335 research outputs found
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.Comment: 8 pages, 8 figures, submitted to Astronomische Nachrichte
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.Comment: 8 pages, 5 figure, accepted for publication in Comptes Rendus
Physiqu
Spherical single-roll dynamos at large magnetic Reynolds numbers
This paper concerns kinematic helical dynamos in a spherical fluid body
surrounded by an insulator. In particular, we examine their behaviour in the
regime of large magnetic Reynolds number \Rm, for which dynamo action is
usually concentrated upon a simple resonant stream-surface. The dynamo
eigensolutions are computed numerically for two representative single-roll
flows using a compact spherical harmonic decomposition and fourth-order
finite-differences in radius. These solutions are then compared with the growth
rates and eigenfunctions of the Gilbert and Ponty (2000) large \Rm asymptotic
theory. We find good agreement between the growth rates when \Rm>10^4, and
between the eigenfunctions when \Rm>10^5.Comment: 36 pages, 8 figures. V2: incorrect labels in Fig3 corrected. The
article appears in Physics of Fluids, 22, 066601, and may be found at
http://pof.aip.org/phfle6/v22/i6/p066601_s1 . (Copyright 2010 American
Institute of Physics. This article may be downloaded for personal use only.
Any other use requires prior permission of the author and the American
Institute of Physics
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.Comment: 22 pages, 14 figure
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.Comment: 22 pages, 18 figures, to appear in J. Comp. Phy
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.Comment: 13 pages, LaTeX2e, improved references, to appear in J. Math. Phy
On the effects of turbulence on a screw dynamo
In an experiment in the Institute of Continuous Media Mechanics in Perm
(Russia) an non--stationary screw dynamo is intended to be realized with a
helical flow of liquid sodium in a torus. The flow is necessarily turbulent,
that is, may be considered as a mean flow and a superimposed turbulence. In
this paper the induction processes of the turbulence are investigated within
the framework of mean--field electrodynamics. They imply of course a part which
leads to an enhanced dissipation of the mean magnetic field. As a consequence
of the helical mean flow there are also helical structures in the turbulence.
They lead to some kind of --effect, which might basically support the
screw dynamo. The peculiarity of this --effect explains measurements
made at a smaller version of the device envisaged for the dynamo experiment.
The helical structures of the turbulence lead also to other effects, which in
combination with a rotational shear are potentially capable of dynamo action. A
part of them can basically support the screw dynamo. Under the conditions of
the experiment all induction effects of the turbulence prove to be rather weak
in comparison to that of the main flow. Numerical solutions of the mean--field
induction equation show that all the induction effects of the turbulence
together let the screw dynamo threshold slightly, at most by one per cent,
rise. The numerical results give also some insights into the action of the
individual induction effects of the turbulence.Comment: 15 pages, 7 figures, in GAFD prin
Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility
In an experiment at the Riga sodium dynamo facility, a slowly growing
magnetic field eigenmode has been detected over a period of about 15 seconds.
For a slightly decreased propeller rotation rate, additional measurements
showed a slow decay of this mode. The measured results correspond satisfactory
with numerical predictions for the growth rates and frequencies
Magnetic Field Saturation in the Riga Dynamo Experiment
After the dynamo experiment in November 1999 had shown magnetic field
self-excitation in a spiraling liquid metal flow, in a second series of
experiments emphasis was placed on the magnetic field saturation regime as the
next principal step in the dynamo process. The dependence of the strength of
the magnetic field on the rotation rate is studied. Various features of the
saturated magnetic field are outlined and possible saturation mechanisms are
discussed.Comment: 4 pages, 8 figure
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