Inverse dynamo problem in a cylinder

Abstract

An inverse dynamo problem is presented in which we search for either kinematic dynamos which produce the same external magnetic fields or an invisible dynamo. The existence of flows which produce the same external magnetic fields is proved. However, we have not found general conditions necessary for such kind of dynamos. An “invisible dynamo” operates in an electrically conducting region surrounded by vacuum and generates a magnetic field trapped in the electrically conducting region so that no magnetic field exists in the vacuum. Invisible magnetic decay modes exist in cylinders, but no invisible growing field supported by the dynamo mechanism has been found.

Keywords:

• Inverse dynamo problem
• Invisible dynamo
• Kinematic dynamo
• Helical flows
• Ponomarenko dynamo

Acknowledgements

This research has been supported by the Alexander von Humboldt Foundation, the Grant Agency of the Academy of Sciences of the Czech Republic (Grant No. IAA300120704) and partially by the Grant Agency of the Czech Republic (Grant No. 205/04/P182) and INTAS Foundation (Grant No. 03-51-5807).