198 research outputs found
Energy of eigen-modes in magnetohydrodynamic flows of ideal fluids
Analytical expression for energy of eigen-modes in magnetohydrodynamic flows
of ideal fluids is obtained. It is shown that the energy of unstable modes is
zero, while the energy of stable oscillatory modes (waves) can assume both
positive and negative values. Negative energy waves always correspond to
non-symmetric eigen-modes -- modes that have a component of wave-vector along
the equilibrium velocity. These results suggest that all non-symmetric
instabilities in ideal MHD systems with flows are associated with coupling of
positive and negative energy waves. As an example the energy of eigen-modes is
calculated for incompressible conducting fluid rotating in axial magnetic
field.Comment: 10 pages, 3 figure
Magnetorotational Instability in Liquid Metal Couette Flow
Despite the importance of the magnetorotational instability (MRI) as a
fundamental mechanism for angular momentum transport in magnetized accretion
disks, it has yet to be demonstrated in the laboratory. A liquid sodium
alpha-omega dynamo experiment at the New Mexico Institute of Mining and
Technology provides an ideal environment to study the MRI in a rotating metal
annulus (Couette flow). A local stability analysis is performed as a function
of shear, magnetic field strength, magnetic Reynolds number, and turbulent
Prandtl number. The later takes into account the minimum turbulence induced by
the formation of an Ekman layer against the rigidly rotating end walls of a
cylindrical vessel. Stability conditions are presented and unstable conditions
for the sodium experiment are compared with another proposed MRI experiment
with liquid gallium. Due to the relatively large magnetic Reynolds number
achievable in the sodium experiment, it should be possible to observe the
excitation of the MRI for a wide range of wavenumbers and further to observe
the transition to the turbulent state.Comment: 12 pages, 22 figures, 1 table. To appear in the Astrophysical Journa
Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow
We consider the nonaxisymmetric modes of instability present in Taylor-Couette flow under the application of helical magnetic fields, mainly for magnetic Prandtl numbers close to the inductionless limit, and conduct a full examination of marginal stability in the resulting parameter space. We allow for the azimuthal magnetic field to be generated by a combination of currents in the inner cylinder and fluid itself and introduce a parameter governing the relation between the strength of these currents. A set of governing eigenvalue equations for the nonaxisymmetric modes of instability are derived and solved by spectral collocation with Chebyshev polynomials over the relevant parameter space, with the resulting instabilities examined in detail. We find that by altering the azimuthal magnetic field profiles the azimuthal magnetorotational instability, nonaxisymmetric helical magnetorotational instability, and Tayler instability yield interesting dynamics, such as different preferred mode types and modes with azimuthal wave number m>1 . Finally, a comparison is given to the recent WKB analysis performed by Kirillov et al. [Kirillov, Stefani, and Fukumoto, J. Fluid Mech. 760, 591 (2014)] and its validity in the linear regime
Alfvenic Heating of Protostellar Accretion Disks
We investigate the effects of heating generated by damping of Alfven waves on
protostellar accretion disks. Two mechanisms of damping are investigated,
nonlinear and turbulent, which were previously studied in stellar winds
(Jatenco-Pereira & Opher 1989a, b). For the nominal values studied, f=delta
v/v_{A}=0.002 and F=varpi/Omega_{i}=0.1, where delta v, v_{A} and varpi are the
amplitude, velocity and average frequency of the Alfven wave, respectively, and
Omega_{i} is the ion cyclotron frequency, we find that viscous heating is more
important than Alfven heating for small radii. When the radius is greater than
0.5 AU, Alfvenic heating is more important than viscous heating. Thus, even for
the relatively small value of f=0.002, Alfvenic heating can be an important
source of energy for ionizing protostellar disks, enabling angular momentum
transport to occur by the Balbus-Hawley instability.Comment: 21 pages, 9 figures. Accepted for publication in Ap
Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette Flow
In this paper we present axisymmetric nonlinear simulations of magnetized
Ekman and Stewartson layers in a magnetized Taylor-Couette flow with a
centrifugally stable angular-momemtum profile and with a magnetic Reynolds
number below the threshold of magnetorotational instability. The magnetic field
is found to inhibit the Ekman suction. The width of the Ekman layer is reduced
with increased magnetic field normal to the end plate. A uniformly-rotating
region forms near the outer cylinder. A strong magnetic field leads to a steady
Stewartson layer emanating from the junction between differentially rotating
rings at the endcaps. The Stewartson layer becomes thinner with larger Reynolds
number and penetrates deeper into the bulk flow with stronger magnetic field
and larger Reynolds number. However, at Reynolds number larger than a critical
value , axisymmetric, and perhaps also nonaxisymmetric, instabilities
occur and result in a less prominent Stewartson layer that extends less far
from the boundary.Comment: 24 pages, 12 figures, accepted by PRE, revision according to referee
Modeling the Parker instability in a rotating plasma screw pinch
We analytically and numerically study the analogue of the Parker (magnetic
buoyancy) instability in a uniformly rotating plasma screw pinch confined in a
cylinder. Uniform plasma rotation is imposed to create a centrifugal
acceleration, which mimics the gravity required for the classical Parker
instability. The goal of this study is to determine how the Parker instability
could be unambiguously identified in a weakly magnetized, rapidly rotating
screw pinch, in which the rotation provides an effective gravity and a radially
varying azimuthal field is controlled to give conditions for which the plasma
is magnetically buoyant to inward motion. We show that an axial magnetic field
is also required to circumvent conventional current driven magnetohydrodynamic
(MHD) instabilities such as the sausage and kink modes that would obscure the
Parker instability. These conditions can be realized in the Madison Plasma
Couette Experiment (MPCX). Simulations are performed using the extended MHD
code NIMROD for an isothermal compressible plasma model. Both linear and
nonlinear regimes of the instability are studied, and the results obtained for
the linear regime are compared with analytical results from a slab geometry.
