859 research outputs found
Large-scale dynamos at low magnetic Prandtl numbers
Using direct simulations of hydromagnetic turbulence driven by random
polarized waves it is shown that dynamo action is possible over a wide range of
magnetic Prandtl numbers from 10^-3 to 1. Triply periodic boundary conditions
are being used. In the final saturated state the resulting magnetic field has a
large-scale component of Beltrami type. For the kinematic phase, growth rates
have been determined for magnetic Prandtl numbers between 0.01 and 1, but only
the case with the smallest magnetic Prandtl number shows large-scale magnetic
fields. It is less organized than in the nonlinear stage. For small magnetic
Prandtl numbers the growth rates are comparable to those calculated from an
alpha squared mean-field dynamo. In the linear regime the magnetic helicity
spectrum has a short inertial range compatible with a -5/3 power law, while in
the nonlinear regime it is the current helicity whose spectrum may be
compatible with such a law. In the saturated case, the spectral magnetic energy
in the inertial range is in slight excess over the spectral kinetic energy,
although for small magnetic Prandtl numbers the magnetic energy spectrum
reaches its resistive cut off wavenumber more quickly. The viscous energy
dissipation declines with the square root of the magnetic Prandtl number, which
implies that most of the energy is dissipated via Joule heat.Comment: 8 pages, 12 figures, Astrophys. J. (in press
Study on the large scale dynamo transition
Using the magnetohydrodynamic (MHD) description, we develop a nonlinear
dynamo model that couples the evolution of the large scale magnetic field with
turbulent dynamics of the plasma at small scale by electromotive force (e.m.f.)
in the induction equation at large scale. The nonlinear behavior of the plasma
at small scale is described by using a MHD shell model for velocity field and
magnetic field fluctuations.The shell model allow to study this problem in a
large parameter regime which characterizes the dynamo phenomenon in many
natural systems and which is beyond the power of supercomputers at today. Under
specific conditions of the plasma turbulent state, the field fluctuations at
small scales are able to trigger the dynamo instability. We study this
transition considering the stability curve which shows a strong decrease in the
critical magnetic Reynolds number for increasing inverse magnetic Prandlt
number in the range and slows an increase in
the range . We also obtain hysteretic behavior across the dynamo
boundary reveling the subcritical nature of this transition. The system,
undergoing this transition, can reach different dynamo regimes, depending on
Reynolds numbers of the plasma flow. This shows the critical role that the
turbulence plays in the dynamo phenomenon. In particular the model is able to
reproduce the dynamical situation in which the large-scale magnetic field jumps
between two states which represent the opposite polarities of the magnetic
field, reproducing the magnetic reversals as observed in geomagnetic dynamo and
in the VKS experiments.Comment: 5 pages, 4 figure
On geometric properties of passive random advection
We study geometric properties of a random Gaussian short-time correlated
velocity field by considering statistics of a passively advected metric tensor.
That describes universal properties of fluctuations of tensor objects frozen
into the fluid and passively advected by it. The problem of one-point
statistics of co- and contravariant tensors is solved exactly, provided the
advected fields do not reach dissipative scales, which would break the symmetry
of the problem. Asymptotic in time duality of the problem is established, which
in the three-dimensional case relates the probabilities of the volume
deformations into "tubes" and into "sheets".Comment: latex, 8 page
A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space
A class of simple kinetic systems is considered, described by the 1D
Vlasov-Landau equation with Poisson or Boltzmann electrostatic response and an
energy source. Assuming a stochastic electric field, a solvable model is
constructed for the phase-space turbulence of the particle distribution. The
model is a kinetic analog of the Kraichnan-Batchelor model of chaotic
advection. The solution of the model is found in Fourier-Hermite space and
shows that the free-energy flux from low to high Hermite moments is suppressed,
with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma
echo). This implies that Landau damping is an ineffective route to dissipation
(i.e., to thermalisation of electric energy via velocity space). The full
Fourier-Hermite spectrum is derived. Its asymptotics are at low wave
numbers and high Hermite moments () and at low Hermite
moments and high wave numbers (). These conclusions hold at wave numbers
below a certain cut off (analog of Kolmogorov scale), which increases with the
amplitude of the stochastic electric field and scales as inverse square of the
collision rate. The energy distribution and flows in phase space are a simple
and, therefore, useful example of competition between phase mixing and
nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but
more complicated multi-dimensional systems that have not so far been amenable
to complete analytical solution.Comment: 35 pages, minor edits, final version accepted by JP
A Spherical Plasma Dynamo Experiment
We propose a plasma experiment to be used to investigate fundamental
properties of astrophysical dynamos. The highly conducting, fast-flowing plasma
will allow experimenters to explore systems with magnetic Reynolds numbers an
order of magnitude larger than those accessible with liquid-metal experiments.
