The Dependence of Dynamo α\alpha-Effect on Reynolds Numbers, Magnetic Prandtl Number, and the Statistics of MHD Turbulence

We generalize the derivation of dynamo coefficient $\alpha$ of Field et al (1999) to include the following two aspects: first, the de-correlation times of velocity field and magnetic field are different; second, the magnetic Prandtl number can be arbitrary. We find that the contributions of velocity field and magnetic field to the $\alpha$ effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds number and large magnetic Reynolds number, $\alpha$-coefficient may not be small if the de-correlation times of velocity field and magnetic field are shorter than the eddy turn-over time of the MHD turbulence. We also show that under certain circumstances, for example if the kinetic helicity and current helicity are comparable, $\alpha$ depends insensitively on magnetic Prandtl number, while if either the kinetic helicity or the current helicity is dominated by the other one, a different magnetic Prandtl number will significantly change the dynamo $\alpha$ effect.Comment: 44 pages, 4 figures, to appear in ApJ (vol. 552

Jupiter's magnetosphere

Magnetosphere, ionosphere, and thermal radiation of planet Jupite

Electrodynamic effects of Jupiter's satellite Io

Electrodynamic effects of Jupiters satellite I

The magnetospheric radiation belt and tail plasma sheet

Magnetospheric radiation belt and tail plasma shee

Nonlinear Alpha Effect in Dynamo Theory

We extend the standard two-scale theory of the turbulent dynamo coefficient $\alpha$ to include the nonlinear back reaction of the mean field $\bar B$ on the turbulence. We calculate the turbulent emf as a power series in $\bar B$, assuming that the base state of the turbulence ($\bar B=0$) is isotropic, and, for simplicity, that the magnetic diffusivity equals the kinematic viscosity. The power series converges for all $\bar B$, and for the special case that the spectrum of the turbulence is sharply peaked in $k$, our result is proportional to a tabulated function of the magnetic Reynolds number $R_M$ and the ratio $\beta$ of $\bar B$ (in velocity units) to the rms turbulent velocity $v_0$. For $\beta\to 0$ (linear regime) we recover the results of Steenbeck et al. (1966) as modified by Pouquet et al. (1976). For $R_M\gg 1$, the usual astrophysical case, $\alpha$ starts to decrease at $\beta \sim 1$, dropping like $\beta^{-2}$ as $\beta \to \infty$. Hence for large $R_M$, $\alpha$ saturates at $\bar B\sim v_0$, as estimated by Kraichnan (1979), rather than at $\bar B\sim R^{-1/2}_Mv_0$, as inferred by Cattaneo and Hughes (1996) from their numerical simulations at $R_M$=100. We plan to carry out simulations with various values of $R_M$ to investigate the discrepency.Comment: 41 pages, 1 Postscript figure, accepted for publication to Ap

Discussion of the Electromotive Force Terms in the Model of Parker-unstable Galactic Disks with Cosmic Rays and Shear

We analyze the electromotive force (EMF) terms and basic assumptions of the linear and nonlinear dynamo theories in our three-dimensional (3D) numerical model of the Parker instability with cosmic rays and shear in a galactic disk. We also apply the well known prescriptions of the EMF obtained by the nonlinear dynamo theory (Blackman & Field 2002 and Kleeorin et al. 2003) to check if the EMF reconstructed from their prescriptions corresponds to the EMF obtained directly from our numerical models. We show that our modeled EMF is fully nonlinear and it is not possible to apply any of the considered nonlinear dynamo approximations due to the fact that the conditions for the scale separation are not fulfilled.Comment: 15 pages, 12 figure

B polarization of the CMB from Faraday rotation

We study the effect of Faraday rotation due to a homogeneous magnetic field on the polarization of the cosmic microwave background (CMB). Scalar fluctuations give rise only to parity-even E-type polarization of the CMB. However in the presence of a magnetic field, a non-vanishing parity-odd B-type polarization component is produced through Faraday rotation. We derive the exact solution for the E and B modes generated by scalar perturbations including the Faraday rotation effect of a uniform magnetic field, and evaluate their cross-correlations with temperature anisotropies. We compute the angular autocorrelation function of the B-modes in the limit that the Faraday rotation is small. We find that primordial magnetic fields of present strength around $B_0=10^{-9}$G rotate E-modes into B-modes with amplitude comparable to those due to the weak gravitational lensing effect at frequencies around $\nu=30$ GHz. The strength of B-modes produced by Faraday rotation scales as $B_0/\nu^2$. We evaluate also the depolarizing effect of Faraday rotation upon the cross correlation between temperature anisotropy and E-type polarization.Comment: 11 pages, 4 figures. Minor changes to match the published versio

Generation of Cosmological Seed Magnetic Fields from Inflation with Cutoff

Inflation has the potential to seed the galactic magnetic fields observed today. However, there is an obstacle to the amplification of the quantum fluctuations of the electromagnetic field during inflation: namely the conformal invariance of electromagnetic theory on a conformally flat underlying geometry. As the existence of a preferred minimal length breaks the conformal invariance of the background geometry, it is plausible that this effect could generate some electromagnetic field amplification. We show that this scenario is equivalent to endowing the photon with a large negative mass during inflation. This effective mass is negligibly small in a radiation and matter dominated universe. Depending on the value of the free parameter of the theory, we show that the seed required by the dynamo mechanism can be generated. We also show that this mechanism can produce the requisite galactic magnetic field without resorting to a dynamo mechanism.Comment: Latex, 16 pages, 2 figures, 4 references added, minor corrections; v4: more references added, boundary term written in a covariant form, discussion regarding other gauge fields added, submitted to PRD; v5: matched with the published versio

Emergence of a Twisted Magnetic Flux Bundle as a Source of Strong Flare Activity

Sunspot proper motions and flares of a super active region NOAA 5395, which was the biggest and the most flare-active region in the 22nd sunspot cycle, were analyzed in details. We measured sunspot proper motions by using the H-alpha - 5.0 A images obtained with the 60-cm Domeless Solar Telescope (DST) at Hida Observatory, Kyoto University and found some peculiar vortex-like motions of small satellite spots successively emerged from the leading edge of this sunspot group. To explain these motions of small sunspots, we proposed a schematic model of the successive emergence of twisted and winding magnetic flux ropes coiling around a trunk of magnetic flux tube. The location of the strongest flare activity was found to coincide with very the site of the vortex-like motions of sunspots. We conclude that the flare-productive magnetic shear is produced by the emergence of the twisted magnetic flux bundle. Magnetic energy is stored in the twisted flux tubes which are originally formed in the convection zone and released as flares in the course of the emergence of the twisted flux tubes above the photosphere.Comment: 19 pages LaTeX, 8 figures, ApJ accepted high resolution figures : e-mail to [email protected]

On a mechanism for enhancing magnetic activity in tidally interacting binaries

We suggest a mechanism for enhancing magnetic activity in tidally interacting binaries. We suppose that the deviation of the primary star from spherical symmetry due to the tidal influence of the companion leads to stellar pulsation in its fundamental mode. It is shown that stellar radial pulsation amplifies torsional Alfv{\'e}n waves in a dipole-like magnetic field, buried in the interior, according to the recently proposed swing wave-wave interaction (Zaqarashvili 2001). Then amplified Alfv{\'e}n waves lead to the onset of large-scale torsional oscillations, and magnetic flux tubes arising towards the surface owing to magnetic buoyancy diffuse into the atmosphere producing enhanced chromospheric and coronal emission.Comment: Accepted in Ap