arXiv subjects

Frank Stefani

Publications and source records attributed to Frank Stefani.

At least 73 records · Page 4Linked to original sources

arXiv2012

A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit

The magnetorotational instability (MRI) plays a key role for cosmic structure formation by triggering turbulence in the rotating flows of accretion disks that would be otherwise hydrodynamically stable. In the limit of small magnetic Prandtl number, the helical and the azimuthal version of MRI are known to be governed by a quite different scaling behaviour than the standard MRI with a vertical applied magnetic field. Using the short-wavelength approximation for an incompressible, resistive, and viscous rotating fluid we present a unified description of helical and azimuthal MRI, and we identify the universal character of the Liu limit Ro= -0.8284 for the critical Rossby number. From this universal behaviour we are also lead to the prediction of higher azimuthal wavenumber for rather small ratios of azimuthal to axial applied fields.

astro-ph.SR↗

arXiv2011

Experimental evidence for Tayler instability in a liquid metal column

In the current-driven, kink-type Tayler instability (TI) a sufficiently strong azimuthal magnetic field becomes unstable against non-axisymmetric perturbations. The TI has been discussed as a possible ingredient of the solar dynamo mechanism and a source of the helical structures in cosmic jets. It is also considered as a size limiting factor for liquid metal batteries. We report on a liquid metal TI experiment using a cylindrical column of the eutectic alloy GaInSn to which electrical currents of up to 8 kA are applied. We present results of external magnetic field measurements that indicate the occurrence of the TI in good agreement with numerical predictions. The interference of TI with the competing large scale convection, resulting from Joule heating, is also discussed.

astro-ph.SR↗

arXiv2011

Integral equations in MHD: theory and application

The induction equation of kinematic magnetohydrodynamics is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent developments concerning the numerical implementation of this scheme and its applications to various forward and inverse problems in dynamo theory and applied MHD.

physics.flu-dyn↗

arXiv2011

Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable rotating shear flows, e.g., in accretion disks. What laws of differential rotation are susceptible to the destabilization by axial, azimuthal, or helical magnetic field? The answer to this question, which is vital for astrophysical and experimental applications, inevitably leads to the study of spectral and geometrical singularities on the instability threshold. The singularities provide a connection between seemingly discontinuous stability criteria and thus explain several paradoxes in the theory of MRI that were poorly understood since the 1950s.

astro-ph.SR↗

arXiv2011

How to circumvent the size limitation of liquid metal batteries due to the Tayler instability

Recently, a new type of battery has been proposed that relies on the principle of self-assembling of a liquid metalloid positive electrode, a liquid electrolyte, and a liquid metal negative electrode. While this configuration has been claimed to allow arbitrary up-scaling, there is a size limitation of such a system due to a current-driven kink-type instability that is known as the Tayler instability. We characterize this instability in large-scale self-assembled liquid metal batteries and discuss various technical means how it can be avoided.

physics.flu-dyn↗

arXiv2011

Paradoxes of magnetorotational instability and their geometrical resolution

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable accretion discs. By using the WKB approximation and methods of singular function theory, we resolve two different paradoxes of MRI that appear in the limits of infinite and vanishing magnetic Prandtl number. For the latter case we derive a new strict limit of the critical Rossby number. This new limit of ${\rm Ro_c}=-0.802$, which appears for a finite Lundquist number of ${\rm Lu}=0.618$, extends the formerly known inductionless Liu limit of ${\rm Ro_c}=-0.828$ valid at ${\rm Lu}=0$.

astro-ph.SR↗

arXiv2010

Energy oscillations and a possible route to chaos in a modified Riga dynamo

Starting from the present version of the Riga dynamo experiment with its rotating magnetic eigenfield dominated by a single frequency we ask for those modifications of this set-up that would allow for a non-trivial magnetic field behaviour in the saturation regime. Assuming an increased ratio of azimuthal to axial flow velocity, we obtain energy oscillations with a frequency below the eigenfrequency of the magnetic field. These new oscillations are identified as magneto-inertial waves that result from a slight imbalance of Lorentz and inertial forces. Increasing the azimuthal velocity further, or increasing the total magnetic Reynolds number, we find transitions to a chaotic behaviour of the dynamo.

