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:
La reconecci on es el proceso mediante el cual los campos magn eticos cambian de topolog a en un medio conductor, y es fundamental para entender diferentes procesos, incluyendo la turbulencia interestelar y los dinamos estelares y gal acticos. Para explicar el campo gal actico, las r afagas y el ciclo solar, la reconecci on debe ser r apida y propagarse a la velocidad de Alfv en. Trabajos anteriores consideraban uidos laminares y obten an tasas de reconecci on peque~nas. Mostramos que la presencia de una componente aleatoria del campo magn etico permite una recon- necci on r apida ya que, a diferencia del caso laminar donde el proceso avanza l nea por l nea, en el caso turbulento participan muchas l neas simult aneamente. Una fracci on importante de la energ a magn etica se va a la turbulencia MHD, lo cual aumenta la tasa de reconecci on al aumentar la parte aleatoria del campo. Como consecuencia, los dinamos solares y gal acticos tambi en se vuelven r apidos.

Abstract:
I review recent work on the radial transport of angular momentum in ionized, Keplerian accretion disks. Proposed mechanisms include hydrodynamic and MHD local instabilities and long range effects mediated by wave transport. The most promising models incorporate the Velikhov-Chandrasekhar instability, caused by an instability of the magnetic field embedded in a differentially rotating disk. This has the important feature that the induced turbulent motions necessarily transport angular momentum outward. By contrast, convective modes may transport angular momentum in either direction. Combining the magnetic field instability with an $\alpha-\Omega$ dynamo driven by internal waves leads to a model in which the dimensionless viscosity scales as $(H/r)^{4/3}$. However, this model has a phenomenology which is quite different from the $\alpha$ disk model. For example, an active disk implies some source of excitation for the internal waves. In binary systems with a mass ratio of order unity the most likely exciting mechanism is a parametric instability due to tidal forces. This implies that in systems where the accretion stream is intermittent, like MV Lyrae or TT Ari, epochs when the mass flow is absent or very small will be epochs in which the disk shrinks and becomes relatively inactive and dark. This model also implies that forced vertical mixing is important, even in convectively stable disks. I discuss various observational tests of this model and the focus of current theoretical work.

Abstract:
Recent work on the transport of angular momentum in accretion disks suggests that the Velikhov-Chandrasekhar instability, in which a large scale magnetic field generates small scale eddys in a shearing environment, may be ultimately responsible for this process. Although there is considerable controversy about the origin and maintenance of this field in accretion disks, it turns out that it is possible to argue, quite generally, using scaling arguments, that this process is sensitive to the total pressure in an AGN disk, rather than the pressure contributed by gas alone. We conclude that the resolution of the conceptual difficulties implied by the presence of strong thermal and viscous instabilities in radiation pressure and electron scattering dominated does not lie in models that couple the total dissipation rate to the gas pressure alone, or to some weighted mean of the gas and radiation pressures.

Abstract:
We suggest a new model for the structure of a magnetic field embedded high $\beta$ turbulent plasma, based on the popular notion that the magnetic field will tend to separate into individual flux tubes. We point out that interactions between the flux tubes will be dominated by coherent effects stemming from the turbulent wakes created as the fluid streams by the flux tubes. Balancing the attraction caused by shielding effects with turbulent diffusion we find that flux tubes have typical radii comparable to the local Mach number squared times the large scale eddy length, are arranged in a one dimensional fractal pattern, have a radius of curvature comparable to the largest scale eddies in the turbulence, and have an internal magnetic pressure comparable to the ambient pressure. When the average magnetic energy density is much less than the turbulent energy density the radius, internal magnetic field and curvature scale of the flux tubes will be smaller than these estimates. Realistic resistivity does not alter the macroscopic properties of the fluid or the large scale magnetic field. In either case we show that the Sweet-Parker reconnection rate is much faster than an eddy turnover time. Realistic stellar plasmas are expected to either be in the ideal limit (e.g. the solar photosphere) or the resistive limit (most of the solar convection zone). All current numerical simulations of three dimensional MHD turbulence are in the viscous regime and are inapplicable to stars or accretion disks.

Abstract:
Reconnection is the process by which magnetic fields in a conducting fluid change their topology. This process is essential for understanding a wide variety of astrophysical processes, including stellar and galactic dynamos and astrophysical turbulence. To account for solar flares, solar cycles and the structure of the galactic magnetic field reconnection must be fast, propagating with a speed close to the Alfven speed. We show that the presence of a random magnetic field component substantially enhances the reconnection rate and enables fast reconnection, i.e. reconnection that does not depend on fluid resistivity. The enhancement of the reconnection rate is achieved via a combination of two effects. First of all, only small segments of magnetic field lines are subject to direct Ohmic annihilation. Thus the fraction of magnetic energy that goes directly into fluid heating goes to zero as fluid resistivity vanishes. However, the most important enhancement comes from the fact that unlike the laminar fluid case where reconnection is constrained to proceed line by line, the presence of turbulence enables many magnetic field lines to enter the reconnection zone simultaneously. A significant fraction of magnetic energy goes into MHD turbulence and this enhances reconnection rates through an increase in the field stochasticity. In this way magnetic reconnection becomes fast when field stochasticity is accounted for. As a consequence solar and galactic dynamos are also fast, i.e. do not depend on fluid resistivity.

