5. MHD-Tage
Abstracts
T. Aiouaz
Kiepenheuer Institute for Solar Physics, Freiburg
e-mail: tayeb@kis.uni-freiburg.de
Coronal funnels are open magnetic structures connecting
the chromosphere with the solar corona (Axford and McKenzie 1997; Marsch and Tu
1997; Hackenberg et al. 1999). We investigate the stationary plasma flow
out of funnels with a flux-tube model. The funnel area function is
derived from an analytical 2-D magnetic field model and the funnel
height is approximately 10 Mm.
Thus we obtain a realistic area function being valid into the upper
corona. The plasma in the funnel is treated with One-fluid equations
including radiative losses, thermal conduction, heating by
cyclotron-damped Alfv´en waves. We adjust the parameters to the
quantities measured in the lower solar corona (100 000 km above the
photosphere) by SUMER data onboard SOHO . We obtained 2D plasma
properties (e.g. density, temperatures flow speed) within the funnel.
R. Arlt
AIP Potsdam
e-mail: rarlt@aip.de
Dynamo action from axisymmetric flows has been suggested by
various authors according to analytical and numerical investigations. We will
address dynamo action from axisymmetric flows in radiative stellar
shells where no convection can drive a dynamo. Radiation pressure
must lead to differential rotation though, which in turn drives
a meridional, axisymmetric flow. All these combinations of differential
rotation and meridional flow do not act as a kinematic dynamo. We
studied magnetic Reynolds numbers numerically up to about 10000.
It was found that slight deviations from the flows known to drive
kinematic dynamos destroy the capability of exciting a dynamo.
U. Christensen
Universität Göttingen
e-mail: urc@uni-geophys.gwdg.de
The study of the geodynamo and other planetary dynamos has entered
a new stage 7 years ago, when fully self-consistent
MHD simulations of convection-driven dynamos became possible.
While the turbulent flow cannot be resolved because of computational
limitations, the magnetic Reynolds number of order 100-1000 in the
metallic planetary cores is well accessible and there is no need
to parameterize the magnetic induction process. Many published models
exhibit dipole-dominated magnetic fields
of similar strength as the geomagnetic field. Systematic parameter
studies are possible at low supercritical Rayleigh number and
high magnetic Prandtl number (low magnetic diffusivity). Dipole
reversals are only found at parameters that are closer to planetary
values. The mechanism of magnetic field generation seems to differ in various
numerical models
despite the similarity of the field morphologies at the surface of
the sphere. At low Rayleigh number, both the poloidal and the toroidal
magnetic field are regenerated by helical convective motion
(alpha^2-dynamo). At higher Rayleigh number part of the toroidal
field is also generated by differential rotation (alpha^2-omega-dynamos).
Dynamo models have been used to investigate the influence
of boundary conditions, such as inhomogeneous heat flux at the
core-mantle boundary, different modes of driving convection, or
varying size of the inner core during Earth's evolution on the
magnetic field. Finally, possible causes for the presence or absence
of dynamos in planets other than Earth will be discussed.
W. Dobler, A. Brandenburg, M. Stix
Kiepenheuer Institute for Solar Physics, Freiburg
e-mail: Dobler@kis.uni-freiburg.de
We present results from numerical MHD simulations of fully convective
spheres.
The model is characterised by a spherically symmetric gravity potential,
localised heating in the centre and cooling in a surface layer.
We focus on the generation and evolution of magnetic fields and the profiles of
differential rotation and meridional circulation.
D. Elstner, G Rüdiger
AIP Potsdam
e-mail: delstner@aip.de
The question is answered whether
alpha²-shell-dynamos are able to produce a cyclic activity or not.
Only kinematic dynamos are considered and only the solutions with the
lowest dynamo number (~ normalized alpha-effect) are studied without
restrictions about the axial symmetry of the solution.
There exist oscillatory solutions but only in a very limited range of
the parameter space.
