arXiv subjects

Garcia de Andrade

Publications and source records attributed to Garcia de Andrade.

At least 37 records · Page 2Linked to original sources

arXiv2009

Cosmic dynamo analogue and decay of magnetic fields in 3D Ricci flows

Magnetic curvature effects, investigated by Barrow and Tsagas (BT) [Phys Rev D \textbf{77},(2008)],as a mechanism for magnetic field decay in open Friedmann universes ($Λ<0$), are applied to dynamo geometric Ricci flows in 3D curved substrate in laboratory. By simple derivation, a covariant three-dimensional magnetic self-induced equation, presence of these curvature effects, indicates that de Sitter cosmological constant ($Λ\ge{0}$), leads to enhancement in the fast kinematic dynamo action which adds to stretching of plasma flows. From the magnetic growth rate, the strong shear case, anti-de Sitter case ($Λ<0$) BT magnetic decaying fields are possible while for weak shear, fast dynamos are possible. The self-induced equation in Ricci flows is similar to the equation derived by BT in $(3+1)$-spacetime continuum. Lyapunov-de Sitter metric is obtained from Ricci flow eigenvalue problem. In de Sitter analogue there is a decay rate of $γ\approx{-Λ}\approx{-10^{-35}s^{-2}}$ from corresponding cosmological constant $Λ$, showing that, even in the dynamo case, magnetic field growth is slower than de Sitter inflation, which strongly supports to BT result.

gr-qc↗

arXiv2009

Ricci dynamo stretch-shear plasma flows and magnetic energy bounds

Geometrical tools, used in Einstein's general relativity (GR), are applied to dynamo theory, in order to obtain fast dynamo action bounds to magnetic energy, from Killing symmetries in Ricci flows. Magnetic field is shown to be the shear flow tensor eigendirection, in the case of marginal dynamos. Killing symmetries of the Riemann metric, bounded by Einstein space, allows us to reduce the computations. Techniques used are similar to those strain decomposition of the flow in Sobolev space, recently used by Nuñez [JMP \textbf{43} (2002)] to place bounds in the magnetic energy in the case of hydromagnetic dynamos with plasma resistivity. Contrary to Nuñez case, we assume that the dynamos are kinematic, and the velocity flow gradient is decomposed into expansion, shear and twist. The effective twist vanishes by considering that the frame vorticity coincides with Ricci rotation coefficients. Eigenvalues are here Lyapunov exponents. In analogy to GR, where curvature plays the role of gravity, here Ricci curvature seems to play the role of diffusion.

math-ph↗

arXiv2009

Stretch-Twist-Fold and slow filamentary dynamos in liquid sodium Madison Dynamo Experiments

Recently Ricca and Maggione [MHD (2008)] have presented a very simple and interesting model of stretch-twist-fold dynamo in diffusive media based on numerical simulations of Riemannian flux tubes. In this paper we present a yet simpler way of analytically obtaining fast and slow dynamo, generated by by the curvature energy of magnetic filaments in diffusive media. geometrical model for the galactic or accretion disk dynamo in shear flows is presented. In the fast dynamo case it is shown that the absence of stretching leads to the absence of fast dynamos and when torsion of filaments vanishes the dynamo action cannot be support as well. This is the Cowling-Zeldovich theorem for planar flows. Isotropy of the magnetic fields hypothesis is used to compute the fast nature of dynamo. A similar result using non-holonomic Frenet frame has been recently obtained for filamentary dynamos [Garcia de Andrade, AN (2008)]. The stretch-twist-fold (STF) filamented models discussed here may serve to formulate future experiments in the Madison Dynamo Experiment (MDE) facility [Nornberg et al, Phys Plasmas (2008)]. Though their running experiments deal with magnetic fields that are orthogonal to the flow, other topologies are also used here, with an eye in future experiments. Unstretched filaments in MDE shows Vishik anti-fast dynamo action applies [Garcia de Andrade[Phys Plasmas (2008)].

physics.flu-dyn↗

arXiv2009

Slow dynamo modes in compact Riemannian plasma devices from Brazilian spherical tokamak data