Abstract:
We examine the effect of weak, small scale magnetic field structure on the rate of reconnection in a strongly magnetized plasma. This affects the rate of reconnection by reducing the transverse scale for reconnection flows, and by allowing many independent flux reconnection events to occur simultaneously. Allowing only for the first effect and using Goldreich and Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we find that the lower limit for the reconnection speed is the Alfven speed times the Lundquist number to the power (-3/16). The upper limit on the reconnection speed is typically a large fraction of Alfven speed. We argue that generic reconnection in turbulent plasmas will normally occur at close to this upper limit. The fraction of magnetic energy that goes directly into electron heating scales as Lundquist number to the power (-2/5) and the thickness of the current sheet scales as the Lundquist number to the power (-3/5). A significant fraction of the magnetic energy goes into high frequency Alfven waves. We claim that the qualitative sense of these conclusions, that reconnection is fast even though current sheets are narrow, is almost independent of the local physics of reconnection and the nature of the turbulent cascade. As the consequence of this the Galactic and Solar dynamos are generically fast, i.e. do not depend on the plasma resistivity.

Abstract:
Astrophysical fluids are generically turbulent and this must be taken into account for most transport processes. We discuss how the preexisting turbulence modifies magnetic reconnection and how magnetic reconnection affects the MHD turbulent cascade. We show the intrinsic interdependence and interrelation of magnetic turbulence and magnetic reconnection, in particular, that strong magnetic turbulence in 3D requires reconnection and 3D magnetic turbulence entails fast reconnection. We follow the approach in Eyink, Lazarian & Vishniac 2011 to show that the expressions of fast magnetic reconnection in Lazarian & Vishniac 1999 can be recovered if Richardson diffusion of turbulent flows is used instead of ordinary Ohmic diffusion. This does not revive, however, the concept of magnetic turbulent diffusion which assumes that magnetic fields can be mixed up in a passive way down to a very small dissipation scales. On the contrary, we are dealing the reconnection of dynamically important magnetic field bundles which strongly resist bending and have well defined mean direction weakly perturbed by turbulence. We argue that in the presence of turbulence the very concept of flux-freezing requires modification. The diffusion that arises from magnetic turbulence can be called reconnection diffusion as it based on reconnection of magnetic field lines. The reconnection diffusion has important implications for the continuous transport processes in magnetized plasmas and for star formation. In addition, fast magnetic reconnection in turbulent media induces the First order Fermi acceleration of energetic particles, can explain solar flares and gamma ray bursts. However, the most dramatic consequence of these developments is the fact that the standard flux freezing concept must be radically modified in the presence of turbulence.

Abstract:
We consider stochastic reconnection in a magnetized, partially ionized medium. Stochastic reconnection is a generic effect, due to field line wandering, in which the speed of reconnection is determined by the ability of ejected plasma to diffuse away from the current sheet along magnetic field lines, rather than by the details of current sheet structure. We consider the limit of weak stochasticity, so that the mean magnetic field energy density is greater than either the turbulent kinetic energy density or the energy density associated with the fluctuating component of the field. We consider field line stochasticity generated through a turbulent cascade, which leads us to consider the effect of neutral drag on the turbulent cascade of energy. In a collisionless plasma, neutral particle viscosity and ion-neutral drag will damp mid-scale turbulent motions, but the power spectrum of the magnetic perturbations extends below the viscous cutoff scale. We give a simple physical picture of the magnetic field structure below this cutoff, consistent with numerical experiments. We provide arguments for the reemergence of the turbulent cascade well below the viscous cut-off scale and derive estimates for field line diffusion on all scales. We note that this explains the persistence of a single power law form for the turbulent power spectrum of the interstellar medium, from scales of tens of parsecs down to thousands of kilometers. We find that under typical conditions in the ISM stochastic reconnection speeds are reduced by the presence of neutrals, but by no more than an order of magnitude.

Abstract:
Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux threading a fluid element, or the field topology. Classical dynamo theory evades this limit by assuming that magnetic reconnection is fast, even for vanishing resistivity, and that the large scale field can be generated by the action of kinetic helicity. Both these claims have been severely criticized, and the latter appears to conflict with strong theoretical arguments based on magnetic helicity conservation and a series of numerical simulations. Here we discuss recent efforts to explain fast magnetic reconnection through the topological effects of a weak stochastic magnetic field component. We also show how mean-field dynamo theory can be recast in a form which respects magnetic helicity conservation, and how this changes our understanding of astrophysical dynamos. Finally, we comment briefly on why an asymmetry between small scale magnetic and velocity fields is necessary for dynamo action, and how it can arise naturally.