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F. Stefani

Publications and source records attributed to F. Stefani.

65 records · Page 4Linked to original sources
arXiv2009

Generation of axisymmetric modes in cylindrical kinematic mean-field dynamos of VKS type

In an attempt to understand why the dominating magnetic field observed in the von-Kármán-Sodium (VKS) dynamo experiment is axisymmetric, we investigate in the present paper the ability of mean field models to generate axisymmetric eigenmodes in cylindrical geometries. An $α$-effect is added to the induction equation and we identify reasonable and necessary properties of the $α$ distribution so that axisymmetric eigenmodes are generated. The parametric study is done with two different simulation codes. We find that simple distributions of $α$-effect, either concentrated in the disk neighbourhood or occupying the bulk of the flow, require unrealistically large values of the parameter $α$ to explain the VKS observations.

physics.flu-dyn↗
arXiv2009

Cylindrical anisotropic $α^{2}$ dynamos

We explore the influence of geometry variations on the structure and the time-dependence of the magnetic field that is induced by kinematic $α^{2}$ dynamos in a finite cylinder. The dynamo action is due to an anisotropic $α$ effect which can be derived from an underlying columnar flow. The investigated geometry variations concern, in particular, the aspect ratio of height to radius of the cylinder, and the thickness of the annular space to which the columnar flow is restricted. Motivated by the quest for laboratory dynamos which exhibit Earth-like features, we start with modifications of the Karlsruhe dynamo facility. Its dynamo action is reasonably described by an $α^{2}$ mechanism with anisotropic $α$ tensor. We find a critical aspect ratio below which the dominant magnetic field structure changes from an equatorial dipole to an axial dipole. Similar results are found for $α^{2}$ dynamos working in an annular space when a radial dependence of $α$ is assumed. Finally, we study the effect of varying aspect ratios of dynamos with an $α$ tensor depending both on radial and axial coordinates. In this case only dominant equatorial dipoles are found and most of the solutions are oscillatory, contrary to all previous cases where the resulting fields are steady.

physics.geo-ph↗
arXiv2007

Coexisting stochastic and coherence resonance in a mean-field dynamo model for Earth's magnetic field reversals

Using a spherical symmetric mean field alpha^2-dynamo model for Earth's magnetic field reversals, we show the coexistence of the noise-induced phenomena coherence resonance and stochastic resonance. Stochastic resonance has been recently invoked to explain the 100 kyr periodicity in the distribution of the residence time between reversals. The comparison of the resulting residence time distribution with the paleomagnetic one allows for some estimate of the effective diffusion time of the Earth's core which may be 100 kyr or slightly below rather than 200 kyr as it would result from the molecular resistivity.

astro-ph↗
arXiv2007

The Hot-Spot Phenomenon and its Countermeasures in Bipolar Power Transistors by Analytical Electro-Thermal Simulation

This communication deals with a theoretical study of the hot spot onset (HSO) in cellular bipolar power transistors. This well-known phenomenon consists of a current crowding within few cells occurring for high power conditions, which significantly decreases the forward safe operating area (FSOA) of the device. The study was performed on a virtual sample by means of a fast, fully analytical electro-thermal simulator operating in the steady state regime and under the condition of imposed input base current. The purpose was to study the dependence of the phenomenon on several thermal and geometrical factors and to test suitable countermeasures able to impinge this phenomenon at higher biases or to completely eliminate it. The power threshold of HSO and its localization within the silicon die were observed as a function of the electrical bias conditions as for instance the collector voltage, the equivalent thermal resistance of the assembling structure underlying the silicon die, the value of the ballasting resistances purposely added in the emitter metal interconnections and the thickness of the copper heat spreader placed on the die top just to the aim of making more uniform the temperature of the silicon surface.

