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Register a new userFast Magnetic Reconnection with Turbulence in High Lundquist Number Limit
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We use extensive 3D resistive MHD simulations to study how large-scale current sheets will undergo fast reconnection in the high Lundquist number $S$ limit (above $sim 10^4$), when the system is subject to different externally driven turbulence levels and the self-generated turbulence produced by 3D reconnection dynamics. We find that the normalized global reconnection rate $sim 0.01 - 0.13$, weakly dependent on $S$. Global reconnection with the classic inflow/outflow configurations is observed, and 3D flux ropes are hierarchically formed and ejected from reconnection regions. A statistical separation of the reconnected magnetic field lines follows a super-diffusive behavior, from which the rate is measured to be very similar to that obtained from the mixing of tracer populations. We find that the reconnection rate scales roughly linearly with the turbulence level during the peak of reconnection. This scaling is consistent with the turbulence properties produced by both the externally driven and self-generation processes. These results imply that large-scale thin current sheets tend to undergo rigorous reconnection.
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A numerical study of magnetic reconnection in the large-Lundquist-number ($S$), plasmoid-dominated regime is carried out for $S$ up to $10^7$. The theoretical model of Uzdensky {it et al.} [Phys. Rev. Lett. {bf 105}, 235002 (2010)] is confirmed and partially amended. The normalized reconnection rate is $ ormEeffsim 0.02$ independently of $S$ for $Sgg10^4$. The plasmoid flux ($Psi$) and half-width ($w_x$) distribution functions scale as $f(Psi)sim Psi^{-2}$ and $f(w_x)sim w_x^{-2}$. The joint distribution of $Psi$ and $w_x$ shows that plasmoids populate a triangular region $w_xgtrsimPsi/B_0$, where $B_0$ is the reconnecting field. It is argued that this feature is due to plasmoid coalescence. Macroscopic monster plasmoids with $w_xsim 10$% of the system size are shown to emerge in just a few Alfven times, independently of $S$, suggesting that large disruptive events are an inevitable feature of large-$S$ reconnection.
We present the results of two-dimensional and three-dimensional magnetohydrodynamical numerical simulations of relativistic magnetic reconnection, with particular emphasis on the dynamics of the plasma in a Petschek-type configuration with high Lundquist numbers, Ssim 10^5-10^8. The numerical scheme adopted, allowing for unprecedented accuracy for this type of calculations, is based on high order finite volume and discontinuous Galerkin methods as recently proposed by citet{Dumbser2009}. The possibility of producing high Lorentz factors is discussed, showing that Lorentz factors close to sim 4 can be produced for a plasma parameter sigma_m=20. Moreover, we find that the Sweet-Parker layers are unstable, generating secondary magnetic islands, but only for S > S_c = 10^8, much larger than what is reported in the Newtonian regime. Finally, the effects of a mildly anisotropic Ohm law are considered in a configuration with a guide magnetic field. Such effects produce only slightly faster reconnection rates and Lorentz factors of about 1% larger with respect to the perfectly isotropic Ohm law.
The process of magnetic reconnection when studied in Nature or when modeled in 3D simulations differs in one key way from the standard 2D paradigmatic cartoon: it is accompanied by much fluctuations in the electromagnetic fields and plasma properties. We developed a diagnostics to study the spectrum of fluctuations in the various regions around a reconnection site. We define the regions in terms of the local value of the flux function that determines the distance form the reconnection site, with positive values in the outflow and negative values in the inflow. We find that fluctuations belong to two very different regimes depending on the local plasma beta (defined as the ratio of plasma and magnetic pressure). The first regime develops in the reconnection outflows where beta is high and is characterized by a strong link between plasma and electromagnetic fluctuations leading to momentum and energy exchanges via anomalous viscosity and resistivity. But there is a second, low beta regime: it develops in the inflow and in the region around the separatrix surfaces, including the reconnection electron diffusion region itself. It is remarkable that this low beta plasma, where the magnetic pressure dominates, remain laminar even though the electromagnetic fields are turbulent.
The rate of magnetic field diffusion plays an essential role in several astrophysical plasma processes. It has been demonstrated that the omnipresent turbulence in astrophysical media induces fast magnetic reconnection, which consequently leads to large-scale magnetic flux diffusion at a rate independent of the plasma microphysics. This process is called ``reconnection diffusion (RD) and allows for the diffusion of fields which are dynamically important. The current theory describing RD is based on incompressible magnetohydrodynamic (MHD) turbulence. In this work, we have tested quantitatively the predictions of the RD theory when magnetic forces are dominant in the turbulence dynamics (Alfv{e}nic Mach number $M_A < 1$). We employed the textsc{Pencil Code} to perform numerical simulations of forced MHD turbulence, extracting the values of the diffusion coefficient $eta_{RD}$ using the Test-Field method. Our results are consistent with the RD theory ($eta_{RD} sim M_A^{3}$ for $M_A < 1$) when turbulence approaches the incompressible limit (sonic Mach number $M_S lesssim 0.02$), while for larger $M_S$ the diffusion is faster ($eta_{RD} sim M_A^{2}$). This work shows for the first time simulations of compressible MHD turbulence with the suppression of the cascade in the direction parallel to the mean magnetic field, which is consistent with incompressible weak turbulence theory. We also verified that in our simulations the energy cascading time does not follow the scaling with $M_A$ predicted for the weak regime, in contradiction with the RD theory assumption. Our results generally support and expand the RD theory predictions.
One of the main questions in magnetic reconnection is the origin of triggering behavior with on/off properties that accounts, once it is activated, for the fast magnetic energy conversion to kinetic and thermal energies at the heart of explosive events in astrophysical and laboratory plasmas. Over the past decade progress has been made on the initiation of fast reconnection via the plasmoid instability and what has been called ideal tearing, which sets in once current sheets thin to a critical inverse aspect ratio $(a/L)_c$: as shown by Pucci and Velli (2014), at $(a/L)_c sim S^{-1/3}$ the time scale for the instability to develop becomes of the order of the Alfven time and independent of the Lundquist number (here defined in terms of current sheet length $L$). However, given the large values of $S$ in natural plasmas, this transition might occur for thicknesses of the inner resistive singular layer which are comparable to the ion inertial length $d_i$. When this occurs, Hall currents produce a three-dimensional quadrupole structure of magnetic field, and the dispersive waves introduced by the Hall effect accelerate the instability. Here we present a linear study showing how the ideal tearing mode critical aspect ratio is modified when Hall effects are taken into account, including more general scaling laws of the growth rates in terms of sheet inverse aspect ratio: the critical inverse aspect ratio is amended to $a/L simeq (di/L)^ {0.29} (1/S)^{0.19}$, at which point the instability growth rate becomes Alfvenic and does not depend on either of the (small) parameters $d_i/L, 1/S$. We discuss the implications of this generalized triggering aspect ratio for recently developed phase diagrams of magnetic reconnection.
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