Low Lundquist Number Research Articles

Quasi-periodic Oscillations in Flares and Coronal Mass Ejections Associated with Magnetic Reconnection

Abstract We propose a mechanism for quasi-periodic oscillations of both coronal mass ejections (CMEs) and flare loops as related to magnetic reconnection in eruptive solar flares. We perform two-dimensional numerical MHD simulations of magnetic flux rope eruption, with three different values of the global Lundquist number. In the low Lundquist number run, no oscillatory behavior is found. In the moderate Lundquist number run, on the other hand, quasi-periodic oscillations are excited both at the bottom of the flux rope and at the flare loop top. In the high Lundquist number run, quasi-periodic oscillations are also excited; in the meanwhile, the dynamics become turbulent owing to the formation of multiple plasmoids in the reconnection current sheet. In high and moderate Lundquist number runs, thin reconnection jets collide with the flux rope bottom or flare loop top and dig them deeply. Steep oblique shocks are formed as termination shocks where reconnection jets are bent (rather than decelerated) in the horizontal direction, resulting in supersonic backflows. The structure becomes unstable, and quasi-periodic oscillations of supersonic backflows appear at locally confined high-beta regions at both the flux rope bottom and flare loop top. We compare the observational characteristics of quasi-periodic oscillations in erupting flux ropes, post-CME current sheets, flare ribbons, and light curves with corresponding dynamical structures found in our simulation.

Laboratory Observation of Resistive Electron Tearing in a Two-Fluid Reconnecting Current Sheet.

The spontaneous formation of plasmoids via the resistive electron tearing of a reconnecting current sheet is observed in the laboratory. These experiments are performed during driven, antiparallel reconnection in the two-fluid regime within the Magnetic Reconnection Experiment. It is found that plasmoids are present even at a very low Lundquist number, and the number of plasmoids scales with both the current sheet aspect ratio and the Lundquist number. The reconnection electric field increases when plasmoids are formed, leading to an enhanced reconnection rate.

Magnetic turbulence and pressure gradient feedback effect of the 1/2 mode soft-hard magnetohydrodynamic limit in large helical device

The aim of this study was to analyze the feedback process between the magnetic turbulence and the pressure gradients in Large Helical Device (LHD) inward-shifted configurations as well as its role in the transition between the soft-hard magnetohydrodynamic (MHD) regimes for instabilities driven by the mode 1/2 in the middle plasma. In the present paper, we summarize the results of two simulations with different Lundquist numbers, S=2.5×105 and 106, assuming a plasma in the slow reconnection regime. The results for the high Lundquist number simulation show that the magnetic turbulence and the pressure gradient in the middle plasma region of LHD are below the critical value to drive the transition to the hard MHD regime, therefore only relaxations in the soft MHD limit are triggered (1/2 sawtooth-like events) [Phys. Plasmas 19, 082512 (2012)]. In the case of the simulation with low Lundquist number, the system reaches the hard MHD limit and a plasma collapse is observed.

Nature of axial tail instability and bubble‐blob formation in near‐Earth plasma sheet

ABSTRACTPrevious global magnetohydrodynamic (MHD) simulations of substorm events have identified the dynamic presence of an axial tail instability that is uniform in the dawn‐dusk direction in the near‐Earth plasma sheet. The axial tail instability is found to be a major cause of the initial growing MHD force imbalance on closed field lines prior to the subsequent magnetic reconnection and substorm expansion onset processes. In this work, energy principle analysis indicates that a two‐dimensional thin current sheet configuration in the magnetotail is typically stable to the axial mode within the framework of ideal MHD model. However, linear resistive MHD calculations find axial tail instabilities on closed field lines in the generalized Harris sheet configurations. The properties of these instabilities are similar to the axial tail modes observed in the global MHD simulations. The axial tail mode is unstable in regimes of low Lundquist number and regions with small normal component of magnetic field. Such resistive axial tail instability would by many researchers be considered as tearing instability in a two‐dimensional tail configuration. Unlike the conventional tearing mode of Harris sheet, the linear axial tail instability does not involve any reconnection process. Instead, the nature of the mode is dominantly a slippage process among neighboring flux tubes as facilitated by resistive dissipation. A natural consequence of the axial tail instability is shown to be the formation of bubble‐blob pairs in the pressure and entropy profiles in the near‐Earth plasma sheet.

Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods

This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD. The discussion considers the implementation of a stabilized FE formulation in context of a fully-implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, including both low-Lundquist number (e.g., an MHD Faraday conduction pump and a hydromagnetic Rayleigh–Bernard linear stability calculation) and moderately-high Lundquist number (magnetic island coalescence problem) examples. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.

Three-dimensional magnetohydrodynamic simulations of the Helicity Injected Torus with Steady Inductive drive

The Helicity Injected Torus with Steady Inductive drive (HIT-SI) [P. E. Sieck, W. T. Hamp, V. A. Izzo, T. R. Jarboe, B. A. Nelson, R. G. O’Neill, A. J. Redd, and R. J. Smith, IEEE Conference Record—Abstracts. 31st IEEE International Conference On Plasma Science (IEEE Catalog No. 04CH37537), 2004, p. 160] is a spheromak driven by steady inductive helicity injection (SIHI) and consists of the toroidally symmetric spheromak confinement region and two nonsymmetric helicity injectors. The three-dimensional (3D) magnetohydrodynamic code NIMROD [A. H. Glasser, C. R. Sovinec, R. A. Nebel, T. A. Gianakon, S. J. Plimpton, M. S. Chu, and D. D. Schnack, Plasma Phys. Controlled Fusion, 41, A747 (1999)] is used to simulate HIT-SI operation, but the code’s toroidally symmetric boundary requires a creative treatment of the injectors. Sustained HIT-SI operation is simulated with nonaxisymmetric boundary conditions. In driven simulations at low Lundquist number S no n=0 fields are generated as a result of relaxation of the predominantly n=1 injector fields until the injectors are quickly shut off. At S=500, an n=0 component arises due to relaxation during sustainment. As S is increased further, the ratio of n=0 (equilibrium) fields to n=1 (injector) fields increases. The effects of a thin insulating boundary layer on the plasma decay time are also discussed.

Review of controlled laboratory experiments on physics of magnetic reconnection

We review results from the most recent experiments in the past 2 decades in which magnetic reconnection has been generated and studied in controlled laboratory settings. As a whole, research on the fundamental physics of the reconnection process and its hydromagnetic consequences has been largely theoretical. Laboratory experiments are crucial for understanding the fundamental physics of magnetic reconnection since they can provide well‐correlated plasma parameters at multiple plasma locations simultaneously, while satellites can only provide information from a single location at a given time in a space plasma. Thanks to the significant progress of data acquisition technology, the detailed magnetic field structures of the reconnection regions were measured and plasma acceleration and strong ion heating were identified. Extensive data have been accumulated in the electron MHD plasma regimes [in which electrons are magnetized] with relatively low Lundquist number of S = 1 – 10 as well as in MHD plasmas with S = 100 – 1000. This article puts a special focus on the most recent plasma merging experiments in the MHD regime since they are new and have been published in the past several years. Two distinctly different shapes of diffusion regions were identified both in the electron MHD plasma regime [Stenzel and Gekelman, 1983] and in the MHD plasmas in MRX [Yamada et al., 1997b]. The familiar two‐dimensional (2‐D) feature, a double‐Y‐shaped diffusion region, was identified when there is no or very little axial magnetic field (third vector component). In cohelicity merging with a sizable third field component, an O‐shaped diffusion region appears and the reconnection rate decreases substantially; this is attributed to the axial field pressure and the incompressibility of the plasma. Another important achievement is the experimental verification of a generalized Sweet‐Parker model [Ji et al., 1998]. In this recent work it is found that the observed reconnection rate can be explained by a generalized Sweet‐Parker model, which incorporates compressibility, downstream pressure and the effective resistivity. The latter is often enhanced over its classical values in the collisionless limit. A significant implication of this result is that the generalized Sweet‐Parker model is valid in certain 2‐D reconnection cases with axisymmetric geometry. In MHD plasmas, the thickness of this thin current layer is found to be of the order of the ion gyroradius and the ion skin depth as well.