cond-mat.mtrl-sci↗
arXiv2006

Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

The intention of the ''von Karman sodium'' (VKS) experiment is to study the hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much effort has been devoted to the optimization of the mean flow and the lateral boundary conditions in order to minimize the critical magnetic Reynolds number and hence the necessary motor power. The main focus of this paper lies on the role of ''lid layers'', i.e. layers of liquid sodium between the impellers and the end walls of the cylinder. First, we study an analytical test flow to show that lid layers can have an ambivalent effect on the efficiency of the dynamo. The critical magnetic Reynolds number shows a flat minimum for a small lid layer thickness, but increases for thicker layers. For the actual VKS geometry it is shown that static lid layers yield a moderate increase of the critical magnetic Reynolds number by approximately 12 per cent. A more dramatic increase by 100 until 150 per cent can occur when some rotational flow is taken into account in those layers. Possible solutions of this problem are discussed for the real dynamo facility.

physics.flu-dyn↗
arXiv2006

A paradigmatic model of Earth's magnetic field reversals

The irregular polarity reversals of the Earth's magnetic field have attracted much interest during the last decades. Despite the fact that recent numerical simulations of the geodynamo have shown nice polarity transitions, the very reason and the basic mechanism of reversals are far from being understood. Using a paradigmatic mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha we attribute the essential features of reversals to the magnetic field dynamics in the vicinity of an exceptional point of the spectrum of the non-selfadjoint dynamo operator. At such exceptional (branch) points of square root type two real eigenvalues coalesce and continue as a complex conjugated pair of eigenvalues. Special focus is laid on the comparison of numerically computed time series with paleomagnetic observations. It is shown that the considered dynamo model with high supercriticality can explain the observed time scale and the asymmetric shape of reversals with a slow decay and a fast field recovery.

physics.geo-ph↗
arXiv2004

The MHD alpha^2-dynamo, Z_2-graded pseudo-Hermiticity, level crossings and exceptional points of branching type

The spectral branching behavior of the 2x2 operator matrix of the magneto-hydrodynamic alpha^2-dynamo is analyzed numerically. Some qualitative aspects of level crossings are briefly discussed with the help of a simple toy model which is based on a Z_2-graded-pseudo-Hermitian 2x2 matrix. The considered issues comprise: the underlying SU(1,1) symmetry and the Krein space structure of the system, exceptional points of branching type and diabolic points, as well as the algebraic and geometric multiplicity of corresponding degenerate eigenvalues.

math-ph↗
arXiv2003

The Integral Equation Method for a Steady Kinematic Dynamo Problem

With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust and accurate tools for the numerical solution of many problems in other fields of physics. The paper is intended to facilitate the use of integral equation solvers in dynamo theory. In concrete, the integral equation method is employed to solve the eigenvalue problem for a hydromagnetic dynamo model with a spherically symmetric, isotropic helical turbulence parameter alpha. Three examples of the function alpha(r) with steady and oscillatory solutions are considered. A convergence rate proportional to the inverse squared of the number of grid points is achieved. Based on this method, a convergence accelerating strategy is developed and the convergence rate is improved remarkably. Typically, quite accurate results can be obtained with a few tens of grid points. In order to demonstrate its suitability for the treatment of dynamos in other than spherical domains, the method is also applied to alpha^2 dynamos in rectangular boxes. The magnetic fields and the electric potentials for the first eigenvalues are visualized.

astro-ph↗
arXiv2003

Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem

The isospectrality problem is studied for the operator of the spherical hydromagnetic alpha^2-dynamo. It is shown that this operator is formally pseudo-Hermitian (J-symmetric) and lives in a Krein space. Based on the J-symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the alpha^2-dynamo operator matrix. An intrinsic structural inconsistency is obtained in the set of associated matrix Riccati equations. This inconsistency is interpreted as a no-go theorem which forbids the construction of isospectral alpha^2-dynamo operator classes with the help of first-order differential intertwining operators.

math-ph↗
arXiv1996

A new field-theoretical formulation for the motion of an electron in a quenched disorder potential

Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.

cond-mat↗