Superconducting limits and applications

A material stays superconducting only while three quantities are below their critical values. Exceeding any one of them returns it to the normal state.

Limiting factors

1. Critical temperature $T_c$: above $T_c$ thermal energy breaks the Cooper pairs (e.g. Hg 4.2 K, Nb$_3$Sn 18 K, YBCO 92 K).
2. Critical magnetic field $H_c$: a field above $H_c$ destroys superconductivity. It depends on temperature: $H_c(T) = H_0[1 - (T/T_c)^2]$.
3. Critical current density $J_c$: a current produces its own field; when this field at the surface reaches $H_c$, superconductivity is lost. For a wire of radius $r$: $I_c = 2\pi r H_c$.

The three form a critical surface; the material is superconducting only inside it.

Applications

• MRI and NMR magnets: NbTi coils give strong, stable fields with no power loss.
• Maglev trains: superconducting magnets for levitation (e.g. Japan's SCMaglev).
• Particle accelerators: bending magnets in the LHC.
• SQUIDs: extremely sensitive magnetometers (brain and heart signals).
• Power cables and fault current limiters: low-loss transmission and fast fault limiting.
• SMES: superconducting magnetic energy storage.
• Josephson junction devices: fast switching and quantum computing qubits.