Back Reaction to the Spectrum of Magnetic Field in the Kinetic Dynamo Theory --- Modified Kulsrud and Anderson Equation ---

We take account of the lowest order back reaction on the fluid and modify the Kulsrud and Anderson equation $\partial_t{\cal E}_M= 2 \gamma {\cal E}_M$ obtained in the kinetic dynamo theory, where ${\cal E}_M$ is the energy density of the magnetic field. Furthermore, we apply our present result to some astrophysical stages where the magnetic field is expected to be amplified by the dynamo mechanism.Comment: 9 pages, LaTex, to appear in Prog. Theor. Phy

A Numerical Simulation of the Reconnection Layer in 2D Resistive MHD

In this paper we present a two-dimensional, time dependent, numerical simulation of a reconnection current layer in incompressible resistive magnetohydrodynamics with uniform resistivity in the limit of very large Lundquist numbers. We use realistic boundary conditions derived consistently from the outside magnetic field, and we also take into account the effect of the back pressure from flow into the the separatrix region. We find that within a few Alfven times the system evolves from an arbitrary initial state to a steady state consistent with the Sweet--Parker model, even if the initial state is Petschek-like.Comment: 33 pages, 17 figure

Small-scale microwave background anisotropies due to tangled primordial magnetic fields

An inhomogeneous cosmological magnetic field creates vortical perturbations that survive Silk damping on much smaller scales than compressional modes. This ensures that there is no sharp cut-off in anisotropy on arc-minute scales. As we had pointed out earlier, tangled magnetic fields, if they exist, will then be a potentially important contributor to small-angular scale CMBR anisotropies. Several ongoing and new experiments, are expected to probe the very small angular scales, corresponding to multipoles with l>1000. In view of this observational focus, we revisit the predicted signals due to primordial tangled magnetic fields, for different spectra and different cosmological parameters. We also identify a new regime, where the photon mean-free path exceeds the scale of the perturbation, which dominates the predicted signal at very high l. A scale-invariant spectrum of tangled fields which redshifts to a present value B_{0}=3\times 10^{-9} Gauss, produces temperature anisotropies at the 10 micro Kelvin level between l ~ 1000-3000. Larger signals result if the univese is lambda dominated, if the baryon density is larger, or if the spectral index of magnetic tangles is steeper, n > -3. The signal will also have non-Gaussian statistics. We predict the distinctive form of the increased power expected in the microwave background at high l in the presence of significant tangled magnetic fields. We may be on the verge of detecting or ruling out the presence of tangled magnetic fields which are strong enough to influence the formation of large-scale structure in the Universe.Comment: 5 pages, 2 figures, submitted to MNRAS Letter

Magnetic reconnection with anomalous resistivity in two-and-a-half dimensions I: Quasi-stationary case

In this paper quasi-stationary, two-and-a-half-dimensional magnetic reconnection is studied in the framework of incompressible resistive magnetohydrodynamics (MHD). A new theoretical approach for calculation of the reconnection rate is presented. This approach is based on local analytical derivations in a thin reconnection layer, and it is applicable to the case when resistivity is anomalous and is an arbitrary function of the electric current and the spatial coordinates. It is found that a quasi-stationary reconnection rate is fully determined by a particular functional form of the anomalous resistivity and by the local configuration of the magnetic field just outside the reconnection layer. It is also found that in the special case of constant resistivity reconnection is Sweet-Parker and not Petschek.Comment: 15 pages, 4 figures, minor changes as compared to the 1st versio

Characteristic Lengths of Magnetic Field in Magnetohydrodynamic Turbulence

In the framework of turbulence dynamo, flow motions amplify a weak seed magnetic field through the stretching of field lines. Although the amplification process has been a topic of active research, less attention has been paid to the length scales of magnetic field. In this paper, we described a numerical study on characteristic lengths of magnetic field in magnetohydrodynamic turbulence. We considered the case of very weak or zero mean magnetic field, which is applicable to the turbulence in the intergalactic space. Our findings are as follows. (1) At saturation, the peak of magnetic field spectrum occurs at $\sim L_0/2$, where $L_0$ is the energy injection scale, while the most energy containing scale is $\sim L_0/5$. The peak scale of spectrum of projected, two-dimensional field is $\sim L_0$. (2) During the stage of magnetic field amplification, the energy equipartition scale shows a power-law increase of $\sim t^{1.5}$, while the integral and curvature scales show a linear increase. The equipartition, integral, and curvature scales saturate at $\sim L_0$, $\sim 0.3L_0$, and $\sim 0.15L_0$, respectively. (3) The coherence length of magnetic field defined in the Faraday rotation measure (RM) due to the intergalactic magnetic field (IGMF) is related to the integral scale. We presented a formula that expresses the standard deviation of RM, $\sigma_{RM}$, in terms of the integral scale and rms strength of the IGMF, and estimated that $\sigma_{RM}$ would be $\sim 100$ and $\sim$ a few rad m$^{-2}$ for clusters and filaments, respectively.Comment: To appear in ApJ Letters; published versio

Inverse Cascade of Primordial Magnetic Field in MHD Turbulence

The feature of the spectrum of primordial magnetic field is studied by using renormalization group analysis in magnetohydrodynamics. Taking account of the renormalized resistivity at the fixed point, we show that the scaling of the typical scale with time obeys $L(t) \sim t^{2/5}$ for random initial condition.Comment: 7 pages, LaTex, to appear in Phys.Lett.

Extended Scaling Laws in Numerical Simulations of MHD Turbulence

Magnetised turbulence is ubiquitous in astrophysical systems, where it notoriously spans a broad range of spatial scales. Phenomenological theories of MHD turbulence describe the self-similar dynamics of turbulent fluctuations in the inertial range of scales. Numerical simulations serve to guide and test these theories. However, the computational power that is currently available restricts the simulations to Reynolds numbers that are significantly smaller than those in astrophysical settings. In order to increase computational efficiency and, therefore, probe a larger range of scales, one often takes into account the fundamental anisotropy of field-guided MHD turbulence, with gradients being much slower in the field-parallel direction. The simulations are then optimised by employing the reduced MHD equations and relaxing the field-parallel numerical resolution. In this work we explore a different possibility. We propose that there exist certain quantities that are remarkably stable with respect to the Reynolds number. As an illustration, we study the alignment angle between the magnetic and velocity fluctuations in MHD turbulence, measured as the ratio of two specially constructed structure functions. We find that the scaling of this ratio can be extended surprisingly well into the regime of relatively low Reynolds number. However, the extended scaling becomes easily spoiled when the dissipation range in the simulations is under-resolved. Thus, taking the numerical optimisation methods too far can lead to spurious numerical effects and erroneous representation of the physics of MHD turbulence, which in turn can affect our ability to correctly identify the physical mechanisms that are operating astrophysical systems

On the two-dimensional magnetic reconnection with nonuniform resistivity

In this paper two theoretical approaches for the calculation of the rate of quasi-stationary, two-dimensional magnetic reconnection with nonuniform anomalous resistivity are considered in the framework of incompressible magnetohydrodynamics (MHD). In the first, ``global'' equations approach the MHD equations are approximately solved for a whole reconnection layer, including the upstream and downstream regions and the layer center. In the second, ``local'' equations approach the equations are solved across the reconnection layer, including only the upstream region and the layer center. Both approaches give the same approximate answer for the reconnection rate. Our theoretical model is in agreement with the results of recent simulations of reconnection with spatially nonuniform resistivity by Baty, Priest and Forbes (2006), contrary to their conclusions.Comment: 7 pages, 1 figur