Leonid M. Malyshkin

Magnetic reconnection with anomalous resistivity in two-and-a-half dimensions. I. Quasistationary case

In this paper quasistationary, “two-and-a-half-dimensional” magnetic reconnection is studied in the framework of incompressible resistive magnetohydrodynamics. A new theoretical approach for the calculation of the reconnection rate is presented. This approach is based on the 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 quasistationary 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 [Electromagnetic Phenomena, edited by B. Lehnert (Cambridge University Press, New York, 1958), p. 123; Astrophys. J., Suppl. 8, 177 (1963)] and not Petschek [AAS-NASA Symposium on Solar Flares NASA SP5 (National Aeronau...

Model of Hall reconnection.

The rate of quasistationary, two-dimensional magnetic reconnection is calculated in the framework of incompressible Hall magnetohydrodynamics, which includes the Hall and electron pressure terms in Ohms law. The Hall-magnetohydrodynamics 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 di 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 di/L, where L is the scale length of the external magnetic field in the upstream region outside the electron layer and the ion layer thickness is found to be di.

Magnetic reconnection in partially ionized plasmas

We review the theory of magnetic reconnection in weakly ionized gases. The theory is relevant to reconnection in the interstellar medium, protostellar and protoplanetary disks, the outer envelopes of cool stars, and a new laboratory experiment. In general, partial ionization introduces three effects beyond the obvious one: increased resistivity due to electron-neutral collisions. First, magnetic neutral sheets are steepened by plasma-neutral drift, setting up the conditions for reconnection. Second, when ion-neutral friction is strong, the effective ion mass is increased by ρ/ρi, the ratio of total to plasma mass density. This reduces the Alfven speed vA by a factor of ρ/ρi and increases the ion skin depth δi by ρ/ρi. As a result, entrainment of neutrals slows MHD reconnection but permits the onset of fast collisionless reconnection at a larger Lundquist number S, or for a longer current sheet, than in the fully ionized plasma case. These effects, taken together, promote fast collisionless reconnection wh...

Magnetized Turbulent Dynamos in Protogalaxies

The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in the calculation of the turbulent dynamo, it has been customary to assume that there is no back-reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of this theory to protogalaxies is rather limited. The reason is that in protogalaxies, the temperature is very high, and the viscosity is dominated by magnetized ions. As the magnetic field strength grows in time, the ion cyclotron time becomes shorter than the ion collision time, and the plasma becomes strongly magnetized. As a result, the ion viscosity becomes the Braginskii viscosity. Thus, in protogalaxies the back-reaction sets in much earlier, at field strengths much lower than those that correspond to field-turbulence energy equipartition, and the turbulent dynamo becomes what we call the magnetized turbulent dynamo. In this paper we lay the theoretical groundwork for the magnetized turbulent dynamo. In particular, we predict that the magnetic energy growth rate in magnetized dynamo theory is up to 10 times larger than that in kinematic dynamo theory. We also briefly discuss how the Braginskii viscosity can aid the development of the inverse cascade of magnetic energy after energy equipartition is reached.

Onset of Fast Magnetic Reconnection in Partially Ionized Gases

We consider quasi-stationary two-dimensional magnetic reconnection in a partially ionized incompressible plasma. We find that when the plasma is weakly ionized and the collisions between the ions and the neutral particles are significant, the transition to fast collisionless reconnection due to the Hall effect in the generalized Ohms law is expected to occur at much lower values of the Lundquist number, as compared to a fully ionized plasma case. We estimate that these conditions for fast reconnection are satisfied in molecular clouds and in protostellar disks.

Magnetic Dynamo action at Low Magnetic Prandtl Numbers

Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid-metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum.

Model of two-fluid reconnection.

A theoretical model of quasistationary, two-dimensional magnetic reconnection is presented in the framework of incompressible two-fluid magnetohydrodynamics. The results are compared with recent numerical simulations and experiment.

Magnetic Dynamo Action in Random Flows with Zero and Finite Correlation Times

Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here, we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible, non-helical, homogeneous, and isotropic flow. In the Kazantsev dynamo model, the statistics of the driving flow are assumed to be instantaneously correlated in time. Here, we compare the results of the model with the dynamo properties of a simulated flow that has similar spatial characteristics as the Kazantsev flow but different temporal statistics. In particular, the simulated flow is a solution of the forced Navier-Stokes equations and hence has a finite correlation time. We find that the Kazantsev model typically predicts a larger magnetic growth rate and a magnetic spectrum that peaks at smaller scales. However, we show that by filtering the diffusivity spectrum at small scales it is possible to bring the growth rates into agreement and simultaneously align the magnetic spectra.

Magnetic Dynamo Action in Helical Turbulence

We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model. We present the numerical solution of the model for the practically important case of Kolmogorov distribution of velocity fluctuations, with a large magnetic Reynolds number. We find that in contrast to the nonhelical case where growing magnetic fields are described by a few bound eigenmodes concentrated inside the inertial interval of the velocity field, in the helical case the number of bound eigenmodes considerably increases; moreover, new unbound eigenmodes appear. Both bound and unbound eigenmodes contribute to the large-scale magnetic field. This indicates a limited applicability of the conventional alpha model of a large-scale dynamo action, which captures only unbound modes.

MAGNETIC DYNAMO ACTION IN ASTROPHYSICAL TURBULENCE

We investigate the structure of magnetic fields amplified by turbulent velocity fluctuations, in the framework of the kinematic Kazantsev-Kraichnan model. We consider Kolmogorov distribution of velocity fluctuations, and assume that both Reynolds number and magnetic Reynolds number are very large. We present the full numerical solution of the model for the spectra and the growth rates of magnetic fluctuations. We consider astrophysically relevant limits of large and small magnetic Prandtl numbers, and address both helical and nonhelical cases.