Zeeman-Doppler Imaging (ZDI) is a powerful inversion method to reconstruct stellar magnetic surface fields. The reconstruction process is usually solved by translating the inverse problem into a regularized least-square or optimization problem. In this contribution we will emphasize that ZDI is an inherent non-linear problem and the corresponding regularized optimization is, like many non-linear problems, potentially prone to local minima. We show how this problem will be exacerbated by using an inadequate forward model. To facilitate a more consistent full radiative transfer driven approach to ZDI we describe a two-stage strategy that consist of a principal component analysis (PCA) based line profile reconstruction and a fast approximate polarized radiative transfer method to synthesize local Stokes profiles. Moreover, we introduce a novel statistical inversion method based on artificial neural networks (ANN) which provide a fast calculation of a first guess model and allows to incorporate better physical constraints into the inversion process.

One of the five key science projects for the Square Kilometre Array (SKA) is “The Origin and Evolution of Cosmic Magnetism”, in which radio polarimetry will be used to reveal what cosmic magnets look like and what role they have played in the evolving Universe. Many of the SKA prototypes now being built are also targeting magnetic fields and polarimetry as key science areas. Here I review the prospects for innovative new polarimetry and Faraday rotation experiments with forthcoming facilities such as ASKAP, LOFAR, the ATA, the EVLA, and ultimately the SKA. Sensitive wide-field polarisation surveys with these telescopes will provide a dramatic new view of magnetic fields in the Milky Way, in nearby galaxies and clusters, and in the high-redshift Universe.

We review general properties and capabilities of the instrumentation employed to diagnose cosmic magnetic fields using medium-size and large optical telescopes. During the last decade these spectropolarimeters and high-resolution spectrographs have been successfully used to detect and characterize magnetic fields in stars across the H-R diagram. A new generation of high-resolution spectropolarimeters will benefit from the large collecting area of the future E-ELT and currently operating 8-m class telescopes. We review plans to develop spectropolarimeters for these very large telescopes and outline a number of science cases where new spectropolarimetric instrumentation is expected to play a key role.

We present the design of the new PEPSI spectropolarimeter to be installed at the Large Binocular Telescope (LBT) in Arizona to measure the full set of Stokes parameters in spectral lines and outline its precision and the accuracy limiting factors.

One of the first post-focus instruments of the new solar telescope GREGOR will be a Fabry-Perot spectrometer, which is an upgrade of the Göttingen Fabry-Perot interferometer at the Vacuum Tower Telescope (VTT) on Tenerife. This spectrometer is equipped with a full-Stokes polarimeter. The modulation is performed with two ferroelectric liquid crystals, one acting nominally as quarter-wave plate, and the other as half-wave plate. A modified Savart plate serves as polarimetric beam splitter. With the present liquid crystals, the optimum wavelength range of this polarimeter is between 580 and 660 nm. The spectro-polarimeter will benefit from the capabilities of the new telescope GREGOR which will provide a spatial resolution of about 0″.1 (75 km on the solar surface). Thus we will be able to investigate small magnetic features, and we will study their development with high cadence.

We investigate the cosmological evolution of large- and small-scale magnetic fields in galaxies at high redshifts. Results from simulations of hierarchical structure formation cosmology provide a tool to develop an evolutionary model of regular magnetic fields coupled to galaxy formation and evolution. Turbulence in protogalactic halos generated by thermal virialization can drive an efficient turbulent dynamo. The mean-field dynamo theory is used to derive the timescales of amplification and ordering of regular magnetic fields in disk and dwarf galaxies. For future observations with the SKA, we predict an anticorrelation at fixed redshift between galaxy size and the ratio between ordering scale and galaxy size. Undisturbed dwarf galaxies should host fully coherent fields at z < 1, spiral galaxies at z < 0.5.

We present our attempts to detect magnetic fields in filamentary large-scale structure (LSS) by observing polarized synchrotron emission emitted by structure formation shocks. Little is known about the strength and order of magnetic fields beyond the largest clusters of galaxies, and synchrotron emission holds enormous promise as a means of probing magnetic fields in these low density regions. We report on observations taken at the Green Bank Telescope which reveal a possible Mpc extension to the Coma cluster relic. We also highlight the major obstacle that diffuse galactic foreground emission poses for any search for large-scale, low surface-brightness extragalactic emission. Finally we explore cross-correlation of diffuse radio emission with optical tracers of LSS as a means to statistically detecting magnetic fields in the presence of this confounding foreground emission.

Turbulent reconnection is studied by means of three dimensional (3D) compressible magnetohydrodynamical numerical calculations. The process of homogeneous turbulence is set up by adding three-dimensional solenoidal random forcing implemented in the spectral space at small wave numbers with no correlation between velocity and forcing. We apply the initial Harris current sheet configuration together with a density profile calculated from the numerical equilibrium of magnetic and gas pressures. We assume that there is no external driving of the reconnection. The reconnection develops as a result of the initial vector potential perturbation. We use open boundary conditions. Our main goal is to find the dependencies of reconnection rate on different properties of turbulence. The results of our simulations show that turbulence significantly affects the topology of magnetic field near the diffusion region. We present that the reconnection speed does not depend on the Reynolds numbers as well the magnetic diffusion. In addition, a fragmentation of current sheet decreases the disparity in inflow/outflow ratios. When we apply the large scale and more powerful turbulence the reconnection is faster.