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Magnetic fields of planets, stars and galaxies are generated by self-excitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilising rotational flows that would be otherwise hydrodynamically stable. For a long time, both hydromagnetic dynamo action as well as magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. In this paper, we summarise the results of liquid metal experiments devoted to the dynamo effect and various magnetic instabilities such as the helical and the azimuthal magnetorotational instability and the Tayler instability. We discuss in detail our plans for a precession-driven dynamo experiment and a large-scale Tayler–Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear. [ABSTRACT FROM AUTHOR]

The induction equation of magnetohydrodynamics (MHD) is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent developments concerning the numerical implementation of this scheme and its applications to various forward and inverse problems in dynamo theory and applied MHD. [ABSTRACT FROM PUBLISHER]

The eigenvalues and eigenfunctions of a linear α2-dynamo have been computed for different spatial distributions of an isotropic α-effect. Oscillatory solutions are obtained when α exhibits a sign change in the radial direction. The time-dependent solutions arise at the so-called exceptional points where two stationary modes merge and continue as an oscillatory eigenfunction with conjugate complex eigenvalues. The close proximity of oscillatory and non-oscillatory solutions may serve as the basic ingredient for reversal models that describe abrupt polarity switches of a dipole induced by noise. Whereas the presence of an inner core with different magnetic diffusivity has remarkable little impact on the character of the dominating dynamo eigenmodes, the introduction of equatorial symmetry breaking considerably changes the geometric character of the solutions. Around the dynamo threshold, the leading modes correspond to hemispherical dynamos even when the symmetry breaking is small. This behavior can be explained by an approximate dipole-quadrupole degeneration for the unperturbed problem. More complicated scenarios may occur in the case of more realistic anisotropies of α- and β-effect or through nonlinearities caused by the back-reaction of the magnetic field (magnetic quenching). [ABSTRACT FROM PUBLISHER]

We explore the influence of geometry variations on the structure and the time-dependence of the magnetic field that is induced by kinematic α2 dynamos in a finite cylinder. The dynamo action is due to an anisotropic α effect which can be derived from an underlying columnar flow. The investigated geometry variations concern, in particular, the aspect ratio of height to radius of the cylinder, and the thickness of the annular space to which the columnar flow is restricted. Motivated by the quest for laboratory dynamos which exhibit Earth-like features, we start with modifications of the Karlsruhe dynamo facility. Its dynamo action is reasonably described by an α2 mechanism with anisotropic α tensor. We find a critical aspect ratio below which the dominant magnetic field structure changes from an equatorial dipole to an axial dipole. Similar results are found for α2 dynamos working in an annular space when a radial dependence of α is assumed. Finally, we study the effect of varying aspect ratios of dynamos with an α tensor depending both on radial and axial coordinates. In this case only dominant equatorial dipoles are found and most of the solutions are oscillatory, contrary to all previous cases where the resulting fields are steady. [ABSTRACT FROM AUTHOR]