Anti-dynamo modes are usually found in spheromaks plasma devices experiments due to the fact that Cowling anti-dynamo theorem is naturally applied to axisymmetric devices and flows. In this paper full consideration is given to the existence of slow dynamo modes in the case of compact Riemannian plasma devices without boundaries, such as tokamaks, stellarators and torsatrons. It is shown that a perturbed untwisted flow given by a decaying mode magnetic field is able to generate a slow twisted dynamo plasma flow where the unperturbed flow is also a steady flow. When the slow dynamo limit is obtained for high Reynolds magnetic numbers $Rm$, the unperturbed plasma flow achieve equilibrium as in spheromaks. The data of aspect ratio and other data obtained from the Brazilian spherical tokamak at the National institute for space research are used to obtain a numerical estimate for the maximum magnetic growth rate of the magnetic field of the slow dynamo action as $γ_{1max}\approx{\frac{0.26}{a}{\times}\frac{v_{1θ}}{B_{1s}}}$ for a toroidal initial magnetic field $B_{0}\approx{0.4T}$ and an aspect data tokamak of 1.5. For a tokamak internal radius of $a\approx{0.2m}$ one obtains a maximum growth rate for the slow dynamo as $γ_{1max}\approx{1.3{\times}\frac{v_{1θ}}{B_{1s}}}$, where $v_{1θ}$ is the poloidal perturbed diffusive flow. The safety factor is given by $q\approx{-1}$ which is $q<1$ implying stability of spherical tokamak plasma.

physics.plasm-ph↗

arXiv2009

Dynamo experiments in torsioned toroidal devices

Recently Shukurov, Stepanov and Sokoloff [\textbf{Phys. Rev. E 69 (2008)}] have suggested that Moebius flows can support dynamo action. In this report, it is shown that a steady perturbation of a magnetic field in a general twisted Riemannian flux tube may support dynamo action. Instead of the twist number used in the above reference, the focus here is on the Frenet torsion of the magnetic flux tube. A relation between the constant torsion of the screw dynamo torus, its internal radius, and the ratio between toroidal and poloidal flow. Solution of self-induction equation for the screw dynamo torsioned flow, can be solved to yield a Frenet torsion as high as $τ_{0}\approx{7.5{\times}Ω^θHz^{-1}m^{-1}}$, for an applied random magnetic field of $ \approx{45 G}$ for an induced steady perturbation of $B_{1}\approx{0.03G}$, as in the Perm Riemannian torus experiment. The Moebius strip plays the role of the propeller divertor which imprints the angular velocity $Ω^θ$, around the torus axis, to the dynamo flow, here this role is played by torsion. Actually this situation is already familiar to plasma physicists, where in stellarators torsion substitutes very well the role played by external magnetic fields in tokamaks making magnetic fields twist along plasma toroidal devices. Weak torsion of the torus channel is assumed.

physics.flu-dyn↗

arXiv2009

Slow dynamos and decay of monopole magnetic fields in the early Universe

Previously Liao and Shuryak [\textbf{Phys. Rev C (2008)}] have investigated electrical flux tubes in monopole plasmas, where magnetic fields are non-solenoidal in quark-QCD plasmas. In this paper slow dynamos in diffusive plasma [{\textbf{Phys. Plasmas \textbf{15} (2008)}}] filaments (thin tubes) are obtained in the case of monopole plasmas. In the absence of diffusion the magnetic field decays in the Early Universe. The torsion is highly chaotic in dissipative large scale dynamos in the presence of magnetic monopoles. The magnetic field is given by the Heaviside step function in order to represent the non-uniform stretching of the dynamo filament. These results are obtained outside the junction condition. Stringent limits to the monopole flux were found by Lewis et al [\textbf{Phys Rev D (2000)}] by using the dispute between the dynamo action and monopole flux. Since magnetic monopoles flow dispute the dynamo action, it seems reasonable that their presence leads to a slow dynamo action in the best hypothesis or a decay of the magnetic field. Hindmarsh et al have computed the magnetic energy decay in the early universe as ${E}_{M}\approx{t^{-0.5}}$, while in our slow dynamo case linearization of the growth rate leads to a variation od magnetic energy of $δ{E}_{M}\approx{t}$, due to the presence of magnetic monopoles. Da Rios equations of vortex filaments are used to place constraints on the geometry of monopole plasma filaments.

astro-ph.CO↗

arXiv2008

Lyapunov spectra instability of chaotic dynamo Ricci flows in twisted magnetic flux tubes

