Silsbee rule



Silsbee rule, Silsbee's rule or Silsbee criterion - a criterion describing the critical (maximum) value of magnetic field, above which a superconductor looses its superconducting state, and becomes a normal resistive conductor.

The phenomenon is thought to occur due to the magnetic field destroying the symmetry between up and down spins in Cooper pairs or pairons. The density of current capable of such action is called depairing current density.

The original rule was proposed in 1916 by F.B. Silsbee, and regarded only the value of transport current, without any other external magnetic field applied. However, the behaviour can be extended to the condition where the collapse of superconductivity is caused by the addition of magnetic field generated by the transport current and the externally applied field and it is then sometimes referred to as the generalised Silsbee's rule.

The value of critical field depends on the type of material, but it is also decreases with increasing temperature.

Type I and type II superconductors
Silsbee rule is directly applicable to type I superconductors, where the collapse of the superconducting state is sharp. For the type II superconductors the transition is gradual and the rule denotes only a point after which the vortex state (mixed) develops. Therefore, some authors talk about "breakdown of Silsbee rule".

In type I superconductors the critical fields are lower, not exceeding around 2 T. In type II they can reach much greater values, for instance 44 T for Nb3Al. Such materials are therefore much more applicable for practical applications.

Equation
For type I superconductors the critical value of the transport current Ic (i.e. the main current in the conductor) can be calculated as:

$$I_c = 2 \cdot \pi \cdot r \cdot \left(H_c - 2 \cdot H_t \right)$$

where: r - radius of the superconductor (m), Hc - value of critical field strength (A/m), Ht - value of applied transverse magnetic field strength (A/m)