Magnetohydrodynamic calculations with a nonmonotonic q profile and equilibrium, sheared toroidal flow

The linear and nonlinear stability of a nonmonotonic q profile is examined using a reduced set of magnetohydrodynamic (MHD) equations with an equilibrium, sheared toroidal flow. The reversed shear profile is shown to be unstable to a rich variety of resistive MHD modes including pressure-driven instabilities and tearing instabilities possessing a tearing/interchange character at low Lundquist number, S, and taking on a double/triple tearing structure at high S. Linear calculations show that the destabilizing effect of toroidal velocity shear on tearing modes is enhanced at finite pressure. In addition, this velocity shear decreases the stabilizing effect of finite pressure seen previously for tearing modes at high S. Nonlinear calculations show the generation of a large, m=1, n=0, Reynolds-stress-driven poloidal flow in the absence of significant flow damping. Calculations in which the poloidal flow was heavily damped show that sub-Alfvénic, sheared toroidal flows have a minimal effect on weakly coupled, localized instabilities.

Stabilization and saturation of the ideal tilt mode in a driven annular field-reversed configuration

The coaxial slow source (CSS) is a device that was designed as a means of forming annular field-reversed configurations (AFRCs) for magnetic fusion on relatively slow (50–100 μs) time scales. Such configurations are predicted to be ideally unstable to magnetohydrodynamic tilting modes in which one-half of the torus shifts in the positive axial direction and the other half in the negative direction. These instabilities have been observed to grow and saturate at finite amplitude in the CSS as formation progresses. Stable operating regimes of fill pressure/loop voltage space have also been found. The relatively cold temperature (∼2 eV) of the plasma gives rise to a high classical resistivity, placing the Lundquist number (ratio of resistive to Alfvén time scales) between 0.5 and 10.0. It is proposed that resistivity, along with other dissipation mechanisms such as viscosity and ion–neutral friction, are responsible for the observed stability. Experiments were performed to explore these stability issues. A nonlinear, dynamical systems stability model that accounts for the effects of inductive current drive and dissipation has also been developed, and shows some agreement with the experimental results. The findings of this study are significant for two reasons: (1) It is one of the few clear observations of tilting modes in a FRC-like geometry; and (2) it provides an experimental study of ideally unstable modes in a configuration that does not escape the low Lundquist number regime, finding that the configuration appears stable below a Lundquist number of 0.5.

Resistive tearing-mode instability in a current sheet with equilibrium viscous stagnation-point flow

An analysis is presented of linear stability against tearing modes of a current sheet formed between two oppositely magnetized plasmas forced towards each other in two-dimensional steady stagnation-point flow. The velocity vector in this flow is confined to planes perpendicular to the reversing component of the magnetic field. The unperturbed state is an exact resistive and viscous equilibrium in which the resistive diffusion outwards from the current sheet is exactly balanced by the inward motion associated with the stagnation-point flow. Thus the behaviour of the tearing mode can be examined even when the resistive diffusion time is comparable to or smaller than the growth time of the instability. The linear ordinary differential equation describing the mode structure is integrated numerically. For large Lundquist number S and viscous Reynolds number Re the Furth-Killeen-Rosenbluth scaling of the growth rate is recovered with excellent accuracy. The influence of the stagnation-point flow on the tearing mode is as follows: (i) long-wavelength perturbations are stabilized so that the unstable regime falls between a short-wavelength and a long-wavelength marginal state; (ii) for sufficiently low Lundquist number (S < 12.25) the current sheet is completely stable to tearing-mode perturbations; (iii) the presence of high viscosity reduces the growth rate of the tearing instability. This effect is more important at small wavelength. Finally, application of the results from this study to the problem of solar-wind plasma flow past the earth's magnetosphere is briefly discussed.

Collisional tearing instability in the current sheet with a low magnetic Lundquist number

The growth rate of the collisional tearing instability is calculated for a current sheet with a low magnetic Lundquist number S. The maximum growth rate is found to be γm ≃ 0.075tA−1 tanh (8/S0.5) for 3 ≦ S ≦ 105, where tA is the Alfvén transit time in the current sheet. For S > 300, the growth rate can be written approximately as γm ≃ 0.6tA−1 S−0.5; for S < 50, the growth rate approaches an asymptotic value of ∼0.075tA−1. The present result is applicable to the current sheet associated with the diffusion region of a magnetic reconnection configuration, in which the Lundquist number, based on the thickness of the diffusion region, is typically 2 ≦ S ≦ 100.