1,683 research outputs found
A Solvable Model for Nonlinear Mean Field Dynamo
We formulate a solvable model that describes generation and saturation of
mean magnetic field in a dynamo with kinetic helicity, in the limit of large
magnetic Prandtl number. This model is based on the assumption that the
stochastic part of the velocity field is Gaussian and white in time (the
Kazantsev-Kraichnan ensemble), while the regular part describing the back
reaction of the magnetic field is chosen from balancing the viscous and Lorentz
stresses in the MHD Navier-Stokes equation. The model provides an analytical
explanation for previously obtained numerical results.Comment: 6 page
Turbulent magnetic dynamo excitation at low magnetic Prandtl number
Planetary and stellar dynamos likely result from turbulent motions in
magnetofluids with kinematic viscosities that are small compared to their
magnetic diffusivities. Laboratory experiments are in progress to produce
similar dynamos in liquid metals. This work reviews recent computations of
thresholds in critical magnetic Reynolds number above which dynamo
amplification can be expected for mechanically-forced turbulence (helical and
non-helical, short wavelength and long wavelength) as a function of the
magnetic Prandtl number . New results for helical forcing are discussed,
for which a dynamo is obtained at . The fact that the
kinetic turbulent spectrum is much broader in wavenumber space than the
magnetic spectrum leads to numerical difficulties which are bridged by a
combination of overlapping direct numerical simulations and subgrid models of
magnetohydrodynamic turbulence. Typically, the critical magnetic Reynolds
number increases steeply as the magnetic Prandtl number decreases, and then
reaches an asymptotic plateau at values of at most a few hundred. In the
turbulent regime and for magnetic Reynolds numbers large enough, both small and
large scale magnetic fields are excited. The interactions between different
scales in the flow are also discussed.Comment: 8 pages, 8 figures, to appear in Physics of Plasma
Point force manipulation and activated dynamics of polymers adsorbed on structured substrates
We study the activated motion of adsorbed polymers which are driven over a
structured substrate by a localized point force.Our theory applies to
experiments with single polymers using, for example, tips of scanning force
microscopes to drag the polymer.We consider both flexible and semiflexible
polymers,and the lateral surface structure is represented by double-well or
periodic potentials. The dynamics is governed by kink-like excitations for
which we calculate shapes, energies, and critical point forces. Thermally
activated motion proceeds by the nucleation of a kink-antikink pair at the
point where the force is applied and subsequent diffusive separation of kink
and antikink. In the stationary state of the driven polymer, the collective
kink dynamics can be described by an one-dimensional symmetric simple exclusion
process.Comment: 7 pages, 2 Figure
Hall-MHD small-scale dynamos
Much of the progress in our understanding of dynamo mechanisms has been made
within the theoretical framework of magnetohydrodynamics (MHD). However, for
sufficiently diffuse media, the Hall effect eventually becomes non-negligible.
We present results from three dimensional simulations of the Hall-MHD equations
subjected to random non-helical forcing. We study the role of the Hall effect
in the dynamo efficiency for different values of the Hall parameter, using a
pseudospectral code to achieve exponentially fast convergence. We also study
energy transfer rates among spatial scales to determine the relative importance
of the various nonlinear effects in the dynamo process and in the energy
cascade. The Hall effect produces a reduction of the direct energy cascade at
scales larger than the Hall scale, and therefore leads to smaller energy
dissipation rates. Finally, we present results stemming from simulations at
large magnetic Prandtl numbers, which is the relevant regime in hot and diffuse
media such a the interstellar medium.Comment: 11 pages and 11 figure
Stochastic Flux-Freezing and Magnetic Dynamo
We argue that magnetic flux-conservation in turbulent plasmas at high
magnetic Reynolds numbers neither holds in the conventional sense nor is
entirely broken, but instead is valid in a novel statistical sense associated
to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The
latter phenomenon is due to the explosive separation of particles undergoing
turbulent Richardson diffusion, which leads to a breakdown of Laplacian
determinism for classical dynamics. We discuss empirical evidence for
spontaneous stochasticity, including our own new numerical results. We then use
a Lagrangian path-integral approach to establish stochastic flux-freezing for
resistive hydromagnetic equations and to argue, based on the properties of
Richardson diffusion, that flux-conservation must remain stochastic at infinite
magnetic Reynolds number. As an important application of these results we
consider the kinematic, fluctuation dynamo in non-helical, incompressible
turbulence at unit magnetic Prandtl number. We present results on the
Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate
a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of
field-line motion is an essential ingredient of both. We finally consider
briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure
Is nonhelical hydromagnetic turbulence peaked at small scales?
Nonhelical hydromagnetic turbulence without an imposed magnetic field is
considered in the case where the magnetic Prandtl number is unity. The magnetic
field is entirely due to dynamo action. The magnetic energy spectrum peaks at a
wavenumber of about 5 times the minimum wavenumber in the domain, and not at
the resistive scale, as has previously been argued. Throughout the inertial
range the spectral magnetic energy exceeds the kinetic energy by a factor of
about 2.5, and both spectra are approximately parallel. At first glance, the
total energy spectrum seems to be close to k^{-3/2}, but there is a strong
bottleneck effect and it is suggested that the asymptotic spectrum is k^{-5/3}.
This is supported by the value of the second order structure function exponent
that is found to be \zeta_2=0.70, suggesting a k^{-1.70} spectrum.Comment: 6 pages, 6 figure
Self-similar turbulent dynamo
The amplification of magnetic fields in a highly conducting fluid is studied
numerically. During growth, the magnetic field is spatially intermittent: it
does not uniformly fill the volume, but is concentrated in long thin folded
structures. Contrary to a commonly held view, intermittency of the folded field
does not increase indefinitely throughout the growth stage if diffusion is
present. Instead, as we show, the probability-density function (PDF) of the
field strength becomes self-similar. The normalized moments increase with
magnetic Prandtl number in a powerlike fashion. We argue that the
self-similarity is to be expected with a finite flow scale and system size. In
the nonlinear saturated state, intermittency is reduced and the PDF is
exponential. Parallels are noted with self-similar behavior recently observed
for passive-scalar mixing and for map dynamos.Comment: revtex, 4 pages, 5 figures; minor changes to match published versio
Steady state existence of passive vector fields under the Kraichnan model
The steady state existence problem for Kraichnan advected passive vector
models is considered for isotropic and anisotropic initial values in arbitrary
dimension. The model includes the magnetohydrodynamic (MHD) equations, linear
pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition
to reproducing the previously known results for the MHD and linear pressure
model, we obtain the values of the Kraichnan model roughness parameter
for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction
Magnetic Field Amplification by Small-Scale Dynamo Action: Dependence on Turbulence Models and Reynolds and Prandtl Numbers
The small-scale dynamo is a process by which turbulent kinetic energy is
converted into magnetic energy, and thus is expected to depend crucially on the
nature of turbulence. In this work, we present a model for the small-scale
dynamo that takes into account the slope of the turbulent velocity spectrum
v(l) ~ l^theta, where l and v(l) are the size of a turbulent fluctuation and
the typical velocity on that scale. The time evolution of the fluctuation
component of the magnetic field, i.e., the small-scale field, is described by
the Kazantsev equation. We solve this linear differential equation for its
eigenvalues with the quantum-mechanical WKB-approximation. The validity of this
method is estimated as a function of the magnetic Prandtl number Pm. We
calculate the minimal magnetic Reynolds number for dynamo action, Rm_crit,
using our model of the turbulent velocity correlation function. For Kolmogorov
turbulence (theta=1/3), we find that the critical magnetic Reynolds number is
approximately 110 and for Burgers turbulence (theta=1/2) approximately 2700.
Furthermore, we derive that the growth rate of the small-scale magnetic field
for a general type of turbulence is Gamma ~ Re^((1-theta)/(1+theta)) in the
limit of infinite magnetic Prandtl numbers. For decreasing magnetic Prandtl
number (down to Pm approximately larger than 10), the growth rate of the
small-scale dynamo decreases. The details of this drop depend on the
WKB-approximation, which becomes invalid for a magnetic Prandtl number of about
unity.Comment: 13 pages, 8 figures; published in Phys. Rev. E 201
Reconnection in a Weakly Stochastic Field
We examine the effect of weak, small scale magnetic field structure on the
rate of reconnection in a strongly magnetized plasma. This affects the rate of
reconnection by reducing the transverse scale for reconnection flows, and by
allowing many independent flux reconnection events to occur simultaneously.
Allowing only for the first effect and using Goldreich and Sridhar's model of
strong turbulence in a magnetized plasma with negligible intermittency, we find
that the lower limit for the reconnection speed is the Alfven speed times the
Lundquist number to the power (-3/16). The upper limit on the reconnection
speed is typically a large fraction of Alfven speed. We argue that generic
reconnection in turbulent plasmas will normally occur at close to this upper
limit. The fraction of magnetic energy that goes directly into electron heating
scales as Lundquist number to the power (-2/5) and the thickness of the current
sheet scales as the Lundquist number to the power (-3/5). A significant
fraction of the magnetic energy goes into high frequency Alfven waves. We claim
that the qualitative sense of these conclusions, that reconnection is fast even
though current sheets are narrow, is almost independent of the local physics of
reconnection and the nature of the turbulent cascade. As the consequence of
this the Galactic and Solar dynamos are generically fast, i.e. do not depend on
the plasma resistivity.Comment: Extended version accepted to ApJ, 44pages, 2 figure
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