A. Gailitis, O. Lielausis, E. Platacis
Institute of Physics, Latvia
G. Gerbeth, Th. Gundrum, F. Stefani
FZ Rossendorf
e-mail: gailitis@sal.lv
In June 2002, a new experimental campaign was carried out at the Riga
dynamo facility. The new experiments have delivered magnetic
field data with
higher radial resolution and with sampling rates up to 10 kHz. The range of
propeller rotation rates has been extended to higher values, giving new
information on the kinematic and the saturation regime for higher magnetic
Reynolds numbers.
R. Grundmann
TU Dresden
e-mail: grundman@tfd.mw.tu-dresden.de
t.b.a.
U. Günther
FZ Rossendorf
e-mail: u.guenther@fz-rossendorf.de
The spherical MHD mean-field dynamo is considered from a
mathematical viewpoint. It is shown that its 2x2 operator matrix is
formally pseudo-Hermitian (J-symmetric), lives
in a Krein space and has
paired complex eigenvalues.
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 alpha²-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 alpha²-dynamo
operator classes with the help
of first-order differential intertwining operators.
G. Hornig
Ruhr-Universität Bochum
e-mail: gh@tp4.ruhr-uni-bochum.de
Magnetic helicity is an important tool to describe complex magnetic
fields. It is also a very robust invariant and therefore helps to
understand the evolution of astrophysical plasmas. However, magnetic
helicity measures only the lowest (2nd-) order linkage of magnetic
flux. Although higher order linkage of magnetic flux is known to exist
there are up to now no simple integrals to measure it, except for some
singular cases . A short review is given on the methods which exist so
far to measure higher order linkage of magnetic flux and ways to extend
these methods to the most general case are discussed.
R. Kaiser
Universität Bayreuth
e-mail: ralf.kaiser@uni-bayreuth.de
Die Annahme, dass es sich bei einem
Kugelblitz um ein Hoch-Temperatur-Plasma handelt,
ähnlich einem gewöhnlichen Blitz,
legt eine Beschreibung im Rahmen der
idealen MHD nahe. In diesem Vortrag werden
notwendige Bedingungen fuer ideale MHD-Gleichgewichte,
die geeignet sind einen Kugelblitz zu beschreiben,
formuliert und ein spezielles Gleichgewicht,
das diese Bedingungen erfüllt,
diskutiert. Insbesondere werden charakteristische Zahlen
berechnet, Stabilität und Helizität diskutiert,
sowie Deformationen des sphärischen Plasmarandes
betrachtet.
Ch. Karcher, V. Kucourek, and M. Conrath
TU Ilmanau
e-mail: christian.karcher@tu-ilmenau.de
The shaping of a liquid metal drop using high-frequency magnetic fields
is investigated experimentally, numerically and analytically. The
motivation for this study comes from electron beam evaporation of liquid
metals. In this process, turbulent convection within the melt leads to
highly unwelcome heat losses through the water-cooled side walls of the
crucible. Therefore, to increase efficiency, it would be favourable to
fix the melt puddle horizontally by a magnetic field. In the experiments
we use drops of the low-melting liquid metal GaInSn. The drop surface is
submitted to an electromagnetic pressure generated by an inductor that
is fed by a high-frequency electrical current. We record the contour of
drops of variable volume while varying inductor current and frequency.
The results are compared with predictions of both numerical simulations
and a simple analytical model.
E. Kurt, F. H. Busse
Universität Bayreuth
e-mail: erol.kurt@uni-bayreuth.de
The magnetic Ekman-Couette layer problem is
a basic model of magnetic activities at the
boundary of the Earth's liquid core and at the
tachocline in the Sun below the convection zone.
