2,005 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
Nonlinear magneto-optical resonances at D1 excitation of 85Rb and 87Rb in an extremely thin cell
Nonlinear magneto-optical resonances have been measured in an extremely thin
cell (ETC) for the D1 transition of rubidium in an atomic vapor of natural
isotopic composition. All hyperfine transitions of both isotopes have been
studied for a wide range of laser power densities, laser detunings, and ETC
wall separations. Dark resonances in the laser induced fluorescence (LIF) were
observed as expected when the ground state total angular momentum F_g was
greater than or equal to the excited state total angular momentum F_e. Unlike
the case of ordinary cells, the width and contrast of dark resonances formed in
the ETC dramatically depended on the detuning of the laser from the exact
atomic transition. A theoretical model based on the optical Bloch equations was
applied to calculate the shapes of the resonance curves. The model averaged
over the contributions from different atomic velocity groups, considered all
neighboring hyperfine transitions, took into account the splitting and mixing
of magnetic sublevels in an external magnetic field, and included a detailed
treatment of the coherence properties of the laser radiation. Such a
theoretical approach had successfully described nonlinear magneto-optical
resonances in ordinary vapor cells. Although the values of certain model
parameters in the ETC differed significantly from the case of ordinary cells,
the same physical processes were used to model both cases. However, to describe
the resonances in the ETC, key parameters such as the transit relaxation rate
and Doppler width had to be modified in accordance with the ETC's unique
features. Agreement between the measured and calculated resonance curves was
satisfactory for the ETC, though not as good as in the case of ordinary cells.Comment: v2: substantial changes and expanded theoretical model; 13 pages, 10
figures; accepted for publication in Physical Review
Universal Nonlinear Small-Scale Dynamo
We consider astrophysically relevant nonlinear MHD dynamo at large Reynolds
numbers (Re). We argue that it is universal in a sense that magnetic energy
grows at a rate which is a constant fraction C_E of the total turbulent
dissipation rate. On the basis of locality bounds we claim that this
"efficiency of small-scale dynamo", C_E, is a true constant for large Re and is
determined only by strongly nonlinear dynamics at the equipartition scale. We
measured C_E in numerical simulations and observed a value around 0.05 in
highest resolution simulations. We address the issue of C_E being small, unlike
Kolmogorov constant which is of order unity.Comment: 4 pages 3 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
- …