Role of soft-iron impellers on the mode selection in the VKS dynamo experiment

A crucial point for the understanding of the von-K\'arm\'an-Sodium (VKS) dynamo experiment is the influence of soft-iron impellers. We present numerical simulations of a VKS-like dynamo with a localized permeability distribution that resembles the shape of the flow driving impellers. It is shown that the presence of soft-iron material essentially determines the dynamo process in the VKS experiment. % An axisymmetric magnetic field mode can be explained by the combined action of the soft-iron disk and a rather small $\alpha$-effect parametrizing the induction effects of unresolved small scale flow fluctuations

On the Perturbations of Viscous Rotating Newtonian Fluids

The perturbations of weakly-viscous, barotropic, non-self-gravitating, Newtonian rotating fluids are analyzed via a single partial differential equation. The results are then used to find an expression for the viscosity-induced normal-mode complex eigenfrequency shift, with respect to the case of adiabatic perturbations. However, the effects of viscosity are assumed to have been incorporated in the unperturbed (equilibrium) model. This paper is an extension of the normal-mode formalism developed by Ipser & Lindblom for adiabatic pulsations of purely-rotating perfect fluids. The formulas derived are readily applicable to the perturbations of thin and thick accretion disks. We provide explicit expressions for thin disks, employing results from previous relativistic analyses of adiabatic normal modes of oscillation. In this case, we find that viscosity causes the fundamental p- and g- modes to grow while the fundamental c-mode could have either sign of the damping rate.Comment: Accepted for publication by The Astrophysical Journal. 11 pages, no figure

The R-Mode Oscillations in Relativistic Rotating Stars

The axial mode oscillations are examined for relativistic rotating stars with uniform angular velocity. Using the slow rotation formalism and the Cowling approximation, we have derived the equations governing the r-mode oscillations up to the second order with respect to the rotation. In the lowest order, the allowed range of the frequencies is determined, but corresponding spatial function is arbitrary. The spatial function can be decomposed in non-barotropic region by a set of functions associated with the differential equation of the second-order corrections. The equation however becomes singular in barotropic region, and a single function can be selected to describe the spatial perturbation of the lowest order. The frame dragging effect among the relativistic effects may be significant, as it results in rather broad spectrum of the r-mode frequency unlike in the Newtonian first-order calculation.Comment: 19 pages, 4 figures, AAS LaTeX, Accepted for publication in The Astrophysical Journa

Bypassing Cowling's theorem in axisymmetric fluid dynamos

We present a numerical study of the magnetic field generated by an axisymmetrically forced flow in a spherical domain. At small enough Reynolds number, Re, the flow is axisymmetric and generates an equatorial dipole above a critical magnetic Reynolds number Rmc . The magnetic field thus breaks axisymmetry, in agreement with Cowling's theorem. This structure of the magnetic field is however replaced by a dominant axial dipole when Re is larger and allows non axisymmetric fluctuations in the flow. We show here that even in the absence of such fluctuations, an axial dipole can also be generated, at low Re, through a secondary bifurcation, when Rm is increased above the dynamo threshold. The system therefore always find a way to bypass the constraint imposed by Cowling's theorem. We understand the dynamical behaviors that result from the interaction of equatorial and axial dipolar modes using simple model equations for their amplitudes derived from symmetry arguments.Comment: 4 pages, 6 figure

Dust-driven Dynamos in Accretion Disks

Magnetically driven astrophysical jets are related to accretion and involve toroidal magnetic field pressure inflating poloidal magnetic field flux surfaces. Examination of particle motion in combined gravitational and magnetic fields shows that these astrophysical jet toroidal and poloidal magnetic fields can be powered by the gravitational energy liberated by accreting dust grains that have become positively charged by emitting photo-electrons. Because a dust grain experiences magnetic forces after becoming charged, but not before, charging can cause irreversible trapping of the grain so dust accretion is a consequence of charging. Furthermore, charging causes canonical angular momentum to replace mechanical angular momentum as the relevant constant of the motion. The resulting effective potential has three distinct classes of accreting particles distinguished by canonical angular momentum, namely (i) "cyclotron-orbit", (ii) "Speiser-orbit", and (iii) "zero canonical angular momentum" particles. Electrons and ions are of class (i) but depending on mass and initial orbit inclination, dust grains can be of any class. Light-weight dust grains develop class (i) orbits such that the grains are confined to nested poloidal flux surfaces, whereas grains with a critical weight such that they experience comparable gravitational and magnetic forces can develop class (ii) or class (iii) orbits, respectively producing poloidal and toroidal field dynamos.Comment: 70 pages, 16 figure

On a mechanism for enhancing magnetic activity in tidally interacting binaries

We suggest a mechanism for enhancing magnetic activity in tidally interacting binaries. We suppose that the deviation of the primary star from spherical symmetry due to the tidal influence of the companion leads to stellar pulsation in its fundamental mode. It is shown that stellar radial pulsation amplifies torsional Alfv{\'e}n waves in a dipole-like magnetic field, buried in the interior, according to the recently proposed swing wave-wave interaction (Zaqarashvili 2001). Then amplified Alfv{\'e}n waves lead to the onset of large-scale torsional oscillations, and magnetic flux tubes arising towards the surface owing to magnetic buoyancy diffuse into the atmosphere producing enhanced chromospheric and coronal emission.Comment: Accepted in Ap

Experimental Identification of the Kink Instability as a Poloidal Flux Amplification Mechanism for Coaxial Gun Spheromak Formation

The magnetohydrodynamic kink instability is observed and identified experimentally as a poloidal flux amplification mechanism for coaxial gun spheromak formation. Plasmas in this experiment fall into three distinct regimes which depend on the peak gun current to magnetic flux ratio, with (I) low values resulting in a straight plasma column with helical magnetic field, (II) intermediate values leading to kinking of the column axis, and (III) high values leading immediately to a detached plasma. Onset of column kinking agrees quantitatively with the Kruskal-Shafranov limit, and the kink acts as a dynamo which converts toroidal to poloidal flux. Regime II clearly leads to both poloidal flux amplification and the development of a spheromak configuration.Comment: accepted for publication in Physical Review Letter

Growth rate degeneracies in kinematic dynamos

We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudovacuum) or tangent (perfect electrical conductor) to the boundaries of the domain. These boundary conditions correspond to well-defined physical limits often used in numerical models and relevant to laboratory experiments. The only constraint is for the velocity field u to be reversible, meaning there exists a transformation changing u into −u. We illustrate this surprising property using S2T2 type of flows in spherical geometry inspired by [Dudley and James, Proc. R. Soc. London A 425, 407 (1989)]. Using both types of boundary conditions, it is shown that the growth rates of the dynamos are identical, although the corresponding magnetic eigenmodes are drastically different

Thermodynamics of MHD flows with axial symmetry

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation