Fluxon

As flux quantization is referred to the effect that the magnetic flux can be only integer multiples of the flux quantum by a ring of superconducting material. The flux quantization is a consequence of the Meissner effect. Instead flux quantum and the names fluxon and Fluxoid are common.

The term fluxon is also used in the discretization of the magnetohydrodynamics using finite element method.

Flux quantum in the superconductor

The quantization of the magnetic flux can be determined by the quantum mechanical view of the distributed current flow in the superconductor:

The flux quantum has an amount of magnetic flux of

Here h is the Planck constant and e is the elementary charge, Wb represents the unity Weber.

The factor in the denominator of the formula refers to a double electron charge. In this double electron charge, the BCS model, which considers the so-called Cooper pairs as the cause of superconductivity is based.

Abrikossow turbulence

A flux quantum in accordance with the Abrikossow turbulence is a needle-shaped crystal ( core ) in a second type superconductor which is surrounded by flowing Supra.

The magnetic field by such a single crystal and its neighborhood has a magnitude of about and is quantized by the phase characteristics of the magnetic vector potential in quantum electrodynamics.

Josephson vortex

The Josephson vortex is the counterpart to Abrikossow turbulence in circular Supra currents without physical core in a superconductor Article 2 The core is in this case the mathematical center of the circle.

The inverse of the flux quantum here is the Josephson constant:

Its value can be measured very accurately and is under current measurement accuracy:

Derivation of the flux quantization

The superconducting state is a quantum mechanical state, extends over macroscopic length scales. It can therefore be described by the macroscopic wavefunction:

This is based ( in a quasi-classical, ie macroscopic approximation) assuming that has a constant amplitude and only the phase S is location-dependent. For this wave function, the London equation

Due to the Meissner effect, the magnetic induction vanishes inside a superconductor. For the static case, which follows also for the interior of the superconductor (one of the Maxwell equations). It is therefore

Summarizes the constants together and integrated on both sides along a closed path C through the inside of the superconductor so obtained

The left-hand side describes the change in the S phase upon passing through the closed path C. Since the wave function is unique, the phase change, only integer multiples of two may be. It is therefore

After applies Stokes' theorem

Where F is limited by face C and the magnetic flux through this surface. is the vector having the magnitude and the direction of the normal to the considered outer face member. This results in a total

The flow through a superconducting ring is quantized so. Experimental results, suggesting that the electron pairs, called Cooper pairs form.

Fluxon in magnetohydrodynamics

In magnetohydrodynamics (MHD ) is called with a discretized fluxon magnetic field line finite amount in a finite element model. Here, the topology of the investigated facts is trying to get under consideration the limited computing capacities as possible.