39 research outputs found
On radiation-zone dynamos
It is shown that the magnetic current-driven (`kink-type') instability
produces flow and field patterns with helicity and even with \alpha-effect but
only if the magnetic background field possesses non-vanishing current helicity
\bar{\vec{B}}\cdot curl \bar{\vec{B}} by itself. Fields with positive
large-scale current helicity lead to negative small-scale kinetic helicity. The
resulting \alpha-effect is positive. These results are very strict for
cylindric setups without z/I>-dependence of the background fields. The sign
rules also hold for the more complicated cases in spheres where the toroidal
fields are the result of the action of differential rotation (induced from
fossil poloidal fields) at least for the case that the global rotation is
switched off after the onset of the instability.Comment: 6 pages, 6 figures, submitted to Proceedings of IAU Symp. 274:
Advances in Plasma Astrophysic
Eddy viscosity and turbulent Schmidt number by kink-type instability of strong toroidal magnetic fields
The potential of the nonaxisymmetric magnetic instability to transport
angular momentum and to mix chemicals is probed considering the stability of a
nearly uniform toroidal field between conducting cylinders with different
rotation rates. The fluid between the cylinders is assumed as incompressible
and to be of uniform density. With a linear theory the neutral-stability maps
for m=1 are computed. Rigid rotation must be subAlfvenic to allow instability
while for differential rotation with negative shear also an unstable domain
with superAlfvenic rotation exists. The rotational quenching of the magnetic
instability is strongest for magnetic Prandtl number Pm=1 and becomes much
weaker for Pm unequal 1. The effective angular momentum transport by the
instability is directed outwards(inwards) for subrotation(superrotation). The
resulting magnetic-induced eddy viscosities exceed the microscopic values by
factors of 10-100. This is only true for superAlfvenic flows; in the
strong-field limit the values remain much smaller. The same instability also
quenches concentration gradients of chemicals by its nonmagnetic fluctuations.
The corresponding diffusion coefficient remains always smaller than the
magnetic-generated eddy viscosity. A Schmidt number of order 30 is found as the
ratio of the effective viscosity and the diffusion coefficient. The magnetic
instability transports much more angular momentum than that it mixes chemicals.Comment: 9 pages, 12 figures, submitte
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.Comment: 4 pages, 5 figure
Critical fields and growth rates of the Tayler instability as probed by a columnar gallium experiment
Many astrophysical phenomena (such as the slow rotation of neutron stars or
the rigid rotation of the solar core) can be explained by the action of the
Tayler instability of toroidal magnetic fields in the radiative zones of stars.
In order to place the theory of this instability on a safe fundament it has
been realized in a laboratory experiment measuring the critical field strength,
the growth rates as well as the shape of the supercritical modes. A strong
electrical current flows through a liquid-metal confined in a resting columnar
container with an insulating outer cylinder. As the very small magnetic Prandtl
number of the gallium-indium-tin alloy does not influence the critical Hartmann
number of the field amplitudes, the electric currents for marginal instability
can also be computed with direct numerical simulations. The results of this
theoretical concept are confirmed by the experiment. Also the predicted growth
rates of the order of minutes for the nonaxisymmetric perturbations are
certified by the measurements. That they do not directly depend on the size of
the experiment is shown as a consequence of the weakness of the applied fields
and the absence of rotation.Comment: 8 pages, 5 figures, accepted by Ap
Stability and instability of hydromagnetic Taylor–Couette flows
Decades ago S. Lundquist, S. Chandrasekhar, P. H. Roberts and R. J. Tayler first posed questions about the stability of Taylor–Couette flows of conducting material under the influence of large-scale magnetic fields. These and many new questions can now be answered numerically where the nonlinear simulations even provide the instability-induced values of several transport coefficients. The cylindrical containers are axially unbounded and penetrated by magnetic background fields with axial and/or azimuthal components. The influence of the magnetic Prandtl number Pm on the onset of the instabilities is shown to be substantial. The potential flow subject to axial fields becomes unstable against axisymmetric perturbations for a certain supercritical value of the averaged Reynolds number Rm¯=√Re⋅Rm (with Re the Reynolds number of rotation, Rm its magnetic Reynolds number). Rotation profiles as flat as the quasi-Keplerian rotation law scale similarly but only for Pm≫1 while for Pm≪1 the instability instead sets in for supercritical Rm at an optimal value of the magnetic field. Among the considered instabilities of azimuthal fields, those of the Chandrasekhar-type, where the background field and the background flow have identical radial profiles, are particularly interesting. They are unstable against nonaxisymmetric perturbations if at least one of the diffusivities is non-zero. For Pm≪1 the onset of the instability scales with Re while it scales with Rm¯ for Pm≫1. Even superrotation can be destabilized by azimuthal and current-free magnetic fields; this recently discovered nonaxisymmetric instability is of a double-diffusive character, thus excluding Pm=1. It scales with Re for Pm→0 and with Rm for Pm→∞.
The presented results allow the construction of several new experiments with liquid metals as the conducting fluid. Some of them are described here and their results will be discussed together with relevant diversifications of the magnetic instability theory including nonlinear numerical studies of the kinetic and magnetic energies, the azimuthal spectra and the influence of the Hall effect