How to calculate Miits (quench integral)?

[Bogdan320]

How to find the value of miits integral for calculations of the propagation of normal zonei in superconductors?

 

[eljose79]

Hello,

Thank you for your question about calculating the value of the integral for the propagation of normal zones in superconductors. This is an important aspect of studying superconductivity and understanding its behavior.

To begin, let us first define what we mean by the "normal zone" in a superconductor. In a superconductor, there are two distinct regions: the superconducting region and the normal region. The superconducting region is where the material exhibits zero electrical resistance and perfect diamagnetism, while the normal region is where the material behaves like a regular conductor.

The propagation of normal zones in superconductors refers to the movement of the boundary between these two regions. This boundary can be influenced by various factors such as temperature, magnetic fields, and current density.

Now, to calculate the value of the integral for the propagation of normal zones, we need to use the Ginzburg-Landau theory. This theory describes the behavior of superconductors near the critical temperature, where the material transitions from the superconducting state to the normal state.

The integral we are interested in is known as the Ginzburg-Landau energy functional, which is given by:

E = ∫ [α(T)Ψ² + β(T)Ψ⁴ + K(T)|∇Ψ|² + |(∇-i2πA)Ψ|²] dV

where α(T) and β(T) are temperature-dependent coefficients, K(T) is known as the Ginzburg-Landau parameter, Ψ is the superconducting order parameter, and A is the vector potential.

This integral can be solved numerically using various methods such as finite element analysis or Monte Carlo simulations. The value of the integral will depend on the specific parameters of the material and external conditions such as temperature and magnetic field.

I hope this helps to answer your question. Please let me know if you have any further inquiries.