87,710 research outputs found
Lyapunov spectra in fast dynamo Ricci flows of negative sectional curvature
Previously Chicone, Latushkin and Montgomery-Smith [\textbf{Comm. Math. Phys.
\textbf{173},(1995)}] have investigated the spectrum of the dynamo operator for
an ideally conducting fluid. More recently, Tang and Boozer [{\textbf{Phys.
Plasmas (2000)}}], have investigated the anisotropies in magnetic field dynamo
evolution, from finite-time, Lyapunov exponents, giving rise to a Riemann
metric tensor, in the Alfven twist in magnetic flux tubes (MFTs). In this paper
one investigate the role of Perelman Ricci flows constraints in twisted
magnetic flux tubes, where the Lyapunov eigenvalue spectra for the Ricci tensor
associated with the Ricci flow equation in MFTs leads to a finite-time Lyapunov
exponential stretching along the toroidal direction of the tube and a
contraction along the radial direction of the tube. It is shown that in the
case of MFTs, the sectional Ricci curvature of the flow, is negative as happens
in geodesic flows of Anosov type. Ricci flows constraints in MFTs substitute
the Thiffeault and Boozer [\textbf{Chaos}(2001)] have vanishing of Riemann
curvature constraint on the Lyapunov exponential stretching of chaotic flows.
Gauss curvature of the twisted MFT is also computed and the contraints on a
negative Gauss curvature are obtained.Comment: Department of theoretical physics-UERJ-Brasi
A Riemannian geometrical method to classify tearing instabilities in plasmas
Riemannian geometrical tools, such as Ricci collineations and Killing
symmetries, so often used in Einstein general theory of gravitation are here
applied to plasma physics to build magnetic surfaces from Einstein plasma
metrics used in tokamak devices. It is shown that the Killing symmetries are
constrains the Einstein magnetic surfaces while the Killing vectors are built
in terms of the displacement of the toroidal surface. The pressure is computed
by applying these constraints to the pressure equations in tokamaks. A method,
based on the sign of the only nontrivial constant Riemann curvature component,
is suggested to classify tearing instability. Throughout the computations two
approximations are considered: The first is the small toroidality and the other
is the small displacement of the magnetic surfaces as Einstein spaces.Comment: Depto de Fisica de Teorica-if-uerj-rio-Brasi
Primordial magnetic fields of non-minimal photon-torsion axial coupling origin
Dynamo action is shown to be induced from homogeneous non-minimal
photon-torsion axial coupling in the quantum electrodynamics (QED) framework in
Riemann flat spacetime contortion decays. The geometrical optics in
Riemann-Cartan spacetime is considering and a plane wave expansion of the
electromagnetic vector potential is considered leading to a set of the
equations for the ray congruence. Since we are interested mainly on the torsion
effects in this first report we just consider the Riemann-flat case composed of
the Minkowskian spacetime with torsion. It is also shown that in torsionic de
Sitter background the vacuum polarisation does alter the propagation of
individual photons, an effect which is absent in Riemannian spaces. It is shown
that the cosmological torsion background inhomogeneities induce Lorentz
violation and massive photon modes in this QED. Magnetic dynamos in this
torsioned spacetime electrodynamics are simpler obtained in Fourier space than
the cosmic ones, previously obtained by Bassett et al Phys Rev D, in Friedmann
universe. By deriving plasma dispersion for linear electrodynamics in Riemann
Cartan spacetime, dynamo action seems to be possible for plasma frequencies in
some polarizations. The important cosmic magnetic field problem of breaking
conformal flatness is naturally solved here since the photon torsion coupling
breaks conformal flatness.Comment: depto de fisica teorica, if uerj, state rio de janeiro universit
Plasma torus dynamos versus laminar plasma dynamos
Earlier Wang et al [Phys Plasmas (2002)] have estimated a growth rate for the
magnetic field of and flow ionization velocity of
in a laminar plasma slow dynamo mode for aspect ratio of
, where is the internal straight cylinder
radius, and L is the length scale of the plasma cylinder. In this paper, fast
dynamo modes in curved Riemannian heliotron are shown to be excited on a plasma
flow yielding a growth rate of for an aspect ratio of
. It is interesting to note that the first growth rate
was obtained in the Wang et al slow dynamo, where the magnetic Reynolds number
of , while in the second one considered in this paper one uses the
limit of . These growth rates are computed by
applying the fast dynamo limit . This limit
is used in the self-induced equation, without the need to solve these equations
to investigate the fast dynamo action of the flow. In this sense the fast
dynamo seems to be excited by the elongation of the plasma device as suggested
by Wang group. The Frenet curvature of the tube is given by
. It is suggested that the small Perm torus
could be twisted [Dobler et al, Phys Rev E (2003)] in order to enhance even
more the fast dynamo effect. By considering the stability of the plasma torus
one obtains a value for the fast dynamo growth rate as high as
from a general expression and a toroidal oscillation of
a chaotic flow of .Comment: UER
Lagrangean stability of slow dynamos in compact 3D Riemannian manifolds
Modifications on a recently introduced fast dynamo operator by Chiconne et al
[Comm Math Phys 173, 379 (1995)] in compact 3D Riemannian manifolds allows us
to shown that slow dynamos are Lagrangean stable, in the sense that the
sectional curvature of the Riemann manifold vanishes. The stability of the
holonomic filament in this manifold will depend upon the sign of the second
derivative of the pressure along the filament and in the non-holonomic case, to
the normal pressure of the filament. Lagrangean instability is also
investigated in this case and again an dynamo operator can be defined in this
case. Negative curvature (Anosov flows) dynamos are also discussed in their
stability aspects.Comment: Departamento de Fisica Teorica-IF-UERJ-Brasi
Geodesic plasma flows instabilities of Riemann twisted solar loops
Riemann and sectional curvatures of magnetic twisted flux tubes in Riemannian
manifold are computed to investigate the stability of the plasma astrophysical
tubes. The geodesic equations are used to show that in the case of thick
magnetic tubes, the curvature of planar (Frenet torsion-free) tubes have the
effect ct of damping the flow speed along the tube. Stability of geodesic flows
in the Riemannian twisted thin tubes (almost filaments), against constant
radial perturbations is investigated by using the method of negative sectional
curvature for unstable flows. No special form of the flow like Beltrami flows
is admitted, and the proof is general for the case of thin magnetic flux tubes.
