Magnetohydrodynamic experiments on cosmic magnetic fields

It is well known that cosmic magnetic fields, including the fields of planets, stars, and galaxies, are produced by the hydromagnetic dynamo effect in moving electrically conducting fluids. It is less well known that cosmic magnetic fields play also an active role in cosmic structure formation by enabling outward transport of angular momentum in accretion disks via the magnetorotational instability (MRI). Considerable theoretical and computational progress has been made in understanding both processes. In addition to this, the last ten years have seen tremendous efforts in studying these effects in the laboratory. In 1999, magnetic field self-excitation was observed in the large scale liquid sodium facilities in Riga and Karlsruhe. Recently, self-excitation was also observed in the French "von Karman sodium" (VKS) experiment, although with the help of iron propellers which complicates the interpretation of the results. The magnetorotational instability was recently observed in the ''Potsdam Rossendorf Magnetic Instability Experiment'' (PROMISE). In the talk, the history of dynamo and MRI experiments is delineated, and some interesting directions of future work are discussed.