Abstract:
We discuss the model of magnetic eld reconnection in the presence of turbulence introduced by us ten years ago. The model does not require any plasma e ects to be involved in order to make the reconnection fast. In fact, it shows that the degree of magnetic eld stochasticity controls the reconnection. The turbulence in the model is assumed to be sub-Alfv nic, with the magnetic eld only slightly perturbed. This ensures that the reconnection happens in generic astrophysical environments and the model does not appeal to any unphysical concepts, similar to the turbulent magnetic di usivity concept, which is employed in the kinematic magnetic dynamo. The interest to that model has recently increased due to successful numerical testings of the model predictions. In view of this, we discuss implications of the model, including the rst-order Fermi acceleration of cosmic rays, that the model naturally entails, bursts of reconnection, that can be associated with Solar ares, as well as, removal of magnetic ux during star-formation.

Abstract:
Magnetic field embedded in a perfectly conducting fluid preserves its topology for all time. Although ionized astrophysical objects, like stars and galactic disks, are almost perfectly conducting, they show indications of changes in topology, `magnetic reconnection', on dynamical time scales. Reconnection can be observed directly in the solar corona, but can also be inferred from the existence of large scale dynamo activity inside stellar interiors. Solar flares and gamma ray busts are usually associated with magnetic reconnection. Previous work has concentrated on showing how reconnection can be rapid in plasmas with very small collision rates. Here we present numerical evidence, based on three dimensional simulations, that reconnection in a turbulent fluid occurs at a speed comparable to the rms velocity of the turbulence, regardless of the value of the resistivity. In particular, this is true for turbulent pressures much weaker than the magnetic field pressure so that the magnetic field lines are only slightly bent by the turbulence. These results are consistent with the proposal by Lazarian and Vishniac (1999) that reconnection is controlled by the stochastic diffusion of magnetic field lines, which produces a broad outflow of plasma from the reconnection zone. This work implies that reconnection in a turbulent fluid typically takes place in approximately a single eddy turnover time, with broad implications for dynamo activity and particle acceleration throughout the universe. In contrast, the reconnection in 2D configurations in the presence of turbulence depends on resistivity, i.e. is slow.

Abstract:
We examine the dynamics of turbulent reconnection in 2D and 3D reduced MHD by calculating the effective dissipation due to coupling between small-scale fluctuations and large-scale magnetic fields. Sweet-Parker type balance relations are then used to calculate the global reconnection rate. Two approaches are employed -- quasi-linear closure and an eddy-damped fluid model. Results indicate that despite the presence of turbulence, the reconnection rate remains inversely proportional to $\sqrt{R_m}$, as in the Sweet-Parker analysis. In 2D, the global reconnection rate is shown to be enhanced over the Sweet-Parker result by a factor of magnetic Mach number. These results are the consequences of the constraint imposed on the global reconnection rate by the requirement of mean square magnetic potential balance. The incompatibility of turbulent fluid-magnetic energy equipartition and stationarity of mean square magnetic potential is demonstrated.

Abstract:
Plasma flows with an MHD-like turbulent inertial range, such as the solar wind, require a generalization of General Magnetic Reconnection (GMR) theory. We introduce the slip-velocity source vector, which gives the rate of development of slip velocity per unit arc length of field line. The slip source vector is the ratio of the curl of the non ideal electric field in the Generalized Ohm's Law and the magnetic field strength. It diverges at magnetic nulls, unifying GMR with magnetic null-point reconnection. Only under restrictive assumptions is the slip velocity related to the gradient of the quasi potential (integral of parallel electric field along field lines). In a turbulent inertial range the curl becomes extremely large while the parallel component is tiny, so that line slippage occurs even while ideal MHD becomes accurate. The resolution of this paradox is that ideal MHD is valid for a turbulent inertial-range only in a weak sense which does not imply magnetic line freezing. The notion of weak solution is explained in terms of spatial coarse-graining and renormalization group (RG) theory. We give an argument for the weak validity of the ideal Ohm's law in the inertial range, via rigorous estimates of the terms in the Generalized Ohm's Law for an electron-ion plasma. All of the nonideal terms (from collisional resistivity, Hall field, electron pressure anisotropy, and electron inertia) are shown to be irrelevant in the RG sense and large-scale reconnection is thus governed solely by ideal dynamics. We briefly discuss some implications for heliospheric reconnection, in particular for deviations from the Parker spiral model of interplanetary magnetic field. Solar wind observations show that reconnection in a turbulence broadened heliospheric current sheet, consistent with the Lazarian-Vishniac theory, leads to slip velocities that cause field lines to lag relative to the spiral model.

Abstract:
We report simulation results for turbulent magnetic reconnection obtained using a newly developed Reynolds-averaged magnetohydrodynamics model. We find that the initial Harris current sheet develops in three ways, depending on the strength of turbulence: laminar reconnection, turbulent reconnection, and turbulent diffusion. The turbulent reconnection explosively converts the magnetic field energy into both kinetic and thermal energy of plasmas, and generates open fast reconnection jets. This fast turbulent reconnection is achieved by the localization of turbulent diffusion. Additionally, localized structure forms through the interaction of the mean field and turbulence.