In the magnetic equilibrium state, the twist of the tube is shown to display
also a damping effect on the toroidal velocity of the plasma flow. It is found
that for positive perturbations and angular speed of the flow, instability is
achieved, since the sectional Ricci curvature of the magnetic twisted tube
metric is negative. Solar flare production may appear from these geometrical
instabilities of the twisted solar loops.Comment: Departamento de Fisica Teorica-IF-UERJ-Rio-Brasi
Riemannian and filamentary geometries..
Riemannian and filamentary geometries are used to investigate the stretched
filamentary dynamos against solar data in solar corona
Slow dynamos in Lorentz tori Anti-de Sitter spacetime embedded in Riemann 2D-space
Earlier Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have
shown that a fast dynamo in compact two-dimensional manifold can be supported
as long as its Riemannian curvature be negative. Recently Klebanov and
Maldacena [Phys Today (2008)] showed that a similar flat spacetime embedding of
a 2D negative Riemannian hyperbolic embedding in 2+1-D space-time, is achieved
by a coordinate transformation. This embedding is used here to obtain a flat
spacetime embedding of a slow dynamo in Riemannian 2D compact manifold of
negative constant curvature. In is shown that a slow dynamo appears in anti-de
Sitter space (AdS) Lorentz tori. This is in agreement with Bassett et al [Phys
Rev D (2001)] cosmic dynamo where suppression of resonance by universe
expansion slow dynamo action in comparison to preheating phases. Other example
of flat embeddings, which keeps some resamblance with AdS slow dynamo, is given
by the embedding of Moebius strip [Shukurov, Stepanov, Sokoloff, PRE (2008)] in
the laboratory
Dynamo action at recombination epoch of open Friedmann universe spatial sections
Chicone et al [Comm Math Phys (1997)] investigated existence of fast dynamos
by analyzing the spectrum kinematic magnetic dynamo. In real non-degenerate
branch of the spectrum, the kinematic dynamo operator lies on a compact
Riemannian 2D space of constant negative curvature. Here, generalization of
Marklund and Clarkson [MNRAS (2005)], general relativistic GR-MHD dynamo
equation to include mean-field dynamos is obtained. In the absence of kinetic
helicity, adiabatic constant and gravitational colapse of
negative Riemann curvature of spatial sections enhance dynamo effect
. Critical time where linear dynamo
effects breaks down de to curvature. At recombination time, COBE temperature
anisotropies, implies that magnetic field growth rate is
. This places a bound on curvature till the
recombination magnetic field is amplified to present value of ,
by dynamo action. At present epoch, negative curvature becomes constant and the
Chicone et al result is shown to be valid in cosmology. Since negative
curvature is non-constant, Hilbert theorem which forbiddes negative constant
curvature surfaces embeddeding in is bypassed.Comment: DFT uerj Brasi
Geodesic dynamo chaotic flows and non-Anosov maps in twisted magnetic flux tubes
Recently Tang and Boozer [{\textbf{Phys. Plasmas (2000)}}], have investigated
the anisotropies in magnetic field dynamo evolution, from local Lyapunov
exponents, giving rise to a metric tensor, in the Alfven twist in magnetic flux
tubes (MFTs). Thiffeault and Boozer [\textbf{Chaos}(2001)] have investigated
the how the vanishing of Riemann curvature constrained the Lyapunov exponential
stretching of chaotic flows. In this paper, Tang-Boozer-Thiffeault differential
geometric framework is used to investigate effects of twisted magnetic flux
tube filled with helical chaotic flows on the Riemann curvature tensor. When
Frenet torsion is positive, the Riemann curvature is unstable, while the
negative torsion induces an stability when time . This enhances
the dynamo action inside the MFTs. The Riemann metric, depends on the radial
random flows along the poloidal and toroidal directions. The Anosov flows has
been applied by Arnold, Zeldovich, Ruzmaikin and Sokoloff [\textbf{JETP
(1982)}] to build a uniformly stretched dynamo flow solution, based on Arnold's
Cat Map. It is easy to show that when the random radial flow vanishes, the
magnetic field vanishes, since the exponential Lyapunov stretches vanishes.
This is an example of the application of the Vishik's anti-fast dynamo theorem
in the magnetic flux tubes. Geodesic flows of both Arnold and twisted MFT
dynamos are investigated. It is shown that a constant random radial flow can be
obtained from the geodesic equation. Throughout the paper one assumes, the
reasonable plasma astrophysical hypothesis of the weak torsion. Pseudo-Anosov
dynamo flows and maps have also been addressed by Gilbert [\textbf{Proc Roy Soc
A London (1993)}Comment: Departamento de Fisica Teorica-IF-UERJ-Rio de Janeiro-Brasi
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