It is also the best known example of a
magnetic flow with varying direction. The
analysis of the Ekman-Couette layer without
magnetic field has exhibited a rich variety of
flow states such as type I and type II instabilities,
solitary and chaotic solutions beside the
periodic ones. Laboratory studies of the
Ekman-Couette problem have been undertaken
in the form of the rotating disk configuration
and satisfactory comparisons with the theoretical
results have been achieved. With the present
study, we aim to identify the effects of a
magnetic field depending on the appropriate
geometry for the two rigid parallel rotating plates.
K.-H. Rädler
AIP Potsdam
e-mail: khraedler@aip.de
In Perm (Russia) an experiment is under preparation in which an unsteady screw flow
of liquid sodium is organized in a torus so that some kind of Ponomarenko dynamo
is to be expected to work during a certain time interval. The effects of the
turbulence, which is necessarily superimposed to the screw flow, on the dynamo
are studied in the framework of the mean-field concept. The most striking result
found under some reasonable assumptions is that despite the non-zero helicity
of the mean flow no alpha-effect occurs. In agreement with this in a pilot test
with a small gallium torus indeed no indication of an alpha-effect could be observed.
Other turbulence effects which are of interest in the dynamo context like, e.g.,
the "omega x j"-effect may well be present. Implications of the results obtained
in this study for cosmic dynamos are discussed, too.
G. Rüdiger
AIP Potsdam
e-mail: gruediger@aip.de
The observed rigid rotation of the solar core is taken as an example of the
existence of an MHD instability of rotation laws decreasing outwards. The
same instability can be studied with MHD Taylor-Couette experiments with
resting or rotating outer cylinders. The linear theory for fluids with
given magnetic Prandtl numbers subject to an axial magnetic field is
presented for axisymmetric and nonaxisymmetric modes.
We find that i) for large magnetic Prandtl number the excitation is
subcritical compared with the hydrodynamical case and ii) that for
small magnetic Prandtl numbers the
instability arises as an oscillation with increasing amplitude, i.e. as
overstability. Nonlinear simulations of the magnetorotational
instability in Kepler disks
are also presented in order to solve the angular momentum problem of star
formation. Finally, the Hall effect is included into the theory
leading to
a completely new electrodynamic instability of plasma flows subject
to external axial
magnetic field, shear and Hall effect.
M. Schüssler
MPI für Aeronomie,
Katlenburg-Lindau
e-mail: msch@linmpi.mpg.de
MHD simulations have become an indispensable tool for studying the
magnetic field dynamics in the solar interior and in its atmosphere
out into the corona. After a brief overview of various research
activities in the area I shall concentrate on two aspects: 1) the
dynamics of the magnetic field in the deep convection zone, which is
related to the dynamo problem, and 2) the interaction of vigorous
convective flows, magnetic fields, and radiation in the solar
photosphere and in the uppermost layers of the convection zone.
R. Simitev, F. H. Busse
Universität Bayreuth
e-mail: radostin.simitev@uni-bayreuth.de
Recent numerical results for convection driven dynamos in
rotating spherical fluids shells are presented.
Studies of the dependence on the Prandtl number indicate
that dynamo
action disappears with increasing of this parameter unless the
magnetic Prandtl number
is also increased.
Relaxation oscillations of convection coupled to magnetic
torsional oscillations
are found at low Prandtl numbers and various types of
reversals of dipolar
dynamos have been identified. Cases of strong intermittency are
reported. Different dynamo symmetry types are mapped onto
the parameter
space.
F. Stefani, G. Gerbeth
FZ Rossendorf
e-mail: F.Stefani@fz-rossendorf.de
We give an overview about our recent activities
to solve inverse problems appearing in various
branches of MHD. The very general problem,
the full reconstruction of velocity or turbulence parameters
of fluid flows with arbitrary magnetic Reynolds numbers
from externally measured magnetic fields varying in
space and time, is tackled from two different corners.
First, we explore the restricted inverse dynamo problem
of determining, from a limited number of spectral data,
the radial profile alpha(r) of an isotropic alpha²
dynamo model. Among our results is the construction of
oscillatory dynamos of this type, which might be of some
interest for stellar dynamos.
