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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 magnetic fields in the inner parts of some spiral galaxies are understood quite well. Their generation is connected with the dynamo mechanism that is based on the joint action of turbulent diffusion and the α-effect. Usually the galactic dynamo is described with the so-called no-z approximation which takes into account that the galaxy disc is quite thin, with the implication that some spatial derivatives may be replaced by algebraic expressions. Some galaxies have outer rings that are situated at some distance from the galactic centre. The magnetic field can be described there also using the no-z model. As the thickness of such objects is comparable with their width, it is necessary to take into account the z-dependence of the field. We have studied the magnetic field evolution using the no-z approximation and torus dynamo model for the torus with rectangular cross-section in the axisymmetric case. [ABSTRACT FROM AUTHOR]

The project DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies) conducted at Helmholtz–Zentrum Dresden–Rossendorf (HZDR) provides a new platform for a variety of liquid sodium experiments devoted to problems of geo- and astrophysical magnetohydrodynamics. The most ambitious experiment within this project is a precession-driven dynamo experiment that currently is under construction. It consists of a cylinder filled with liquid sodium that simultaneously rotates around two axes. The experiment is motivated by the idea of a precession-driven flow as a complementary energy source for the geodynamo or the ancient lunar dynamo. In the present study, we address numerical and experimental examinations in order to identify parameter regions where the onset of magnetic field excitation will be most probable. Both approaches show that in the strongly nonlinear regime the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves that arise from nonlinear self-interactions. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane, which, however, only occurs in a very limited range of the precession ratio. This axisymmetric mode turns out to be beneficial for dynamo action, and kinematic simulations of the magnetic field evolution induced by the time-averaged flow exhibit magnetic field excitation at critical magnetic Reynolds numbers around , which is well within the range of the planned liquid sodium experiment. [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 present article considers dynamo action in flows driven by Ekman and Taylor–Couette instabilities. The system comprises a rotating, horizontal plane layer of electrically conducting fluid. The top of the layer is at rest, while the base has a given velocity that drives a net shear across the layer. The fluid flow in the system is parameterised by a Reynolds number Re, the square root of the Taylor number t, and the angle???between the rotation vector and the vertical. When the rotation vector has a vertical component,???? p/2, then in the limit of large t, the shear takes the form of an thin Ekman layer localised at the bottom boundary. This may be subject to a hydrodynamic Ekman instability which for moderate Re generates steady cat's eyes in a co-moving frame. The flow gives dynamo action, amplifying magnetic fields in the form of sheets concentrated on hyperbolic points and their unstable manifolds. At greater Re, the cat's eyes become three-dimensional, and time-dependent amplifying fields with a more irregular structure. In nonlinear regimes the magnetic field and fluid flow show a relaxation oscillation for moderate Re, and for higher values, oscillatory fluid flows sustain tubes of magnetic field. When the rotation vector is entirely horizontal, ??=p /2, the shear driven is uniform across the layer. This can become subject to a primary Taylor–Couette instability driving a cellular flow, and with a further increase of Re, there is a secondary bifurcation to steady, wavy rolls. This flow supports a dynamo and its properties are studied in kinematic and nonlinear regimes. [ABSTRACT FROM AUTHOR]

The growth of magnetic field is considered in the stretch–fold–shear map in the limit of weak diffusion. Numerical results are given for insulating, perfectly conducting and periodic boundary conditions. The resulting eigenvalue branches and magnetic fields are related to eigenvalue branches for perfect dynamo action, obtained for zero diffusion using a complex variable formulation. The effect of diffusion on these perfect dynamo modes depends on their structure, growth rate and the diffusive boundary conditions employed. In some cases, the effect of diffusion is a small perturbation, giving a correction going to zero in the limit of weak diffusion, with a scaling exponent given analytically. In other cases weak diffusion can entirely destroy a perfect dynamo branch. Diffusive boundary layers can also generate entirely new branches. These different cases are elucidated, and within the framework of the asymptotic approximations used (which do not constitute a rigorous proof), it is seen that for all three boundary conditions employed, the stretch–fold–shear map is a fast dynamo. [ABSTRACT FROM AUTHOR]

In this article we address the problem of magnetic field generation and front propagation in turbulent electrically conducting fluids, involving the velocity with finite correlations times and small magnetic diffusivity. We suggest an integro-differential dynamo equation which involves the non-local terms for both the dynamo source α -term and turbulent transport of the mean magnetic field. We derive a set of formulas which allows us to determine the rate of magnetic front propagation in galaxies valid for arbitrary memory kernels. We illustrate the general results through the use of the exponential correlation functions for memory kernels and 'no-z' approximation. We find that the memory effects have strong influence on for both the growth rate and propagation speed. We perform numerical simulations of exterior front speed, and find that the transport memory essentially decreases the propagation rate. [ABSTRACT FROM AUTHOR]