Abstract:
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, including the situations when turbulent reconnection is self-driven, i.e. the turbulence in the system is generated by the reconnection process itself. We show how turbulent reconnection entails the violation of magnetic flux freezing, the conclusion that has really far reaching consequences for many realistically turbulent astrophysical environments. In addition, we consider observational testing of turbulent reconnection as well as numerous implications of the theory. The former includes the Sun and solar wind reconnection, while the latter include the process of reconnection diffusion induced by turbulent reconnection, the acceleration of energetic particles, bursts of turbulent reconnection related to black hole sources as well as gamma ray bursts. Finally, we explain why turbulent reconnection cannot be explained by turbulent resistivity or derived through the mean field approach.

Abstract:
Magnetic reconnection is a fundamental process of magnetic field topology change. We analyze the connection of this process with turbulence which is ubiquitous in astrophysical environments. We show how Lazarian & Vishniac (1999) model of turbulent reconnection is connected to the experimentally proven concept of Richardson diffusion and discuss how turbulence violates the generally accepted notion of magnetic flux freezing. We note that in environments that are laminar initially turbulence can develop as a result of magnetic reconnection and this can result in flares of magnetic reconnection in magnetically dominated media. In particular, magnetic reconnection can initially develop through tearing, but the transition to the turbulent state is expected for astrophysical systems. We show that turbulent reconnection predictions corresponds to the Solar and solar wind data.

Abstract:
Fast reconnection of magnetic field in turbulent fluids allows magnetic field to change its topology and connections. As a result, the traditional concept of magnetic fields being frozen into the plasma is no longer applicable. The diffusion of plasmas and magnetic field is enabled by reconnection and therefore is termed "reconnection diffusion". We explore the consequences of reconnection diffusion for star formation. In the paper we explain the physics of reconnection diffusion both from macroscopic and microscopic points of view. We quantify the reconnection diffusion rate both for weak and strong MHD turbulence and address the problem of reconnection diffusion acting together with ambipolar diffusion. In addition, we provide a criterion for correctly representing the magnetic diffusivity in simulations of star formation. We show that the role of the plasma effects is limited to "breaking up lines" on small scales and does not affect the rate of reconnection diffusion. We address the existing observational results and demonstrate how reconnection diffusion can explain the puzzles presented by observations, in particular, the observed higher magnetization of cloud cores in comparison with the magnetization of envelopes. We also outline a possible set of observational tests of the reconnection diffusion concept and discuss how the application of the new concept changes our understanding of star formation and its numerical modeling. Finally, we outline the differences of the process of reconnection diffusion and the process of accumulation of matter along magnetic field lines that is frequently invoked to explain the results of numerical simulations

Abstract:
Turbulence is ubiquitous in astrophysical fluids. Therefore it is necessary to study magnetic reconnection in turbulent environments. The model of fast turbulent reconnection proposed in Lazarian & Vishniac 1999 has been successfully tested numerically and it suggests numerous astrophysical implications. Those include a radically new possibility of removing magnetic field from collapsing clouds which we termed "reconnection diffusion", acceleration of cosmic rays within shrinking filaments of reconnected magnetic fields, flares of reconnection, from solar flares to much stronger ones which can account for gamma ray bursts. In addition, the model reveals a very intimate relation between magnetic reconnection and properties of strong turbulence, explaining how turbulent eddies can transport heat in magnetized plasmas. This is a small fraction the astrophysical implications of the quantitative insight into the fundamental process of magnetic reconnection in turbulent media.

Abstract:
For a molecular cloud clump to form stars some transport of magnetic flux is required from the denser, inner regions to the outer regions of the cloud, otherwise this can prevent the collapse. Fast magnetic reconnection which takes place in the presence of turbulence can induce a process of reconnection diffusion (RD). Extending earlier numerical studies of reconnection diffusion in cylindrical clouds, we consider more realistic clouds with spherical gravitational potentials and also account for the effects of the gas self-gravity. We demonstrate that within our setup RD is efficient. We have also identified the conditions under which RD becomes strong enough to make an initially subcritical cloud clump supercritical and induce its collapse. Our results indicate that the formation of a supercritical core is regulated by a complex interplay between gravity, self-gravity, the magnetic field strength and nearly transonic and trans-Alfv\'enic turbulence, confirming that RD is able to remove magnetic flux from collapsing clumps, but only a few of them become nearly critical or supercritical, sub-Alfv\'enic cores, which is consistent with the observations. Besides, we have found that the supercritical cores built up in our simulations develop a predominantly helical magnetic field geometry which is also consistent with observations. Finally, we have evaluated the effective values of the turbulent reconnection diffusion coefficient and found that they are much larger than the numerical diffusion, especially for initially trans-Alfv\'enic clouds, ensuring that the detected magnetic flux removal is due to to the action of the RD rather than to numerical diffusivity.