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Superconductor Module

⚠ Experimental feature. The superconductor module is under active development. The interface and the supported parameter ranges may change without notice.

A superconductor is a material that conducts electric current with essentially zero resistance when cooled below a critical temperature \(T_c\). It also expels the magnetic flux from its interior (the Meissner effect). Both properties are intrinsic. You cannot match them by simply increasing the conductivity of a normal metal. They emerge together below \(T_c\) from a quantum-mechanical condensation of the charge carriers into a single coherent state.

A critical surface in the \((T, B, J)\) space bounds the superconducting state. Three coupled thresholds define it:

  • the critical temperature \(T_c\),
  • the upper critical field \(B_{c2}\) (the magnetic flux density above which superconductivity is destroyed), and
  • the critical current density \(J_c\) (the transport current density above which dissipation appears).

Crossing any one of these limits drives the material back into the normal (resistive) state. Materials with higher critical values can sustain larger currents in stronger fields and are the targets of engineering design.

Type-I and Type-II superconductors

Superconductors fall into two families with very different responses to a magnetic field:

  • Type-I superconductors (pure Pb, Hg, Sn, In, ...) expel the magnetic field completely up to a single critical field \(H_c\) and then turn fully normal. They have low \(H_c\), do not tolerate large currents in a field, and are of no practical engineering interest at scale.

  • Type-II superconductors (NbTi, Nb₃Sn, MgB₂, REBCO, BSCCO, ...) admit magnetic flux above a lower critical field \(H_{c1}\) in the form of quantised vortices that arrange in a regular lattice. Each vortex carries one flux quantum and can move under a Lorentz force, which dissipates energy. Pins on lattice defects suppress this motion, so the material can carry very large currents up to \(H_{c2}\). All practical engineering superconductors are type-II.

Module scope

The Superconductor module extends the Time-Domain Magnetic Model with a constitutive law for type-II superconductors in the mixed (vortex) state. It replaces ordinary Ohm's law on the conductor region by a strongly nonlinear power-law relation between the electric field \(\mathbf{E}\) and the current density \(\mathbf{J}\). This is the standard empirical fit used in engineering practice to describe flux-creep dissipation around the critical current density.

The module is intended for AC-loss studies, fault-current limiters, HTS magnets, and similar applications. In these applications the bulk superconducting response of the conductor, rather than its full microscopic description, is the engineering quantity of interest.

Contents

  • Superconductor Material — power-law E-J characteristic, usage, solver settings, limitations, and reference parameters for common HTS and LTS conductors.