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The ordered magnetic field observed via polarised synchrotr on emission in nearby disc galaxies can be explained by a mean-field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical-flu x initial conditions are potentially able to influence this dynamo via the occurrence of the magnetorotational instability (MRI). We aim to study the influence of various initial field configurations on the sa turated state of the mean-field dynamo. This is motivated by t he observation that different saturation behaviour was previously obtained for different supernova rates. We perform direct numerical simulations (DNS) of three-dimensional local boxes of the vertically stratified, turbulent interstellar me dium, employing shearing-periodic boundary conditions horizontally. Unlike in our previous work, we also impose a vertical seed magnetic field. We run the simulations until the growth o f the magnetic energy becomes negligible. We furthermore perform simulations of equivalent 1D dynamo models, with an algebraic quenching mechanism for the dynamo coeffi cients. We compare the saturation of the magnetic field in the DNS with the algebraic quenching of a mean-field dynamo. The final magnetic field strength found in the direct simulati on is in excellent agreement with a quenchedα dynamo. For supernova rates representative of the Milky Way, field lo sses via a Galactic wind are likely responsible for saturation. We conclude that the relative strength of the turbulen t and regular magnetic fields in spiral galaxies may depend on the galaxy’s star formation rate. We propose that a mean field approach with algebraic quenching may serve as a simple sub-grid scale model for galaxy evolution simulations including a prescribed feedback from magnetic fields. Copyright line will be provided by the publisher

We investigate the stability of the Hall-MHD system and determine its importance for neutron stars at their birth, when they still consist of differentially rotating plasma permeated by extremely strong magnetic fields. We solve the linearised HallMHD equations in a spherical shell threaded by a homogeneous magnetic field. With the fluid/flow coupling and the Hall effect included, the magnetorotational instability and the Hall effect are both acting together. Results differ for magnetic fields aligned with the rotation axis and anti-parallel magnetic fields. For a positive alignment of the magnetic field the instability grows on a rotational time-scale for any sufficiently large magnetic Reynolds number. Even the magnetic fields which are stable against the MRI due to the magnetic diffusion are now susceptible to the shear-Hall instability. In contrast, the negative alignment places strong restrictions on the growth and the magnitude of the fields, hindering the effectiveness of the Hall-MRI. While non-axisymmetric modes of the MRI can be suppressed by strong enough rotation, there is no such restriction when the Hall effect is present. The implications for the magnitude and the topology of the magnetic field of a young neutron star may be significant (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Stability of thin hot Keplerian discs is investigated asymptotically in small disc's aspect ratio, e. The study is carried out in the local approximation for short vertical waves in the disc-thickness scale. Besides the radial rotation shear and the vertical magnetic field, the background configuration is characterized by a vertically near-constant temperature profile with a small vertical gradient. The temperature-gradient term in Ohm's law, which characterizes the thermomagnetic transport is found to be of the order of e. The effect of the thermomagnetic transport slightly modifies the conventional magnetorotational instability (MRI), while a new thermomagnetic instability (TMI) emerges in regions of the wavenumber space where MRI is absent. Explicit solutions are obtained for a wide range of values of plasma beta, β, and thermomagnetic transport coefficient, λ. In particular, it is shown for λ ≪ 1 that the MRI dominates in weak magnetic fields, β ≫ 1, while the TMI is exhibited in strong magnetic fields, β ∼ 1, also with the growth rate of the order of inverse rotation period (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we make an effort to understand the interaction of turbulence generated by the magnetorotational instability (MRI) with turbulence from other sources, such as supernova explosions (SNe) in galactic disks. First we perform a linear stability analysis (LSA) of non-ideal MRI to derive the limiting value of Ohmic diffusion that is needed to inhibit the growth of the instability for different types of rotation laws. With the help of a simple analytical expression derived under first-order smoothing approximation (FOSA), an estimate of the limiting turbulence level and hence the turbulent diffusion needed to damp the MRI is derived. Secondly, we perform numerical simulations in local cubes of isothermal nonstratified gas with external forcing of varying strength to see whether the linear result holds for more complex systems. Purely hydrodynamic calculations with forcing, rotation and shear are made for reference purposes, and as expected, non-zero Reynolds stresses are found. In the magnetohydrodynamic calculations, therefore, the total stresses generated are a sum of the forcing and MRI contributions. To separate these contributions, we perform reference runs with MRI-stable shear profiles (angular velocity increasing outwards), which suggest that the MRI-generated stresses indeed become strongly suppressed as function of the forcing. The Maxwell to Reynolds stress ratio is observed to decrease by an order of magnitude as the turbulence level due to external forcing exceeds the predicted limiting value, which we interpret as a sign of MRI suppression. Finally, we apply these results to estimate the limiting radius inside of which the SN activity can suppress the MRI, arriving at a value of 14 kpc., 12 pages, 12 figures, submitted to Astron. Nachr