Second, we consider the topic of contactless
velocity reconstruction in industrial applications with
moderate magnetic Reynolds numbers from the measured
deformation of two different external magnetic fields.
R. Stieglitz
FZ Karlsruhe
e-mail: robert.stieglitz@iket.fzk.de
t.b.a
E. Tassi, V.S. Titov, G. Hornig
Ruhr-Universität Bochum
e-mail: tassi@tp4.ruhr-uni-bochum.de
Analytical solutions of the steady MHD equations
for an incompressible plasma in curvilinear geometry
are presented. These solutions describe a process of
reconnective annihilation where a current layer is
present in correspondence to one separatrix of the
magnetic field. The resulting distribution of the
magnetic flux on the plane y=0 make these solutions
attractive for modeling the process of magnetic
reconnection occurring during solar flares.
A. Tilgner
Universität Göttingen
e-mail: andreas.tilgner@geo.physik.uni-goettingen.de
Peffley, Cawthorne and Lathrop [Phys. Rev. E 61, 5287 (2000)] report on an
experiment using liquid sodium which studies the approach toward a
self-generating dynamo. Their results challenge the traditional views of
kinematic dynamo theory because (i) the modes of the magnetic field with
the smallest decay rates appear to be nearly axisymmetric and because
(ii) the observed decay rates vary spatially. This report shows
how these observations can be reconciled with kinematic dynamo theory.
V. Titov
Ruhr-Universität Bochum
e-mail: st@tp4.ruhr-uni-bochum.de
I will present a short review of the recent results on
Hyperbolic Flux Tubes (HFTs), which are generic geometrical
features of solar magnetic configurations. In some limiting
cases the HFT degenerates into two genuine separatrix surfaces
intersecting along a so-called separator field line.
So the concept of HFTs is a generalization of the concept of
separators to the case of topologically simple magnetic fields
in the solar corona. The HFTs are of great importance because,
first, the conditions for their appearance in the solar corona
are less restrictive than for the separators and, second, they
are both favourable sites for magnetic reconnection process in
solar flares and other active phenomena on the Sun. I will
discuss the criterion for HFTs and the physical mechanism of
current layer formation (called magnetic pinching) in HFTs.
M. Xu, F. Stefani, G. Gerbeth
FZ Rossendorf
e-mail: M.Xu@fz-rossendorf.de
The integral equation approach to steady dynamos in finite domains
is employed to solve the eigenvalue
problem for spherically symmetric, isotropic
alpha² dynamo models. Three examples of the function
alpha(r) with steady and oscillatory solutions are
considered.
A convergence rate proportional to the
inverse square of the number of grid points is achieved.
Based on this method, a convergence accelerating strategy
is developed and the convergence rate is improved dramatically.
The computed results show a good agreement with
analytical results and results obtained by a differential
equation solver.
Typically, quite accurate results can be obtained
with a few tens of grid points.
D. Krasnov, E. Zienicke, A. Thess, O. Zikanov, T. Boeck
TU Ilmenau
e-mail: egbert.zienicke@tu-ilmenau.de
Linear instability for an isolated Hartmann layer was shown to be at a
critical parameter R=Re/Ha=48250. In contrast to this fact transition
to turbulence for growing R - respective laminarization for decreasing
of R - was observed in a range of 150-250 for R in many experiments
linear stability theory.
We investigate therefore the following transition mechanism numerically
in a MHD-channel flow: optimal disturbances in the shape of 2D streamwise
rolls inside the Hartmann layer can grow considerably before they decay
according to linear stability theory. The energetic maximum of this
disturbances can be strong enough to create inflection points in the
velocity profiles that are unstable against small 3D-perturbations. Our
numerical results show a transition to turbulence already in a regime of
R=250-400 by this mechanism, which is near to the experimental results.
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