Previously Casetti, Clementi and Pettini [\textbf{Phys.Rev.E \textbf{54},6,(1996)}] have investigated the Lyapunov spectrum of Hamiltonian flows for several Hamiltonian systems by making use of the Riemannian geometry. Basically the Lyapunov stability analysis was substituted by the Ricci sectional curvature analysis. In this report we apply Pettini's geometrical framework to determine the potential energy of a twisted magnetic flux tube, from its curved Riemannian geometry. Actually the Lyapunov exponents, are connected to a Riemann metric tensor, of the twisted magnetic flux tubes (MFTs). The Hamiltonian flow inside the tube is actually given by 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. The Jacobi equation for the MFTs is shown to have a constant sectional Ricci curvature which allows us to compute the Jacobi-Levi-Civita (JLC) geodesic deviation for the spread of lines on the tube manifold and chaotic action through the greatest of its Lyapunov exponents. By analyzing the spectra of the twisted MFT, it is shown that the greater exponent is positive and proportional to the random radial flow of the tube, which allows the onset of chaos is guaranted. The randomness in the twisted flow reminds a discussed here is similar of a recent work by Shukurov, Stepanov, and Sokoloff on dynamo action on Moebius flow [\textbf{Phys Rev E 78 (2008)}]. The dynamo action in twisted flux tubes discussed here may also serve as model for dynamo experiments in laboratory.

physics.flu-dyn↗

arXiv2008

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.

math-ph↗

arXiv2008

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 $t\to{\infty}$. 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)}

math-ph↗

arXiv2008

Stretch-Twist torus dynamo in compact Riemannian manifolds

Earlier Arnold, Zeldovich, Ruzmaikin and Sokoloff [\textbf{JETP (1982)}] have computed the eigenvalue of a uniform stretching torus transformation which result on the first Riemann metric solution of the dynamo action problem. Recently some other attempts to obtain Riemann metrics representing dynamo action through conformal maps have been undertaken [{\textbf{Phys. Plasmas 14 (2007)}]. Earlier, Gilbert [\textbf{Proc. Roy. Soc. London A(2003)}] has investigated a more realistic dynamo map solution than the one presented by Arnold et al by producing a shearing of the Arnold's cat map, by eigenvalue problem of a dynamo operator. In this paper, the eigenvalue of the Riemann twisted torus dynamo flow metric is obtained as the ratio between the poloidal and toroidal components of the flow. This result is obtained from the Euler equation. In the twisted torus, the eigenvalue of the Riemann metric is ${m}_{\pm}=\frac{1\pm{\sqrt{5}}}{2}$, which is quite close to the value obtained by Arnold. In the case the viscosity Reynolds number $Re\to{\infty}$, the torus flow is unstable as one approaches the torus axis. In Arnold's dynamo metric the eigenvalues are $χ_{\pm}=\frac{3\pm{\sqrt{5}}}{2}$ which are very close to the above value. Eigenvalues determine the growth rates of the velocity ratio between poloidal and toroidal components of the flow. The curved flow in torus follow previous work by Chen et al [\textbf{Phys Fluids (2006)}]. The $α$-effect dynamo is shown to be a second-order effect in the torus curvature and velocity flow. Loop dynamo flows and maps are also discussed.

math-ph↗

arXiv2008

Conformal maps in periodic flows and in suppression of stretch-twist and fold on Riemannian manifolds

Examples of conformal dynamo maps have been presented earlier [Phys Plasmas \textbf{14}(2007)] where fast dynamos in twisted magnetic flux tubes in Riemannian manifolds were obtained. This paper shows that conformal maps, under the Floquet condition, leads to coincidence between exponential stretching or Lyapunov exponent, conformal factor of fast dynamos. Unfolding conformal dynamo maps can be obtained in Riemann-flat manifolds since here, Riemann curvature plays the role of folding. Previously, Oseledts [Geophys Astrophys Fluid Dyn \textbf{73} (1993)] has shown that the number of twisted and untwisting orbits in a two torus on a compact Riemannian manifold induces a growth of fast dynamo action. In this paper, the stretching of conformal thin magnetic flux tubes is constrained to vanish, in order to obtain the conformal factor for non-stretching non-dynamos. Since thin flux tube can be considered as a twisted or untwisting two-torus map, it is shown that the untwisting, weakly torsion, and non-stretching conformal torus map cannot support a fast dynamo action, a marginal dynamo being obtained. This is an example of an anti-fast dynamo theorem besides the ones given by Vishik and Klapper and Young [Comm Math Phys \textbf{173}(1996)] in ideally high conductive flow. From the Riemann curvature tensor it is shown that new conformal non-dynamo, is actually singular as one approaches the magnetic flux tube axis. Thus conformal map suppresses the stretching directions and twist, leading to the absence of fast dynamo action while Riemann-flat unfolding manifolds favors non-fast dynamos.

