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

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

Magnetic Flux Expulsion in the Powerful Superbubble Explosions and the Alpha-Omega Dynamo

The possibility of the magnetic flux expulsion from the Galaxy in the superbubble (SB) explosions, important for the Alpha-Omega dynamo, is considered. Special emphasis is put on the investigation of the downsliding of the matter from the top of the shell formed by the SB explosion which is able to influence the kinematics of the shell. It is shown that either Galactic gravity or the development of the Rayleigh-Taylor instabilities in the shell limit the SB expansion, thus, making impossible magnetic flux expulsion. The effect of the cosmic rays in the shell on the sliding is considered and it is shown that it is negligible compared to Galactic gravity. Thus, the question of possible mechanism of flux expulsion in the Alpha-Omega dynamo remains open.Comment: MNRAS, in press, 11 pages, 9 figure

A model of Hall reconnection

The rate of quasi-stationary, two-dimensional magnetic reconnection is calculated in the framework of incompressible Hall magnetohydrodynamics (MHD). The calculation is based on the solution of Hall-MHD equations that include Hall and electron pressure terms for electric current. These equations are solved in a local region across the reconnection electron layer, including only the upstream region and the layer center. In the case when the ion inertial length d_i is larger than the Sweet-Parker reconnection layer thickness, the dimensionless reconnection rate is found to be independent of the electrical resistivity and equal to d_i/L, where L is the scale length of the external magnetic field in the upstream region outside the electron layer.Comment: 4 pages, 1 figur

2D Numerical Simulation of the Resistive Reconnection Layer

In this paper we present a two-dimensional 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 backpressure from the flow into the separatrix region. We find that within a few Alfven times the system reaches a steady state consistent with the Sweet--Parker model, even if the initial state is Petschek-like

Nonlinear growth of firehose and mirror fluctuations in turbulent galaxy-cluster plasmas

In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, dB/B ~ 1, on a timescale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas.Comment: revtex, 4 pages, 1 figure; replaced to match published versio

Amplification of magnetic fields by dynamo action in Gaussian-correlated helical turbulence

We investigate the growth and structure of magnetic fields amplified by kinematic dynamo action in turbulence with non-zero kinetic helicity. We assume a simple Gaussian velocity correlation tensor, which allows us to consider very large magnetic Reynolds numbers, up to one trillion. We use the kinematic Kazantsev-Kraichnan model of dynamo and find a complete numerical solution for the correlation functions of growing magnetic fields.Comment: 7 pages, 3 figure

MHD Memes

The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics.Comment: Submitted for publication in IOP Journal of Physics: Conference Series for publication in "Plasma Theory, Wave Kinetics, and Nonlinear Dynamics", Proceedings of KaufmanFest, 5-7 October 2007, University of California, Berkeley, US

Fast and slow two-fluid magnetic reconnection

We present a two-fluid magnetohydrodynamics (MHD) model of quasi-stationary, two-dimensional magnetic reconnection in an incompressible plasma composed of electrons and ions. We find two distinct regimes of slow and fast reconnection. The presence of these two regimes can provide a possible explanation for the initial slow build up and subsequent rapid release of magnetic energy frequently observed in cosmic and laboratory plasmas.Comment: 16 pages, 2 figures, 1 tabl