The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean-field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-like dynamo. In view of this application the second-order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the α-effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.

Coherent structures in the distribution of the Faraday rotation measure (RM) of extragalactic radio sources are isolated using wavelet transformation techniques. A new algorithm of wavelet analysis for data points non‐uniformly distributed on a sphere is developed and implemented. Signatures of the magnetic fields in the local (Orion) arm, the Sagittarius arm (and its extension, the Carina arm), the synchrotron Loop I and, possibly, the Perseus arm have been revealed using the RM catalogues of Simard‐Normandin et al. (551 sources) and Broten et al. (663 sources). Unlike earlier analyses of the RM sky, our approach has allowed us to assess the stability of the results with respect to modifications of the data sample. Only the aforementioned features remain stable under mild sample modifications. We consider separately low‐latitude sources at |b|<10° and, using the model of electron density distribution of Cordes et al., we estimate magnetic field strength by comparing the model wavelet transform with that of the real data. Independent estimates of the mean magnetic field strength in the Orion arm using low‐ and high‐latitude sources converge to 1.4±0.3 μG. Rotation measures of low‐latitude sources provide a clear indication of a magnetic field reversal at a distance 0.6–1 kpc towards the Galactic Centre. Our analysis has revealed for the first time the extension of the reversal in the Carina arm. Low‐latitude sources from the catalogue of Broten et al. indicate a magneto‐ionic structure in the direction of the Perseus arm with the magnetic field direction reversed with respect to that in the Orion arm. The extent of the region with reversed magnetic field near the Sun is 3 kpc or more in the azimuthal direction. The average pitch angle of magnetic field in the nearby spiral arms is 15°, and the mean field strength in the Sagittarius–Carina and Perseus arms is 1.7±0.3 μG and 1.4±1.2 μG, respectively. The line‐of‐sight magnetic field in Loop I is estimated as 0.9±0.3 μG. We find firm evidence of a dominant even symmetry of the local mean magnetic field with respect to the Galactic equator. Our results are compatible with a moderate large‐scale north–south asymmetry, with the magnetic field in the southern hemisphere being stronger in a region of at least 3 kpc in size. It cannot be excluded, however, that the asymmetry is local and results from vertical bending of magnetic lines in a region of about 400 pc in size, with the Sun being located close to the top of a magnetic loop, the magnetic field of which is 0.5 μG stronger than the average field.

Context. The forthcoming new-generation radio telescope SKA (Square Kilometre Array) and its precursors will provide a rapidly growing number of polarized radio sources. Aims. Our analysis looks at what can be learned from these sources concerning the structure and evolution of magnetic fields of external galaxies. Methods. Recognition of magnetic structures is possible from Faraday rotation measures (RM) towards background sources behind galaxies or a continuous RM map obtained from the diffuse polarized emission from the galaxy itself. We constructed models for the ionized gas and magnetic field patterns of different azimuthal symmetries (axisymmetric, bisymmetric and quadrisymmetric spirals, and superpositions) plus a halo magnetic field. RM fluctuations with a Kolmogorov spectrum due to turbulent fields and/or fluctuations in ionized gas density are superimposed. Assuming extrapolated number density counts of polarized sources, we generated a sample of RM values within the solid angle of the galaxy. Applying various templates, we derived the minimum number of background sources and the minimum quality of the observations. For a large number of sources, reconstruction of the field structure without precognition becomes possible. Results. Any large-scale regular component of the magnetic field can be clearly recognized from RM data with the help of the χ 2 criterium. Under favorite conditions, a few dozen polarized sources are enough for a reliable result. A halo field with a vertical component does not affect the results of recognition. The required source number increases for small inclinations of the galaxy's disk and for larger RM turbulence. A flat number density distribution of the sources can be overcome by more sensitive observations. Application of the recognition method to the available RM data in the region around M 31 indicates that there are significant RM contributions intrinsic to the background sources or due to the foreground of the Milky Way. A reliable reconstruction of the field structure needs at least 20 RM values on a cut along the projected minor axis. Conclusions. Recognition or reconstruction of regular field structures from the RM data of polarized background sources is a powerful tool for future radio telescopes. Measuring RM at frequencies around 1 GHz with the SKA, simple field structures can be recognized in galaxies up to about 100 Mpc distance and will allow to test dynamo against primordial or other models of field origin. The low-frequency SKA array and low-frequency precursor telescopes like LOFAR may also have good RM sensitivity if background sources are still significantly polarized at low frequencies.

Context. The origin of the spiral pattern of magnetic fields in disc galaxies is an open question. Aims. Comparison of the regular magnetic field orientation with the gaseous spiral arm pitch angles can tell us whether spiral shock compression is responsible for the magnetic spirals. We also wish to see whether the ridges of different components of the ISM show the large-scale, systematic shifts expected from density wave theory. Methods. We have developed a technique of isolating elongated structures in galactic images, such as spiral arms, using anisotropic wavelets and apply this to maps of the CO, infrared and radio continuum emission of the grand-design spiral galaxy M 51. Results. Systematic shifts between the ridges of CO, infrared and radio continuum emission that are several kpc long are identified, as well as large variations in pitch angle along spiral arms, of a few tens of degrees. We find two types of arms of polarized radio emission: one has a ridge close to the ridge of CO, with similar pitch angles for the CO and polarization spirals and the regular magnetic field; the other does not always coincide with the CO arm and its pitch angle differs from the orientation of its regular magnetic field. Conclusions. The offsets between ridges of regular magnetic field, dense gas and warm dust are compatible with the sequence expected from spiral density wave triggered star formation, with a delay of a few tens of millions of years between gas entering the shock and the formation of giant molecular clouds and a similar interval between the formation of the clouds and the emergence of young star clusters. At the position of the CO arms the orientation of the regular magnetic field is the same as the pitch angle of the spiral arm, but away from the gaseous arms the orientation of the regular field varies significantly. Spiral shock compression can explain the generation of one type of arm of strong polarized radio emission but a different mechanism is probably responsible for a second type of polarization arm.

Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models.In this review we set up a general mathematical framework allowing the description of any MHD shell model. The variety of the latter, with their advantages and weaknesses, is introduced. Finally we consider a number of applications, dealing with free-decaying MHD turbulence, dynamo action, Alfvén waves and the Hall effect. Summary and outlook 65Appendix A L1-models 66 2 Appendix B L2-models 67Appendix C N1-models 68 Appendix D N2-models 68Appendix E Numerical aspects 683 Variables u, b, p, z ± , a, u ± , b ±