astro-ph.EP↗

arXiv2010

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

A crucial point for the understanding of the von-Kármán-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 $α$-effect parametrizing the induction effects of unresolved small scale flow fluctuations.

physics.comp-ph↗

arXiv2009

On the relation of standard and helical magnetorotational instability

The magnetorotational instability (MRI) plays a crucial role for cosmic structure formation by enabling turbulence in Keplerian disks which would be otherwise hydrodynamically stable. With particular focus on MRI experiments with liquid metals, which have small magnetic Prandtl numbers, it has been shown that the helical version of this instability (HMRI) has a scaling behaviour that is quite different from that of the standard MRI (SMRI). We discuss the relation of HMRI to SMRI by exploring various parameter dependencies. We identify the mechanism of transfer of instability between modes through a spectral exceptional point that explains both the transition from a stationary instability (SMRI) to an unstable travelling wave (HMRI) and the excitation of HMRI in the inductionless limit. For certain parameter regions we find new islands of the HMRI.

astro-ph.HE↗

arXiv2009

Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced Ekman pumping

The magnetorotational instability (MRI) is thought to play a key role in the formation of stars and black holes by sustaining the turbulence in hydrodynamically stable Keplerian accretion discs. In previous experiments the MRI was observed in a liquid metal Taylor-Couette flow at moderate Reynolds numbers by applying a helical magnetic field. The observation of this helical MRI (HMRI) was interfered with a significant Ekman pumping driven by solid end-caps that confined the instability only to a part of the Taylor-Couette cell. This paper describes the observation of the HMRI in an improved Taylor-Couette setup with the Ekman pumping significantly reduced by using split end-caps. The HMRI, which now spreads over the whole height of the cell, appears much sharper and in better agreement with numerical predictions. By analyzing various parameter dependencies we conclude that the observed HMRI represents a self-sustained global instability rather than a noise-sustained convective one.

astro-ph.GA↗

arXiv2008

Liquid metal experiments on the helical magnetorotational instability

The magnetorotational instability (MRI) plays an essential role in the formation of stars and black holes. By destabilizing hydrodynamically stable Keplerian flows, the MRI triggers turbulence and enables outward transport of angular momentum in accretion discs. We present the results of a liquid metal Taylor-Couette experiment under the influence of helical magnetic fields that show typical features of MRI at Reynolds numbers of the order 1000 and Hartmann numbers of the order 10. Particular focus is laid on an improved experiment in which split end caps are used to minimize the Ekman pumping.

astro-ph↗

arXiv2008

Determining role of Krein signature for 3D Arnold tongues of oscillatory dynamos

Using a homotopic family of boundary eigenvalue problems for the mean-field $α^2$-dynamo with helical turbulence parameter $α(r)=α_0+γΔα(r)$ and homotopy parameter $β\in [0,1]$, we show that the underlying network of diabolical points for Dirichlet (idealized, $β=0$) boundary conditions substantially determines the choreography of eigenvalues and thus the character of the dynamo instability for Robin (physically realistic, $β=1$) boundary conditions. In the $(α_0,β,γ)-$space the Arnold tongues of oscillatory solutions at $β=1$ end up at the diabolical points for $β=0$. In the vicinity of the diabolical points the space orientation of the 3D tongues, which are cones in first-order approximation, is determined by the Krein signature of the modes involved in the diabolical crossings at the apexes of the cones. The Krein space induced geometry of the resonance zones explains the subtleties in finding $α$-profiles leading to spectral exceptional points, which are important ingredients in recent theories of polarity reversals of the geomagnetic field.