We present local numerical models of accretion disk turbulence driven by the magnetorotational instability with varying shear rate. The resulting turbulent stresses are compared with predictions of a closure model in which triple correlations are modelled in terms of quadratic correlations. This local model uses five nondimensional parameters to describe the properties of the flow. We attempt to determine these closure parameters for our simulations and find that the model does produce qualitatively correct behaviour. In addition, we present results concerning the shear rate dependency of the magnetic to kinetic energy ratio. We find both the turbulent stress ratio and the total stress to be strongly dependent on the shear rate., 8 pages, 5 figures, accepted for publication in Astronomische Nachrichten

One of the most convenient approaches to observe experimentally the magnetorotational instability (MRI) is to use a magnetized Taylor-Couette setup. The flow of liquid metal between two rotating, concentric cylinders can become unstable in the presence of an external magnetic field. One of the issues which should be addressed when designing such an experiment is the influence of plates enclosing the cylinders fromthe top and the bottom. In this paper we discuss properties of the boundary layer which arises near these plates. Our primary concern is the importance of this layer in the MRI experiment PROMISE. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical investigation of the two-dimensional magnetic reconnection is given in the context of the nonlinear evolution of the Magneto-Rotational Instability (MRI). With a careful comparison to various theories using both one- and twodimensional analysis, it is found that a new stabilizing effect of the centrifugal force on tearing instability must be present in the specific geometry of the MRI.Magnetic reconnection might play a key role to the formation of the nonaxisymmetric structures observed in MRI experiments. The results may also be useful for the estimate of the accretion rate in various astrophysical objects. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The magnetorotational instability is investigated within the shearing box approximation in the large Elsasser number regime. In this regime, which is of fundamental importance to astrophysical accretion disk theory, shear is the dominant source of energy, but the instability itself requires the presence of a weaker vertical magnetic field. Dissipative effects are weaker still but not negligible. The regime explored retains the condition that (viscous and ohmic) dissipative forces do not play a role in the leading order linear instability mechanism. However, they are sufficiently large to permit a nonlinear feedback mechanism whereby the turbulent stresses generated by the MRI act on and modify the local background shear in the angular velocity profile. To date this response has been omitted in shearing box simulations and is captured by a reduced pde model derived here from the global MHD fluid equations using multiscale asymptotic perturbation theory. Results from numerical simulations of the reduced pde model indicate a linear phase of exponential growth followed by a nonlinear adjustment to algebraic growth and decay in the fluctuating quantities. Remarkably, the velocity and magnetic field correlations associated with these algebraic growth and decay laws conspire to achieve saturation of the angular momentum transport. The inclusion of subdominant ohmic dissipation arrests the algebraic growth of the fluctuations on a longer, dissipative time scale. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed current-free toroidal field B0(Rin/R) ˆ eφ. It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field. We show here that a nonaxisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field. In the nonlinear regime the magnetic energy of the perturbances is shifted (in the sense of an inverse cascade) to the axisymmetric mode rather than to the modes with m> 1.

Magnetorotational instability (MRI) is one of the most important and most common instabilities in astrophysics, it is widely accepted that it serves as a source of turbulent viscosity in accretion disks -- the most energy efficient objects in the Universe. However it is very difficult to bring this process down on earth and model it in a laboratory experiment. Several different approaches have been proposed, one of the most recent is PROMISE (Potsdam-ROssendorf Magnetorotational InStability Experiment). It consists of a flow of a liquid metal between two rotating cylinders under applied current-free spiral magnetic field. The cylinders must be covered with plates which introduce additional end-effects which alter the flow and make it more difficult to clearly distinguish between MRI stable and unstable state. In this paper we propose simple and inexpensive improvement to the PROMISE experiment which would reduce those undesirable effects., Comment: 8 pages, 9 figures. Accepted to AN

The origin of magnetic fields in the Universe is a cosmology problem. The evolution of the field is a plasma physics problem. I review these problems and focus on magnetogenesis in accretion disks, specifically, the transition from the Biermann battery, which creates seed fields, to amplification by turbulence driven by magnetorotational instability. In collisional disks, there is a gap between the fieldstrength characteristic of the battery and the fieldstrength necessary to sustain magnetorotational instability, but in collisionless disks the transition occurs at low fieldstrength. Because collisionless disks are generally hot, and have short dynamical times, they are likely to be small. Thus, in the battery scenario, magnetic fields on large scales were built from fields created in many small sources. Simple estimates based on turbulent diffusion suggest that galaxies and the cores of galaxy clusters can be magnetized in this way, but not the intergalactic medium at large. The problem of creating a large-scale field remains unsolved. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We study the magnetorotational instability in cylindrical Taylor-Couette flow, with the (vertically unbounded) cylinders taken to be perfect conductors, and with externally imposed spiral magnetic fields. The azimuthal component of this field is generated by an axial current inside the inner cylinder, and may be slightly stronger than the axial field. We obtain an instability beyond the Rayleigh line, for Reynolds numbers of order 1000 and Hartmann numbers of order 10, and independent of the (small) magnetic Prandtl number. For experiments with R_out = 2 R_in = 10 cm and Omega_out = 0.27 Omega_in, the instability appears for liquid sodium for axial fields of ~20 Gauss and axial currents of \~1200 A. For gallium the numbers are ~50 Gauss and ~3200 A. The vertical cell size is about twice the cell size known for nonmagnetic experiments., 5 pages, 7 figures, submitted to Astronomische Nachrichten