Cusp and Y-type magnetic structures and volocity fields at the endpoint of the reconnection layer

We study the two-dimensional global scale magnetic field structure for a system of two merging cylindrical plasmas in a steady state. In the limit of very large magnetic Reynolds numbers the reconnection process is slow, and the plasma almost everywhere finds itself in magnetostatic equilibrium. We show that under certain conditions the classical Syrovatskii-type Y-point configuration, with surface current concentrated only in the reconnection layer, is not possible. Instead, a cusp configuration is formed, with finite surface current in the separatrix. The equilibrium condition, together with constraints on the volume per flux, enables us to determine the shape of the separatrix and the magnetic field in the vicinity of the cusp point. Our solution is characterized by a singular power law dependence of current density on the flux coordinate ({psi}) near the separatrix: j({Psi}) {approx} |{Psi}|{sup -1/2}. This solution gives us the boundary conditions that are needed to find the flow in the reconnection and the separatrix regions

On the Viscous Boundary Layer Near the Center of the Resistive Reconnection Region

This paper studies the behavior of the magnetic field near the center of the reconnection layer in the framework of two-dimensional incompressible resistive magnetohydrodynamics with uniform resistivity in a steady state. Priest and Cowley have presented an argument [1] showing that when the viscosity is zero, the magnetic separatrices do not cross at a finite angle but osculate at the X-point. In the present paper, it is shown that this conclusion is in fact not correct. First, some results of numerical simulations of the reconnection layer are presented. These results contradict the conclusions of Priest and Cowley. In order to explain this contradiction, an analytical theory for the neighborhood of the X-point is developed in the second part of the paper. It is found that, if the viscosity is exactly equal to zero, then one of the critical assumptions of the above mentioned argument, namely the assumption that the stream function can be Taylor-expanded near the X-point, breaks down. In the case of small but finite viscosity, a boundary layer analysis in the vicinity of the neutral point is carried out. Some of the higher derivatives of the stream function become very large near the X-point, leading to a non-zero angle between the separatrices. As viscosity goes to zero, the boundary layer shrinks and one can see the emergence of the non-analytic logarithmic terms in the expansion of the stream function in the outer region. The results of the boundary layer analysis are found to be in good agreement with the numerical simulations

Chern-Simons anomaly as polarization effect

The parity violating Chern-Simons term in the epoch before the electroweak phase transition can be interpreted as a polarization effect associated to massless right-handed electrons (positrons) in the presence of a large-scale seed hypermagnetic field. We reconfirm the viability of a unified seed field scenario relating the cosmological baryon asymmetry and the origin of the protogalactic large-scale magnetic fields observed in astronomy.Comment: 4 pages, latex, matches published versio

Measurement of Lower-hybrid Drift Turbulence in a Reconnecting Current Sheet

We present a detailed study of fluctuations in a laboratory current sheet undergoing magnetic reconnection. The measurements reveal the presence of lower-hybrid-frequency range fluctuations on the edge of current sheets produced in the Magnetic Reconnection Experiment (MRX). The measured fluctuation characteristics are consistent with theoretical predictions for the lower-hybrid drift instability (LHDI). Our observations suggest that the LHDI does not provide any significant turbulent resistivity in MRX current sheets

Protogalactic Extension of the Parker Bound

We extend the Parker bound on the galactic flux $\cal F$ of magnetic monopoles. By requiring that a small initial seed field must survive the collapse of the protogalaxy, before any regenerative dynamo effects become significant, we develop a stronger bound. The survival and continued growth of an initial galactic seed field $\leq 10^{-9}$G demand that ${\cal F} \leq 5 \times 10^{-21} (m/10^{17} {GeV}) {cm}^{-2} {sec}^{-1} {sr}^{-1}$. For a given monopole mass, this bound is four and a half orders of magnitude more stringent than the previous `extended Parker bound', but is more speculative as it depends on assumptions about the behavior of magnetic fields during protogalactic collapse. For monopoles which do not overclose the Universe ($\Omega_m <1$), the maximum flux allowed is now $8 \times 10^{-19}$ cm^{-2} s^{-1} sr^{-1}, a factor of 150 lower than the maximum flux allowed by the extended Parker bound.Comment: 9 pages, 1 eps figur

Shock Waves in the Large-Scale Structure of the Universe

Cosmological shock waves are induced during hierarchical formation of large-scale structure in the universe. Like most astrophysical shocks, they are collisionless, since they form in the tenuous intergalactic medium through electromagnetic viscosities. The gravitational energy released during structure formation is transferred by these shocks to the intergalactic gas as heat, cosmic-rays, turbulence, and magnetic fields. Here we briefly describe the properties and consequences of the shock waves in the context of the large-scale structure of the universe.Comment: Submitted to Astrophysics and Space Science (Special Issue for the proceedings of International Conference on HEDP/HEDLA-08). Pdf with full resolution Figure 1 can be downloaded from http://canopus.cnu.ac.kr/ryu/rk.pd

Effects of non-linearities on magnetic field generation

Magnetic fields are present on all scales in the Universe. While we understand the processes which amplify the fields fairly well, we do not have a "natural" mechanism to generate the small initial seed fields. By using fully relativistic cosmological perturbation theory and going beyond the usual confines of linear theory we show analytically how magnetic fields are generated. This is the first analytical calculation of the magnetic field at second order, using gauge-invariant cosmological perturbation theory, and including all the source terms. To this end, we have rederived the full set of governing equations independently. Our results suggest that magnetic fields of the order of $10^{-30}$ G can be generated (although this depends on the small scale cut-off of the integral), which is largely in agreement with previous results that relied upon numerical calculations. These fields are likely too small to act as the primordial seed fields for dynamo mechanisms.Comment: 21 pages; v2: minor changes, added references; v3: version accepted for publication in JCA

A certain class of Laplace transforms with applications to reaction and reaction-diffusion equations

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, alpha-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.Comment: LaTeX, 12 pages, corrected typo

Hyperbolic heat equation in Kaluza's magnetohydrodynamics

This paper shows that a hyperbolic equation for heat conduction can be obtained directly using the tenets of linear irreversible thermodynamics in the context of the five dimensional space-time metric originally proposed by T. Kaluza back in 1922. The associated speed of propagation is slightly lower than the speed of light by a factor inversely proportional to the specific charge of the fluid element. Moreover, consistency with the second law of thermodynamics is achieved. Possible implications in the context of physics of clusters of galaxies of this result are briefly discussed.Comment: 14 pages, no figure

An evaluation of possible mechanisms for anomalous resistivity in the solar corona

A wide variety of transient events in the solar corona seem to require explanations that invoke fast reconnection. Theoretical models explaining fast reconnection often rely on enhanced resistivity. We start with data derived from observed reconnection rates in solar flares and seek to reconcile them with the chaos-induced resistivity model of Numata & Yoshida (2002) and with resistivity arising out of the kinetic Alfv\'en wave (KAW) instability. We find that the resistivities arising from either of these mechanisms, when localized over lengthscales of the order of an ion skin depth, are capable of explaining the observationally mandated Lundquist numbers.Comment: Accepted, Solar Physic