Based on this comparison, it is found that in a cylindrical pinch the magnetic
buoyancy mechanism dominates at relatively large Mach numbers (M>5), while at
low Mach numbers (M<1) the instability is due to the curvature of magnetic
field lines. At intermediate values of Mach number (1<M<5) the Coriolis force
has a strong stabilizing effect on the plasma. A possible scenario for
experimental demonstration of the Parker instability in MPCX is discussed
Vorticity Budget of Weak Thermal Convection in Keplerian disks
By employing the equations of mean-square vorticity (enstrophy) fluctuations
in strong shear flows, we demonstrate that unlike energy production of
turbulent vorticity in nonrotating shear flows, the turbulent vorticity of weak
convection in Keplerian disks cannot gain energy from vortex stretching/tilting
by background shear unless the asscoiated Reynolds stresses are negative. This
is because the epicyclic motion is an energy sink of the radial component of
mean-square turbulent vorticity in Keplerian disks when Reynolds stresses are
positive. Consequently, weak convection cannot be self-sustained in Keplerian
flows. This agrees with the results implied from the equations of mean-square
velocity fluctuations in strong shear flows. Our analysis also sheds light on
the explanation of the simulation result in which positive kinetic helicity is
produced by the Balbus-Hawley instability in a vertically stratified Keplerian
disk. We also comment on the possibility of outward angular momentum transport
by strong convection based on azimuthal pressure perturbations and directions
of energy cascade.Comment: 8 pages, 1 figure, emulateapj.sty, revised version in response to
referee's comments, accepted by Ap
Compressibility and local instabilities of differentially rotating magnetized gas
We study the stability of compressible cylindrical differentially rotating
flow in the presence of the magnetic field, and show that compressibility
alters qualitatively the stability properties of flows. Apart from the
well-known magnetorotational instability that can occur even in incompressible
flow, there exist a new instability caused by compressibility. The necessary
condition of the newly found instability can easily be satisfied in various
flows in laboratory and astrophysical conditions and reads where and are the radial and azimuthal
magnetic fields, with being the cylindrical radius.
Contrary to the magnetorotational instability that occurs only if
decreases with , the newly found instability operates at any sign of
. The considered instability can arise even in a very strong magnetic
field that suppresses the magnetorotational instability.Comment: 29 pages, 9 figures, accepted for publication in Ap
Hydromagnetic Instability in Differentially Rotating Flows
We study the stability of a compressible differentially rotating flows in the
presence of the magnetic field, and we show that the compressibility profoundly
alters the previous results for a magnetized incompressible flow. The necessary
condition of newly found instability can be easily satisfied in various flows
in laboratory and astrophysical conditions and reads where and are the radial and azimuthal components of
the magnetic field, with being the cylindrical
radius. Contrary to the well-known magnetorotational instability that occurs
only if decreases with , the instability considered in this paper
may occur at any sign of . The instability can operate even in a very
strong magnetic field which entirely suppresses the standard magnetorotational
instability. The growth time of instability can be as short as few rotation
periods.Comment: 5 pages, 3 figure
Metamorphosis of helical magnetorotational instability in the presence of axial electric current
This paper presents numerical linear stability analysis of a cylindrical
Taylor-Couette flow of liquid metal carrying axial electric current in a
generally helical external magnetic field. Axially symmetric disturbances are
considered in the inductionless approximation corresponding to zero magnetic
Prandtl number. Axial symmetry allows us to reveal an entirely new
electromagnetic instability. First, we show that the electric current passing
through the liquid can extend the range of helical magnetorotational
instability (HMRI) indefinitely by transforming it into a purely
electromagnetic instability. Two different electromagnetic instability
mechanisms are identified. The first is an internal pinch-type instability,
which is due to the interaction of the electric current with its own magnetic
field. Axisymmetric mode of this instability requires a free-space component of
the azimuthal magnetic field. When the azimuthal component of the magnetic
field is purely rotational and the axial component is nonzero, a new kind of
electromagnetic instability emerges. The latter driven by the interaction of
electric current with a weak collinear magnetic field in a quiescent fluid
gives rise to a steady meridional circulation coupled with azimuthal rotation.Comment: 10 pages, 12 figures, final versio
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