Related papers: The role of curvature and stretching in dynamo pla…
Curvature and helicity topological bounds for the magnetic energy of the streamlines magnetic structures of a kinematic dynamo flow are computed. The existence of the filament dynamos are determined by solving the magnetohydrodynamic…
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…
Earlier Wang et al [Phys Plasmas (2002)] have estimated a growth rate for the magnetic field of ${\gamma}=0.055$ and flow ionization velocity of $51{km}/{s}$ in a laminar plasma slow dynamo mode for aspect ratio of ${r_{0}}/L\approx{0.6}$,…
We investigate the Lagrangian mechanism of the kinematic ``fluctuation'' magnetic dynamo in turbulent plasma flow at small magnetic Prandtl numbers. The combined effect of turbulent advection and plasma resistivity is to carry infinitely…
The nonlinear dynamo effect of tearing modes is derived with the resistive MHD equations. The dynamo effect is divided into two parts, parallel and perpendicular to the magnetic field. Firstly, the force-free plasma is considered. It is…
By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of turbulent dynamo, and study the dynamo process…
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…
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…
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…
Ricci and sectional curvatures of twisted flux tubes in Riemannian manifold are computed to investigate the stability of the tubes. The geodesic equations are used to show that in the case of thick tubes, the curvature of planar (Frenet…
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…
Previous attempts for building a cosmic dynamo including preheating in inflationary universes [Bassett et al Phys Rev (2001)] has not included mean field dynamos. Here, a mean field dynamo in cosmic scales on a Riemannian spatial…
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…
Recently Shukurov et al [Phys Rev \textbf{E} (2008)] presented a numerical solution of a Moebius strip dynamo flow, to investigate its use in modelling dynamo flows in Perm torus of liquid sodium dynamo experiments. Here, by analogy one…
Spectrum of kinematic fast dynamo operators in Ricci compressible flows in Einstein 2-manifolds is investigated. A similar expression, to the one obtained by Chicone, Latushkin and Montgomery-Smith (Comm Math Phys (1995)) is given, for the…
Kinney et al [PPL \textbf{1},(1994)] have investigated plasma filamentary structure dynamics. More recently, Wilkin et al [Phys Rev Lett \textbf{99}:134501,(2007)] have shown that kinetic energy spectrum of magnetic structures in…
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.…
Small-scale turbulent dynamo is responsible for the amplification of magnetic fields on scales smaller than the driving scale of turbulence in diverse astrophysical media. Most earlier dynamo theories concern the kinematic regime and…
Results from a numerical study of fluctuation dynamo in a collisionless, weakly magnetized plasma are presented. The key difference between this dynamo and its magnetohydrodynamic (MHD) counterpart is the adiabatic production of…
The Riemannian geometry of elastica in one and two dimensions is considered. An example is given of the deflexion or Frenet curvature of the elastic filament rod where the Riemannian curvature vanishes, since the curve is one dimensional.…