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CONDMATH — Result In Brief

Project ID: 202859
Funded under: FP7-IDEAS-ERC
Country: Denmark

Superconductor behaviour in strong magnetic fields

The mathematical model for superconductivity is still being developed and tested. Subjecting superconducting materials to different magnetic field strengths is an important tool in research and industrial applications.
Superconductor behaviour in strong magnetic fields
The EU-funded project CONDMATH (Mathematical problems in superconductivity and Bose-Einstein condensation) has investigated the mathematical understanding of phenomena from modern quantum physics, in particular, superconductivity. Superconductivity is generally well described by a non-linear model proposed by Ginzburg and Landau. The question that has remained is the behaviour of superconducting materials when subjected to strong magnetic fields.

Earlier experiments demonstrated that when subjected to weak magnetic fields, Type II superconductors remain in the globally superconducting state. At a critical strength of the external magnetic field, HC1, superconductivity is broken at point like singularities called vortices. When the strength of the magnetic field is increased to a second critical value, HC2, superconductivity is completely destroyed in the interior and only remains in a narrow boundary region. The third and final critical field, HC3, completely halts superconductivity.

The CONDMATH project has provided a precise understanding of the prevailing conditions for field strengths starting below HC2 and up to HC3. In turn, this has provided a full mathematical understanding of the physical phenomena first described in the 1950s.

The researchers considered a ball-shaped sample subjected to a constant magnetic field pointing from ‘south’ to ‘north’ on the object. Starting with very strong magnetic fields and decreasing their intensity, CONDMATH members calculated a well-defined value of HC3 where superconductivity will appear, in a narrow region near the ‘equator’ of the ball.

When decreasing the intensity of the magnetic field further, superconductivity will remain localised to the boundary of the sample but in a progressively larger ‘tropical’ region. For a given magnetic field strength, the project researchers successfully predicted the size of this ‘tropical’ region.

The second critical field, HC2, is both where the ‘tropical’ region reaches the ‘poles’ of the ball and where superconductivity starts to build up in the interior of the ball. For magnetic field strengths slightly below HC2, superconductivity will be uniformly weak in the interior, but will slowly increase as the field is reduced.

Superconductors can increase the efficiency of any instrument that uses electricity or magnetism once the necessary temperature range is achieved. The economic value of applications in electronics, energy supply, medical imaging, transportation, and other areas is now doubling every five years. Improvements in the theory of superconductivity are important for each new application.

Related information


Superconductivity, Type II semiconductor, non-linear model, magnetic field, Ginzburg-Landau model
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