math-ph↗

arXiv2008

Plasma torus dynamos versus laminar plasma dynamos

Earlier Wang et al [Phys Plasmas (2002)] have estimated a growth rate for the magnetic field of $γ=0.055$ and flow ionization velocity of $51{km}/{s}$ in a laminar plasma slow dynamo mode for aspect ratio of ${r_{0}}/L\approx{0.6}$, where $r_{0}$ 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 $γ=0.318$ for an aspect ratio of ${r_{0}}/L\approx{0.16}$. 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 $Re_{m}=210$, while in the second one considered in this paper one uses the limit of $Re_{m}\to{\infty}$. These growth rates $γ$ are computed by applying the fast dynamo limit $lim_{η\to{0}}γ(η)>0$. 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 $κ_{0}\approx{0.5 m^{-1}}$. 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 $γ=1.712$ from a general expression $γ=0.16ω$ and a toroidal oscillation of a chaotic flow of $ω=\frac{2π}{6}$.

physics.plasm-ph↗

arXiv2008

The role of curvature and stretching in dynamo plasmas

Vishik's antidynamo theorem is applied to non-stretched twisted magnetic flux tube in Riemannian space. Marginal or slow dynamos along curved (folded), torsioned (twisted) and non-stretching flux tubes plasma flows are obtained}. Riemannian curvature of twisted magnetic flux tube is computed in terms of the Frenet curvature in the thin tube limit. It is shown that, for non-stretched filaments fast dynamo action in diffusive case cannot be obtained, in agreement with Vishik's argument, that fast dynamo cannot be obtained in non-stretched flows. \textbf{In this case a non-uniform stretching slow dynamo is obtained}.\textbf{An example is given which generalizes plasma dynamo laminar flows, recently presented by Wang et al [Phys Plasmas (2002)], in the case of low magnetic Reynolds number $Re_{m}\ge{210}$. Curved and twisting Riemannian heliotrons, where non-dynamo modes are found even when stretching is presented, shows that the simple presence of stretching is not enough for the existence of dynamo action. Folding is equivalent to Riemann curvature and can be used to cancell magnetic fields, not enhancing the dynamo action. In this case non-dynamo modes are found for certain values of torsion or Frenet curvature (folding) in the spirit of anti-dynamo theorem. It is shown that curvature and stretching are fundamental for the existence of fast dynamos in plasmas.

math-ph↗

arXiv2008

Acoustic black hole evaporation as plasma diffusion phenomena

Acoustic analogues of Kerr black hole in plasmas are considered, by taking for granted the existence of acoustic ion waves in plasmas. An effective black holes (BH) in curved Riemannian spacetime in a random walk plasmas is endowed with a naked singularity, when plasmas are in the lowest diffusion mode. The plasma particle diffusion is encoded in the effective metric. The diffusive solution has a horizon when the plasma flow reaches the sound velocity in the medium and a shock wave is obtained inside the slab. The sonic black hole curved Riemannian metric is also found in terms of particle number density in plasmas. The sonic BH singularity is found at the center of the plasma diffusive slab from the study of the Ricci curvature scalar for constant diffusion coefficient. It is suggested and shown that the Hawking temperature is proportional to the plasma Kelvin temperature through diffusion coefficient dependence to this temperature. Therefore Unruh sonic or dumb BH is shown to have a relation between Hawking and plasma diffusive temperatures. BH evaporation is analogous to the diffusive phenomena in plasmas, since in both cases Hawking temperature is inversely proportional to mass. It is shown that Hawking analogue temperature of a plasma torus is $T_{H}(torus)\approx{10^{-4}K}$ which is much higher than the gravitational Hawking temperature of a one solar mass BH, ${T_{H}}^{GR}\approx{10^{-8}K}$, but still very small for being detectable in plasma laboratories.