The plasma is confined using a ring-cusp strategy and subject to a toroidal
differentially rotating outer boundary condition. As proof of principle, we
present magnetohydrodynamic simulations of the proposed experiment. When a von
K\'arm\'an-type boundary condition is specified, and the magnetic Reynolds
number is large enough, dynamo action is observed. At different values of the
magnetic Prandtl and Reynolds numbers the simulations demonstrate either
laminar or turbulent dynamo action
The origin and evolution of cluster magnetism
Random motions can occur in the intergalactic gas of galaxy clusters at all
stages of their evolution. Depending on the poorly known value of the Reynolds
number, these motions can or cannot become turbulent, but in any case they can
generate random magnetic fields via dynamo action. We argue that magnetic
fields inferred observationally for the intracluster medium require dynamo
action, and then estimate parameters of random flows and magnetic fields at
various stages of the cluster evolution. Polarization in cluster radio halos
predicted by the model would be detectable with the SKA.Comment: 4 pages, 1 figure, to be published by Astronomische Nachrichten
(proceedings of "The Origin and Evolution of Cosmic Magnetism", 29 August - 2
September 2005, Bologna, Italy); version updated to match the accepted tex
MHD simulations of the magnetorotational instability in a shearing box with zero net flux: the case Pm=4
This letter investigates the transport properties of MHD turbulence induced
by the magnetorotational instability at large Reynolds numbers Re when the
magnetic Prandtl number Pm is larger than unity. Three MHD simulations of the
magnetorotational instability (MRI) in the unstratified shearing box with zero
net flux are presented. These simulations are performed with the code Zeus and
consider the evolution of the rate of angular momentum transport as Re is
gradually increased from 3125 to 12500 while simultaneously keeping Pm=4. To
ensure that the small scale features of the flow are well resolved, the
resolution varies from 128 cells per disk scaleheight to 512 cells per
scaleheight. The latter constitutes the highest resolution of an MRI turbulence
simulation to date. The rate of angular momentum transport, measured using the
alpha parameter, depends only very weakly on the Reynolds number: alpha is
found to be about 0.007 with variations around this mean value bounded by 15%
in all simulations. There is no systematic evolution with Re. For the best
resolved model, the kinetic energy power spectrum tentatively displays a
power-law range with an exponent -3/2, while the magnetic energy is found to
shift to smaller and smaller scales as the magnetic Reynolds number increases.
A couple of different diagnostics both suggest a well-defined injection length
of a fraction of a scaleheight. The results presented in this letter are
consistent with the MRI being able to transport angular momentum efficiently at
large Reynolds numbers when Pm=4 in unstratified zero net flux shearing boxes.Comment: 5 pages, 4 figures, accepted in Astronomy and Astrophysic
Fast growth of magnetic fields in galaxy clusters: a self-accelerating dynamo
We propose a model of magnetic-field growth in galaxy clusters whereby the
field is amplified by a factor of about 10^8 over a cosmologically short time
of ~10^8 yr. Our model is based on the idea that the viscosity of the
intracluster medium during the field-amplification epoch is determined not by
particle collisions but by plasma microinstabilities: these give rise to
small-scale fluctuations, which scatter particles, increasing their effective
collision rate and, therefore, the effective Reynolds number. This gives rise
to a bootstrap effect as the growth of the field triggers the instabilities
which increase the Reynolds number which, in turn, accelerates the growth of
the field. The growth is explosive and the result is that the observed field
strength is reached over a fraction of the cluster lifetime independent of the
exact strength of the seed field (which only needs to be above ~10^{-15} G to
trigger the explosive growth).Comment: latex (AN style), 5 pages, 2 figure
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