---
title: Integral equation for thin conductors solved by finite-elements (Comsol)
description: "HTS Modelling Workgroup | Model files\nIntegral equation for thin conductors solved by finite-elements (Comsol)"
---

[Model files](https://htsmodelling.com/model-files)

# [Integral equation for thin conductors solved by finite-elements (Comsol)](https://htsmodelling.com/model-files/integral-equation-for-thin-conductors)

 Written by [administrator](https://htsmodelling.com/model-files/author/administrator) | Mar 14, 2024 5:57:25 PM

The model calculates current density/field distribution in a superconducting thin conductors in the presence of a time-dependent transport current, background field or combination thereof (as in the figure below). The superconductor is modeled with a power-law. Dependence of Jc on magnetic field and position can be easily incorporated.

The extension of the model to stacks/windings and radial/polygonal cables can be found in these two articles: 

1. [Brambilla et al. 2009 *Supercond. Sci. Tech.* **22** (7) 075018](https://iopscience.iop.org/0953-2048/22/7/075018/)
2. [Brambilla et al. 2012 *IEEE Trans. Appl. Supercond.* **22** (4) 8401006](https://ieeexplore.ieee.org/abstract/document/6248174).

The approach is the same as in the case of a single tape, only the form of the kernel (expressing the electromagnetic interaction with the other tapes).

The figure shows the temporal evolution of the current density along the tape’s width under the simultaneous action of AC transport current and AC magnetic field.

Downloads

References

1. [Brambilla et. al. 2008 *Supercond. Sci. Tech.* **21** (10) 105008](https://iopscience.iop.org/0953-2048/21/10/105008).

[View full post](https://htsmodelling.com/model-files/integral-equation-for-thin-conductors)

```json
{
  "@context" : "http://schema.org",
  "@type" : "BlogPosting",
  "author" : {
    "@type" : "Person",
    "name" : "administrator"
  },
  "dateModified" : "2024-05-06T02:01:14.723Z",
  "datePublished" : "2024-03-14T17:57:25Z",
  "headline" : "Integral equation for thin conductors solved by finite-elements (Comsol)",
  "image" : {
    "@type" : "ImageObject",
    "height" : 480,
    "url" : "https://144281086.fs1.hubspotusercontent-eu1.net/hubfs/144281086/model-files/01-internal-equation/Janimation.gif",
    "width" : 640
  },
  "mainEntityOfPage" : "https://htsmodelling.com/model-files/integral-equation-for-thin-conductors",
  "publisher" : {
    "@type" : "Organization",
    "logo" : {
      "@type" : "ImageObject",
      "height" : 60,
      "url" : "/hs/hsstatic/content_shared_assets/static-1.4092/img/default-amp-logo.png",
      "width" : 60
    },
    "name" : "Model files"
  }
}
```