After the dynamo experiment in November 1999 [A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000)] had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.

In an experiment at the Riga sodium dynamo facility, a slowly growing magnetic field eigenmode has been detected over a period of about 15 seconds. For a slightly decreased propeller rotation rate, additional measurements showed a slow decay of this mode. The measured results correspond satisfactory with numerical predictions for the growth rates and frequencies.

When a ferromagnetic fluid with a horizontal free surface is subjected to a uniform vertical applied magnetic field B0, it is known (Cowley & Rosensweig 1967) that the surface may be unstable when the field strength exceeds a certain critical value Bc. In this paper we consider, by means of an energy minimization principle, the possible forms that the surface may then take. Under the assumption that |μ − 1| [Lt ] 1 (where μ is the magnetic permeability of the fluid), it is shown that when B0 is near to Bc there are three equilibrium configurations for the surface: (i) flat surface, (ii) stationary hexagonal pattern, (iii) stationary square pattern. Configuration (i) is stable for B0 < Bc, (ii) is stable for B0 > Bc and B0−Bc sufficiently small, and (iii) is stable for some higher values of B0. In each configuration the fluid is static, and the surface is in equilibrium under the joint action of gravity, surface tension, and magnetic forces. The amplitude of the surface perturbation in cases (ii) and (iii) is calculated, and hysteresis effects associated with increase and decrease of B0 are discussed.

Cosmic magnetic fields, including the fields of planets, stars, and galaxies, are believed to be caused by dynamo action in moving electrically conducting fluids. While the theory and numerics of hydromagnetic dynamos have flourished during recent decades, an experimental validation of the effect was missing until recently. We sketch the long history towards a working laboratory dynamo. We report on the first successful experiments at the sodium facilities in Riga and Karlsruhe, and on other experiments which are carried out or planned at various places in the world. C. Taking stock 984 V. Further and Future Experiments 984 A. Maryland 984 B. Cadarache 985 C. Madison 985 D. Grenoble 985 E. Perm 986 F. New Mexico 987 VI. Conclusions 987 Acknowledgments 987 References 988

It is widely believed that almost all magnetic fields in a natural environment are the result of the dynamo process—the field generation in moving nearly homogeneous electro-conducting fluids. This dynamo process occurs in the depths of celestial bodies such as the Earth, most of the planets, the Sun, other stars, and even galaxies. The Riga dynamo experiment is not intended as a model of any particular celestial body. It aims at demonstrating the basic dynamo mechanism—that the intense motion in a large volume of a good electro-conducting liquid creates a magnetic field. In the present paper, the set-up and the main results of this experiment are presented, with some focus on the theoretical interpretation of the data.