Inverse problems in magnetohydrodynamics: theoretical and experimental aspects
Inverse problems in magnetohydrodynamics: theoretical and experimental aspects
Stefani, F.; Gerbeth, G.; Günther, U.; Gundrum, T.; Xu, M.
The interaction of magnetic fields with moving electrically conducting fluids is the subject of magnetohydrodynamics. There is a vast area of applications, e.g. in metal casting and crystal growth, where magnetic fields are used to act on the melt flow in order to improve the quality of the products. On the other hand, the moving fluid can also influence externally applied magnetic fields, and for large magnetic Reynolds numbers it can even yield selfexcitation of a magnetic field. This effect, called homogeneous dynamo effect, is at the root of magnetic field generation in planets, stars, and galaxies.
We focus on several inverse problems connected with the determination of velocities or velocity related quantities from magnetic field information that is measurable outside the fluid region. The underlying theory is presented in the framework of the integral equation approach to dynamos in finite domains, which can be cast into a linear inverse problem in case that the magnetic Reynolds number of the flow is not too large.
In this case it is necessary to apply external magnetic fields and to measure the flow induced electromagnetic fields. Two possibilities are considered: one can apply one magnetic field and measure the external induced magnetic field and the electric potential at the fluid boundary, or one can apply two different magnetic fields and measure the corresponding two sets of external induced magnetic fields.This latter contactless method is especially interesting for applications with hot and aggressive fluids or for facilities where the fluid boundary is not accessible for technological reasons. We consider the uniqueness problems of both methods finding that the rough topology of the flow can be determined from the measured data but that the depth dependence of the velocity must be inferred by regularization methods. We present first results of an experiment with a flow of InGaSn exposed to an externally magnetic field pointing subsequently in two different directions.
The linear character of the inverse MHD problem is lost when it comes to dynamos which work exclusively at large magnetic Reynolds numbers. Inverse dynamo problems are well known in geophysics and solar physics where information on the velocity structure is to be drawn from magnetic field data. They have acquired new relevance recently with the liquid sodium experiments in Riga and Karlsruhe. In connections with those experiment there are quite new inverse, design, and optimization problems. We show that even the simplest inverse spectral dynamo problems for very symmetric dynamos are far from trivial, compared to similar problems in quantum mechanics. We present examples where evolution strategies can successfully be employed to solve particular inverse
dynamo problems.

Lecture (Conference)
Inverse problems, design and optimization symposium, 17.19.03.2004, Rio de Janeiro, Brazil 
Contribution to proceedings
Inverse problems, design and optimization symposium, 17.19.03.2004, Rio de Janeiro, Brazil
Proceedings of the Inverse problems, design and optimization (IPDO2004), Vol. II, Rio de Janeiro: Epapers Publishing House Ltd, 8576500302, 151158 
Inverse Problems in Science and Engineering 14(2006)4, 411422
DOI: 10.1080/17415970600573791
Cited 1 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ5859
Publ.Id: 5859