gr-qc↗

arXiv2008

Kerr-Schild Riemannian acoustic black holes in dynamo plasma laboratory

Since Alfven, dynamo and sound waves and the existence of general relativistic black holes are well stablished in plasma physics, this provides enough motivation to investigate the presence of acoustic black-hole effective metric of analogue Einstein's gravity in dynamo flows. From nonlinear dynamo equations, one obtains a non-homogeneous wave equation where it is shown that the non-homogeneous factor is proportional to time evolution of the compressibility factor. In the Navier-Stokes case for a finite Reynolds number the acoustic black-holes also exists on the stretching plasma flows. In the magnetostatic case the dynamo is marginal. Analog models are usually applied to a superfluid analog spacetime, instead of the plasma setting used here. A coupled nonlinear plasma flow solution is found for the dynamo equation where the effective black hole solution of the scalar effective equation yields an imaginary part of the growth of magnetic field. Therefore though the real part of the growth rate of the magnetic field is negative or null, since there is a temporal oscillation in magnetic field, the solution represents a slow dynamo. Thus acoustic black holes are shown to definitely contribute to dynamo action of the effective plasma spacetime. It is suggested that a fast dynamo effective spacetime may also contain an acoustic black hole. I the case of planar waves the effective metric can be cast in Kerr-Schild spacetime form. The Killing symmetries are explicitly given in this metric and the growth of dynamo waves.

gr-qc↗

arXiv2008

Effective black holes from non-Riemannian vortex acoustics in ABC flows

gr-qc↗

arXiv2008

Exponential stretching in filaments as fast dynamos in Euclidean and Riemannian 3D spaces

A new antidynamo theorem for non-stretched twisted magnetic flux tube dynamo is obtained. Though Riemannian curvature cannot be neglected since one considers curved magnetic flux tube axis, the stretch can be neglect since one only considers the limit of thin magnetic flux tubes. The theorem states that marginal or slow dynamos along curved (folded), torsioned (twisted) and non-stretched flux tubes endowed with diffusionless plasma flows, if a constraint is imposed on the relation between poloidal and toroidal magnetic fields in the helical dynamo case. A formula for the stretch of flux tubes is derived. From this formula one shows that the Riemann flux tube is stretched by an interaction between the plasma flow vorticity and torsion, in accordance with our physical intuition. Marginal diffusionless dynamos are shown to exist obtained in the case of flux tube dynamos exponential stretching. Thus slow dynamos can be obtaining on the flux tube under stretching. Filamentary dynamos anti-dynamos are also considered. As flux tubes possess a magnetic axis torsioned filament, it can also be considered as thegerm of a fast dynamo in flux tubes Riemannian curved space. It is shown that for non-stretched filaments only untwist and unfold filaments can provide dynamo action in diffusive case. A condition for exponential stretching and fast dynamos in filaments is given. These results are actually in agreement with Vishik argument that fast dynamo cannot be obtained in non-stretched flows. Actually the flux tube result is the converse of Vishik's lemma.

astro-ph↗

arXiv2008

Stretching Riemannian spherical solar dynamo model from differentia rotation

Stretching solar dynamos from differential rotation in a Riemannian manifold setting is presented. The spherical model follows closely a twisted magnetic flux tube Riemannian geometrical model or flux rope in solar physics, presented previously by Ricca [Solar Physics (1997)]. The spherical model presented here present new and interesting feature concerning its connection with spherical steady solar dynamos. One of this new feature is represented by the fact that the by considering poloidal magnetic field component much weaker than its toroidal counterpart, one obtains a stretch dynamo action where the Riemannian solar spherical line element is proportional to differential rotation. This result is obtained also by using the Vainshtein-Zeldovich stretch, twist and fold (STF) method to generate dynamos. One notes that for high magnetic Reynolds of $R{m}=O({10^{7}})$ the dynamo action is present for a corresponding small stretching factor of $K^{2}=1.6$ where $K^{2}=1$ represents the unstretched dynamo. The constant stretched dynamos considered here are shown to be Riemann-flat, where the Riemann curvature tensor vanishes. Solar cycle dynamos are therefore compatible with the Riemann-flat stretching dynamo model from solar differential rotation presented here.

astro-ph↗