Self-Feeding Turbulent Magnetic Reconnection on Macroscopic Scales

Within a MHD approach we find magnetic reconnection to progress in two entirely different ways. The first is well-known: the laminar Sweet-Parker process. But a second, completely different and chaotic reconnection process is possible. This regime has properties of immediate practical relevance: i) it is much faster, developing on scales of the order of the Alfv\'en time, and ii) the areas of reconnection become distributed chaotically over a macroscopic region. The onset of the faster process is the formation of closed circulation patterns where the jets going out of the reconnection regions turn around and forces their way back in, carrying along copious amounts of magnetic flux

Evolution of Magnetic Fields in Freely Decaying Magnetohydrodynamic Turbulence

We study the evolution of magnetic fields in freely decaying magnetohydrodynamic turbulence. By quasi-linearizing the Navier-Stokes equation, we solve analytically the induction equation in quasi-normal approximation. We find that, if the magnetic field is not helical, the magnetic energy and correlation length evolve in time respectively as E_B \propto t^{-2(1+p)/(3+p)} and \xi_B \propto t^{2/(3+p)}, where p is the index of initial power-law spectrum. In the helical case, the magnetic helicity is an almost conserved quantity and forces the magnetic energy and correlation length to scale as E_B \propto (log t)^{1/3} t^{-2/3} and \xi_B \propto (log t)^{-1/3} t^{2/3}.Comment: 4 pages, 2 figures; accepted for publication in PR

Analytic solutions of the magnetic annihilation and reconnection problems. I. Planar flow profiles

The phenomena of steady-state magnetic annihilation and reconnection in the vicinity of magnetic nulls are considered. It is shown that reconnective solutions can be derived by superposing the velocity and magnetic fields of simple magnetic annihilation models. These solutions contain most of the previous models for magnetic merging and reconnection, as well as introducing several new solutions. The various magnetic dissipation mechanisms are classified by examining the scaling of the Ohmic diffusion rate with plasma resistivity. Reconnection solutions generally allow more favorable "fast" dissipation scalings than annihilation models. In particular, reconnection models involving the advection of planar field components have the potential to satisfy the severe energy release requirements of the solar flare. The present paper is mainly concerned with magnetic fields embedded in strictly planar flows—a discussion of the more complicated three-dimensional flow patterns is presented in Part II [Phys. Plasmas 4, 110 (1997)]

Pesin's Formula for Random Dynamical Systems on RdR^d

Pesin's formula relates the entropy of a dynamical system with its positive Lyapunov exponents. It is well known, that this formula holds true for random dynamical systems on a compact Riemannian manifold with invariant probability measure which is absolutely continuous with respect to the Lebesgue measure. We will show that this formula remains true for random dynamical systems on $R^d$ which have an invariant probability measure absolutely continuous to the Lebesgue measure on $R^d$. Finally we will show that a broad class of stochastic flows on $R^d$ of a Kunita type satisfies Pesin's formula.Comment: 35 page

Fast magnetic reconnection in laser-produced plasma bubbles

Recent experiments have observed magnetic reconnection in high-energy-density, laser-produced plasma bubbles, with reconnection rates observed to be much higher than can be explained by classical theory. Based on fully kinetic particle simulations we find that fast reconnection in these strongly driven systems can be explained by magnetic flux pile-up at the shoulder of the current sheet and subsequent fast reconnection via two-fluid, collisionless mechanisms. In the strong drive regime with two-fluid effects, we find that the ultimate reconnection time is insensitive to the nominal system Alfven time.Comment: 5 pages, 4 figures, accepted by Phys. Rev. Let

Exact solutions for steady-state, planar, magnetic reconnection in an incompressible viscous plasma

The exact planar reconnection analysis of Craig and Henton [Astrophys. J. 450, 280 (1995)] is extended to include the finite viscosity of the fluid and the presence of nonplanar components in the magnetic and velocity fields. It is shown that fast reconnection can be achieved for sufficiently small values of the kinematic viscosity. In particular, the dissipation rate is sustained by the strong amplification of planar magnetic field components advected toward the neutral point. By contrast, nonplanar field components are advected without amplification and so dissipate energy at the slow Sweet–Parker rate

The Spectral Slope and Kolmogorov Constant of MHD turbulence

The spectral slope of strong MHD turbulence has recently been a matter of controversy. While Goldreich-Sridhar model (1995) predicts Kolmogorov's -5/3 slope of turbulence, shallower slopes were often reported by numerical studies. We argue that earlier numerics was affected by driving due to a diffuse locality of energy transfer in MHD case. Our highest-resolution simulation (3072^2x1024) has been able to reach the asymptotic -5/3 regime of the energy slope. Additionally, we found that so-called dynamic alignment, proposed in the model with -3/2 slope, saturates and therefore can not affect asymptotic slope. The observation of the asymptotic regime allowed us to measure Kolmogorov constant C_KA=3.2+-0.2 for purely Alfv\'enic turbulence and C_K=4.1+-0.3 for full MHD turbulence. These values are much higher than the hydrodynamic value of 1.64. The larger value of Kolmogorov constant is an indication of a fairly inefficient energy transfer and, as we show in this Letter, is in theoretical agreement with our observation of diffuse locality. We also explain what has been missing in numerical studies that reported shallower slopes.Comment: 5 pages 3 figure

Current-sheet formation in incompressible electron magnetohydrodynamics

The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonlocal nonlinear approximations are introduced and partially analyzed that are generalizations of the previously known exactly solvable local model neglecting electron inertia. Finally, estimations are made that predict finite-time singularity formation for a class of hydrodynamic models intermediate between that local model and the Eulerian hydrodynamics.Comment: REVTEX4, 5 pages, no figures. Introduction rewritten, new material and references adde

Effect of the curvature and the {\beta} parameter on the nonlinear dynamics of a drift tearing magnetic island

We present numerical simulation studies of 2D reduced MHD equations investigating the impact of the electronic \beta parameter and of curvature effects on the nonlinear evolution of drift tearing islands. We observe a bifurcation phenomenon that leads to an amplification of the pressure energy, the generation of E \times B poloidal flow and a nonlinear diamagnetic drift that affects the rotation of the magnetic island. These dynamical modifications arise due to quasilinear effects that generate a zonal flow at the onset point of the bifurcation. Our simulations show that the transition point is influenced by the \beta parameter such that the pressure gradient through a curvature effect strongly stabilizes the transition. Regarding the modified rotation of the island, a model for the frequency is derived in order to study its origin and the effect of the \beta parameter. It appears that after the transition, an E \times B poloidal flow as well as a nonlinear diamagnetic drift are generated due to an amplification of the stresses by pressure effects