Two mechanisms of the galactic seed field generation are discussed. One of the mechanisms implies a direct generation of the seed magnetic field through a battery process (Lazarian 1992a). The other accounts for the possibility of the preliminary amplification of the magnetic field on a scale of molecular clouds (Lazarian 1992b). This means that the galactic dynamo can feed on the non-zero average value of the magnetic field amplified by such a small-scale dynamo. It is shown that both mechanisms can generate an adequate seed field. These two scenarios of the seed magnetic field generation can be distinguished by an analysis of the present day galactic magnetic structure.

Present-day galactic dynamo theories widely use a concept of the ISM turbulence. In the present paper a statistical method of MHD turbulence study is discussed. The method is based on the solution of the inverse problem for the observational data. It is shown that in many important cases the inverse problem has a unique analytical solution. Examples, including the study of a random density field and a random magnetic field, are discussed.

Magnetic field generation in molecular (atomic) clouds at the early stages of galactic evolution is considered. It is shown that if there is no internal motions immersed the cloud, battery mechanisms (Lazarian 1992a) can account for the generation of thin magnetic shells around clouds insides in plasma with temperature gradients. If turbulent motions are present, the dynamo can be essential. The operation of α — ω, α2 and turbulent dynamos within molecular clouds is discussed. It is shown that the turbulent dynamo leads to generation of magnetic fields in the trace behind the cloud. These magnetic fields within the molecular clouds and in their vicinity are important for the solution of the galactic seed field problem (see Lazarian 1992b) and the formation of structures in clumpy molecular complexes.

A comparison is made of the differences and similarities between the solar dynamo and the geodynamo. Special attention is paid to the energetics, the dynamics, the role of turbulence, and the α- and ω-sources in these dynamos.

The hydromagnetic dynamo Z-model represents a nonlinear dynamic system. Its steady-state solution is derived by step-by-step integration of parabolic partial differential equations of the second order with the use of the finite difference method. Until now, two methods have been used: the semi-implicit method in which the θ-diffusion was carried out implicitly while the r-diffusion explicitly, and the implicit method in which the complete diffusion was carried out implicitly. In the present contribution, a combined semi-implicit method is suggested which reflects not only the singularity at the coordinate system origin but also the decreasing mesh size near the core-mantle boundary. This procedure preserves the advantage of semi-implicit methods and, simultaneously, increases the stability in the most critical boundary layer.

Time evolution of the solution of model Z is considered simply as an aid to obtain the steady state solution. Balance equations of the energy of the azimuthal field EB showes that excluding several beginning time steps the solution exposes the time behaviour with a physical sense.

In the first issue of Journal of Fluid Mechanics Ian Proudman published a paper on the dynamical properties of a fluid between two concentric rotating spheres (Proudman, 1956). The angular velocities of the spheres were assumed only slightly different and the Reynolds number of the flow was large. It was found under non-slip boundary conditions that the cylindrical surface that touches the inner sphere and parallel to the axis of rotation is a singular surface in which velocity gradients are very large. Outside the cylinder the fluid rotates as a rigid body with the same angular velocity as the outer sphere. Inside the cylinder the fluid rotates with an angular velocity intermediate to the angular velocities of the spheres and there is also a meridional circulation. Later Stewartson (1966) presented a detailed investigation of structure of the shear layer near the cylindrical surface. One of the present authors (Ruzmaikin, 1989) pointed out a possible geophysical importance of these solutions. The liquid part of the Earth core occupying a shell between the inner solid core and the rock mantle can be considered as the fluid between two rotating spheres.

The instability due to a vertical uniform temperature gradient is studied in a rapidly rotating horizontal layer of an electrically conducting fluid permeated by an azimuthal magnetic field linearly growing with the distance from the vertical axis of rotation. In addition to the boundary conditions used in So ward's study (1979), that is, force-free surface and perfect electrical and thermal conductivity outside, also other conditions more realistic for the Earth's core are considered, that is, rigid surface and electrically insulating walls. Using the concept of meanfield mlid mean electromotive and ponderomotive forces (E.M.F. and P.M.F.) are calculated and compared for various boundary conditions. The dependence of the E.M.F. and P.M.F. on the electromagnetic boundary conditions is strong (slight) if the boundaries are free (rigid).

A dynamo driven by flows of differential rotation and global convection in a rotating sphere is reviewed as a model of the solar and planetary dynamos. The flows can amplify a magnetic field from an infinitesimal level and thus can generate a magnetic field. The flows periodically reverse the polarity of the field and force the generated field system to propagate along iso-rotation surface in the sphere in form of a wave during the generation process. The flows can also generate the field without reversing its polarity depending on the structure of the flows of the differential rotation. The basic dynamo process with and without polarity reversals is explained in terms of topological deformation of field lines by the flows in the sphere. The oscillatory and steady dynamos are interpreted as corresponding to the solar and planetary dynamos respectively.

Magnetic field observations in the dayside ionosphere of Venus revealed the magnetic flux ropes (Russell and Elphic 1979). General properties of these small-scale magnetic field structures can be explained by the theory of magnetic fluctuations excited by random hydrodynamic flows of ionospheric plasma.

A nonlinear theory of the flux tubes formation based on the Zeldovich's mechanism of amplification of the magnetic fluctuations is proposed. A nonlinear equation describing the evolution of the correlation function of the magnetic field can be derived from the induction equation, the nonlinearity being connected with the Hall effect. The large magnetic Reynolds number limit allows an asymptotic study by a modified WKB method.

On the basis of this theory it is possible to explain why the flux tubes are not observed if there is a strong regular large-scale magnetic field when the ionopause is low. The theory predicts the cross section of the flux ropes in the ionosphere of Venus and the maximum value of the magnetic field inside the flux tube.

An attempt is made to present a review as well on the historical development of knowledge on cosmic magnetic fields as on the development of our understanding of this phenomenon.