| Author | Message | ||
     nikos adamopoulos (nadam) New member Username: nadam Post Number: 2 Registered: 06-2008 |
I calculate first the magnetic field produced by an external magnetic field applied to a superconductor with specific magnetization properties. This runs smoothly with excellent results. Then I want to turn on an external electric current flowing inside the superconductor. One way to do this is to apply the Ampere’s law on the boundary of the superconductor. Therefore I want to insert a constraint in the form LineIntergral(H.dl) = It, where H is the magnetic field vector, dl is measured along the boundary and It is the transport current. FlexPde however does not allow me to perform this common line integral because it seems it needs only scalar quantities and not vector quantities such as H. Is there any way to perform this task? Thank you. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1148 Registered: 06-2003 |
You could, of course, produce a vector integral by integrating the components separately. But if you look closer, you will see that Ampere's Law does not integrate a vector. It integrates the dot product of the field vector and the path direction vector. This dot product produces a scalar result, which can be integrated. In your case, this would be LINE_INTEGRAL(TANGENTIAL(H),"path"). You could use this integral to put a constraint on a current distribution, but not to generate a current. There are an infinite number of current distributions that will give the same integral, and Ampere's Law does not provide information to distinguish them. You need to solve for a current distribution, and having done this, you probably don't need Ampere's Law. | ||
| nikos adamopoulos (nadam) Junior Member Username: nadam Post Number: 3 Registered: 06-2008 |
The constitutive equation is curl(B)=J. The same equation applies both for the case where an electric current is generated due to non homogeneous magnetic field and for the case where a magnetic field is produced due to an externally driven electric current. It is the boundary conditions which can distinguish between the two cases. The boundary conditions are the conditions on the surface of the conductor and the conditions at infinity. These constraints do not seem to give any results. The problem is how to describe the magnetic field produced by an external current when: 1. only the total current that passes through the conductor is known and this is measured in the laboratory apparatus in Amperes, 2. the exact variation of the current density inside the conductor is not known since this depends on the material properties such as anisotropy, magnetic field dependence, geometry. The exact variation of the current density is what is needed to be calculated either in an analytical model or in a numerical model. I would be pleased to receive your comments. | ||
| Marek Nelson (mgnelson) Moderator Username: mgnelson Post Number: 49 Registered: 07-2007 |
It sounds like you have tried to construct a script for FlexPDE. If you post it, we can take a look at it. | ||
| nikos adamopoulos (nadam) Member Username: nadam Post Number: 4 Registered: 06-2008 |
I think I have managed to find a way to treat this problem, even if not being totally correct. I souround the conductor by an intermediate region with the properties of air (this may be not necessary) and then by another region suppossedly being far away from the current carrying conductor. At this distant boundary I set the boundary conditions in line with Ampere's law assuming that the magnetic field will be fully parallel to the boundaries of that extended region. The line integral of the magnetic field is then equal to the current in the conductor, which is allowed to increase with time. It would perhaps be more appropriate to have this distant boundary in the form of a circle but this will require a combination of cartesian and cylindircal coordinates. The ideal boundary condition would be the line integral set on the boundary of the conductor but this does not work. |