86 research outputs found
The Tayler instability of toroidal magnetic fields in a columnar gallium experiment
The nonaxisymmetric Tayler instability of toroidal magnetic fields due to
axial electric currents is studied for conducting incompressible fluids between
two coaxial cylinders without endplates. The inner cylinder is considered as so
thin that even the limit of R_in \to 0 can be computed. The magnetic Prandtl
number is varied over many orders of magnitudes but the azimuthal mode number
of the perturbations is fixed to m=1. In the linear approximation the critical
magnetic field amplitudes and the growth rates of the instability are
determined for both resting and rotating cylinders. Without rotation the
critical Hartmann numbers do {\em not} depend on the magnetic Prandtl number
but this is not true for the growth rates. For given product of viscosity and
magnetic diffusivity the growth rates for small and large magnetic Prandtl
number are much smaller than those for Pm=1. For gallium under the influence of
a magnetic field at the outer cylinder of 1 kG the resulting growth time is 5
s. The minimum electric current through a container of 10 cm diameter to excite
the kink-type instability is 3.20 kA. For a rotating container both the
critical magnetic field and the related growth times are larger than for the
resting column.Comment: 7 pages, 9 figures, submitted to Astron. Nach
Tayler instability of toroidal magnetic fields in MHD Taylor-Couette flows
The nonaxisymmetric 'kink-type' Tayler instability (TI) of toroidal magnetic
fields is studied for conducting incompressible fluids of uniform density
between two infinitely long cylinders rotating around the same axis. It is
shown that for resting cylinders the critical Hartmann number for the unstable
modes does not depend on Pm. By rigid rotation the instability is suppressed
where the critical ratio of the rotation velocity and the Alfven velocity of
the field (only) slightly depends on the magnetic Prandtl number Pm. For Pm=1
the rotational quenching of TI takes its maximum. Rotation laws with negative
shear (i.e. d\Omega/dR<0) strongly destabilize the toroidal field if the
rotation is not too fast. For sufficiently high Reynolds numbers of rotation
the suppression of the nonaxisymmetric magnetic instability always dominates.
The angular momentum transport of the instability is anticorrelated with the
shear so that an eddy viscosity can be defined which proves to be positive. For
negative shear the Maxwell stress of the perturbations remarkably contributes
to the angular momentum transport. We have also shown the possibility of
laboratory TI experiments with a wide-gap container filled with fluid metals
like sodium or gallium. Even the effect of the rotational stabilization can be
reproduced in the laboratory with electric currents of only a few kAmp.Comment: 9 pages, 11 figures, sub
Stratorotational instability in MHD Taylor-Couette flows
The stability of dissipative Taylor-Couette flows with an axial stable
density stratification and a prescribed azimuthal magnetic field is considered.
Global nonaxisymmetric solutions of the linearized MHD equations with toroidal
magnetic field, axial density stratification and differential rotation are
found for both insulating and conducting cylinder walls. Flat rotation laws
such as the quasi-Kepler law are unstable against the nonaxisymmetric
stratorotational instability (SRI). The influence of a current-free toroidal
magnetic field depends on the magnetic Prandtl number Pm: SRI is supported by
Pm > 1 and it is suppressed by Pm \lsim 1. For too flat rotation laws a smooth
transition exists to the instability which the toroidal magnetic field produces
in combination with the differential rotation. This nonaxisymmetric azimuthal
magnetorotational instability (AMRI) has been computed under the presence of an
axial density gradient. If the magnetic field between the cylinders is not
current-free then also the Tayler instability occurs and the transition from
the hydrodynamic SRI to the magnetic Tayler instability proves to be rather
complex. Most spectacular is the `ballooning' of the stability domain by the
density stratification: already a rather small rotation stabilizes magnetic
fields against the Tayler instability. An azimuthal component of the resulting
electromotive force only exists for density-stratified flows. The related
alpha-effect for magnetic SRI of Kepler rotation appears to be positive for
negative d\rho/dz <0.Comment: 10 pages, 13 figures, submitted to Astron. Astrophy
Hydrodynamic stability in accretion disks under the combined influence of shear and density stratification
The hydrodynamic stability of accretion disks is considered. The particular
question is whether the combined action of a (stable) vertical density
stratification and a (stable) radial differential rotation gives rise to a new
instability for nonaxisymmetric modes of disturbances. The existence of such an
instability is not suggested by the well-known Solberg-Hoiland criterion. It is
also not suggested by a local analysis for disturbances in general
stratifications of entropy and angular momentum which is presented in our
Section 2 confirming the results of the Solberg-Hoiland criterion also for
nonaxisymmetric modes within the frame of ideal hydrodynamics but only in the
frame of a short-wave approximation for small m. As a necessary condition for
stability we find that only conservative external forces are allowed to
influence the stable disk. As magnetic forces are never conservative, linear
disk instabilities should only exist in the magnetohydrodynamical regime which
indeed contains the magnetorotational instability as a much-promising
candidate. To overcome some of the used approximations in a numerical
approach,the equations of the compressible adiabatic hydrodynamics are
integrated imposing initial nonaxisymmetric velocity perturbations with m=1 to
m=200.
Only solutions with decaying kinetic energy are found. The system always
settles in a vertical equilibrium stratification according to pressure balance
with the gravitational potential of the central object. keywords: accretion
disks -- hydrodynamic instabilities -- turbulenceComment: 6 pages, 4 figures, 1 table, Astronomy and Astrophysics (subm.
The Occurrence of the Hall--Instability in Crusts of Isolated Neutron Stars
In former papers we showed that during the decay of a neutron star's magnetic
field under the influence of the Hall--drift, an unstable rise of small--scale
field structures at the expense of the large--scale background field may
happen. This linear stability analysis was based on the assumption of a uniform
density throughout the neutron star crust, whereas in reality the density and
all transport coefficients vary by many orders of magnitude. Here, we extend
the investigation of the Hall--drift induced instability by considering
realistic profiles of density and chemical composition, as well as background
fields with more justified radial profiles. Two neutron star models are
considered differing primarily in the assumption on the core matter equation of
state. For their cooling history and radial profiles of density and composition
we use known results to infer the conductivity profiles. These were fed into
linear calculations of a dipolar field decay starting from various initial
configurations. At different stages of the decay, snapshots of the magnetic
fields at the equator were taken to yield background field profiles for the
stability analysis. The main result is that the Hall instability may really
occur in neutron star crusts. Characteristic growth times are in the order of
\lesssim 10^4 ... 10^6 yrs depending on cooling age and background field
strength. The influence of the equation of state and of the initial field
configuration is discussed.Comment: 16 pages, 16 figures, PS, submitted to A&A. Justification/discussion
slightly changed/extended in replying to the referee. Changes on p. 3, 11,
13, framed by XXX mark
Three dimensional simulation of the magnetic stress in a neutron star crust
We present the first fully self-consistent three dimensional model of a neutron star’s magnetic field, generated by electric currents in the star’s crust via the Hall effect. We find that the global-scale field converges to a dipolar Hall-attractor state, as seen in recent axisymmetric models, but that small-scale features in the magnetic field survive even on much longer time scales. These small-scale features propagate toward the dipole equator, where the crustal electric currents organize themselves into a strong equatorial jet. By calculating the distribution of magnetic stresses in the crust, we predict that neutron stars with fields stronger than 1014  G can still be subject to starquakes more than 105  yr after their formation
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