math-ph↗

arXiv2008

Magnetohydrodynamic experiments on cosmic magnetic fields

It is widely known that cosmic magnetic fields, i.e. the fields of planets, stars, and galaxies, are produced by the hydromagnetic dynamo effect in moving electrically conducting fluids. It is less well known that cosmic magnetic fields play also an active role in cosmic structure formation by enabling outward transport of angular momentum in accretion disks via the magnetorotational instability (MRI). Considerable theoretical and computational progress has been made in understanding both processes. In addition to this, the last ten years have seen tremendous efforts in studying both effects in liquid metal experiments. In 1999, magnetic field self-excitation was observed in the large scale liquid sodium facilities in Riga and Karlsruhe. Recently, self-excitation was also obtained in the French "von Karman sodium" (VKS) experiment. An MRI-like mode was found on the background of a turbulent spherical Couette flow at the University of Maryland. Evidence for MRI as the first instability of an hydrodynamically stable flow was obtained in the "Potsdam Rossendorf Magnetic Instability Experiment" (PROMISE). In this review, the history of dynamo and MRI related experiments is delineated, and some directions of future work are discussed.

astro-ph↗

arXiv2008

Inferring basic parameters of the geodynamo from sequences of polarity reversals

The asymmetric time dependence and various statistical properties of polarity reversals of the Earth's magnetic field are utilized to infer some of the most essential parameters of the geodynamo, among them the effective (turbulent) magnetic diffusivity, the degree of supercriticality, and the relative strength of the periodic forcing which is believed to result from the Milankovic cycle of the Earth's orbit eccentricity. A time-stepped spherically symmetric alpha^2-dynamo model is used as the kernel of an inverse problem solver in form of a downhill simplex method which converges to solutions that yield a stunning correspondence with paleomagnetic data.

physics.geo-ph↗

arXiv2008

History and results of the Riga dynamo experiments

On 11 November 1999, a self-exciting magnetic eigenfield was detected for the first time in the Riga liquid sodium dynamo experiment. We report on the long history leading to this event, and on the subsequent experimental campaigns which provided a wealth of data on the kinematic and the saturated regime of this dynamo. The present state of the theoretical understanding of both regimes is delineated, and some comparisons with other laboratory dynamo experiments are made.

astro-ph↗

arXiv2008

Kinematic simulations of dynamo action with a hybrid boundary-element/finite-volume method

The experimental realization of dynamo excitation as well as theoretical and numerical examinations of the induction equation have shown the relevance of boundary conditions for a self-sustaining dynamo. Within the interior of a field producing domain geometric constraints or varying material properties (e.g. electrical conductivity of the container walls or localized high-permeability material) might also play a role. Combining a grid based finite volume approach with the boundary element method in a hybrid FV-BEM scheme offers the flexibility of a local discretization with a stringent treatment of insulating magnetic boundary conditions in almost arbitrary geometries at comparatively low costs. Kinematic simulations of dynamo action generated by a well known prescribed mean flow demonstrate the reliability of the approach. Future examinations are intended to understand the behavior of the VKS-dynamo experiment where the field producing flow is driven by ferrous propellers and the induction effects of conductivity/permeability inhomogeneities might provide the required conditions for the measured dynamo characteristics.

physics.flu-dyn↗

arXiv2007

Measurement of the spatio-temporal distribution of harmonic and transient eddy currents in a liquid metal

Harmonic and transient eddy currents in a liquid metal positioned above an excitation coil are determined by measuring the voltage drop in a simple potential probe. The resulting spatio-temporal eddy current field is compared with the corresponding analytical expressions for a conducting half-space. Further, a deformation of the eddy current distribution due to a non-conducting torus immersed into the liquid metal is measured and compared with numerical results. The method can be generalized to arbitrary geometries, and might help to validate numerical models for non-destructive testing and magnetic inductance tomography.

physics.flu-dyn↗

arXiv2007

The integral equation approach to kinematic dynamo theory and its application to dynamo experiments in cylindrical geometry

The conventional magnetic induction equation that governs hydromagnetic dynamo action is transformed into an equivalent integral equation system. An advantage of this approach is that the computational domain is restricted to the region occupied by the electrically conducting fluid and to its boundary. This integral equation approach is first employed to simulate kinematic dynamos excited by Beltrami-like flows in a finite cylinder. The impact of externally added layers around the cylinder on the onset of dynamo actions is investigated. Then it is applied to simulate dynamo experiments within cylindrical geometry including the von Karman sodium (VKS) experiment and the Riga dynamo experiment. A modified version of this approach is utilized to investigate magnetic induction effects under the influence of externally applied magnetic fields which is also important to measure the proximity of a given dynamo facility to the self-excitation threshold.

astro-ph↗