Meissner effect

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Meissner effect

Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature.

The Meissner effect (or Meissner-Ochsenfeld effect) is the effect by which a weak magnetic field decays rapidly to zero in the interior of a superconductor. The distance to which the field is active is known as the London penetration depth. This active exclusion of magnetic fields is distinct from perfect diamagnetism. It is seen that the magnetic field will be zero inside the material in the superconducting state regardless of what it was before the material became superconducting. It was discovered by Walther Meißner and Robert Ochsenfeld in 1933. The Meissner effect is one of the defining features of superconductivity, and its discovery served to establish that the onset of superconductivity is a phase transition.

1 Theory
2 References
3 See also
4 External links

[edit] Theory

A theoretical explanation of the Meissner effect can be obtained from the London equation and one of Maxwell's equations.

$\nabla \times \vec{J}_{d}= \frac{-\vec{B}}{\mu_0 \lambda^2}$

is the London equation, where $J d$ is the current density, $B$ is the magnetic field and $λ$ is the penetration depth.

$\nabla \times \vec{B} = \mu_0 \vec{J}_d$

is one of Maxwell's equations. Since the magnetic field is solenoidal, we have the relation

$\nabla \times (\nabla \times \vec{B}) = - \nabla^2\vec{B}$

Using the above relations, it is shown that

$\nabla^2\vec{B} = \frac{\vec{B}}{\lambda^2}$

Since the Laplacian of B is zero, it follows that the field inside a superconductor, beyond the penetration depth, decays to zero. The net field is zero because the applied field is canceled by the field produced by the current density $\vec{J}_{d}$ . For large samples, $\vec{J}_{d}$ can be replaced by a surface current density $\vec{K}_{d}$ that decays exponentially into the sample with characteristic length given by the London penetration depth.

The Meissner effect will levitate a magnet as long as the magnetic field does not exceed the critical magnetic field. A magnet that is suspended by the superconductor has two interesting properties; it does not move, and it can spin without friction. The ability for the magnet to stay perfectly still is due to flux pinning, in which the magnetic field lines become trapped within the superconductor at sites of impurity in the crystal structure.

[edit] References

1. M. Tinkham, “Introduction to Superconductivity”, 2nd Ed., Dover Books on Physics (2004). ISBN 0-486-43503-2 (Paperback). A good technical reference.

2. Fritz London, "Superfluids", Volume I, "Macroscopic Thoery of Superconductivity", (1950). Reprinted by Dover. ISBN 0-486-600440. By the man who explained the Meissner effect. pp.34-37 gives a technical discussion of the Meissner effect for a superconducting sphere.

3. Wayne M. Saslow, "Electricity, Magnetism, and Light", Academic (2002). ISBN 0-12-619455-6. pp.486-489 gives a simple mathematical discussion of the surface currents responsible for the Meissner effect, in the case of a long magnet levitated above a superconducting plane.