superconductor

The propagation of a magnetic field into a superconducting wire of circular cross section is analyzed theoretically. Upper and lower bounds are obtained on $t_0$, the time required for the field to reach the axis, and on $R\left(t\right)\mathrm{}$, the inner radius of the normally conducting region. The lower bound is just the approximate result obtained by Sixtus and Tonks, Pippard, and Lipshitz. It has been verified experimentally by Faber for applied fields less than 1.04 times the critical field. It is believed that for large applied fields the actual results should be closer to the upper bounds.