Resistive Tearing Instability Research Articles

Stratified Resistive Tearing Instability

Resistive tearing instabilities are common in fluids that are highly electrically conductive and carry strong currents. We determine the effect of stable stratification on the tearing instability under the Boussinesq approximation. Our results generalise previous work that considered only specific parameter regimes, and we show that the length scale of the fastest-growing mode depends non-monotonically on the stratification strength. We confirm our analytical results by solving the linearised equations numerically, and we discuss whether the instability could operate in the solar tachocline.

Modification of the resistive tearing instability with Joule heating by shear flow

We investigate the influence of background shear flow on linear resistive tearing instabilities with Joule heating for two compressible plasma slab configurations: a Harris current sheet and a force-free, shearing magnetic field that varies its direction periodically throughout the slab, possibly resulting in multiple magnetic nullplanes. To do so, we exploit the latest version of the open-source, magnetohydrodynamic spectroscopy tool Legolas. Shear flow is shown to dramatically alter tearing behavior in the presence of multiple magnetic nullplanes, where the modes become propagating due to the flow. Finally, the tearing growth rate is studied as a function of resistivity, showing where it deviates from analytic scaling laws, as well as the Alfvén speed, the plasma-β, and the velocity parameters, revealing surprising nuance in whether the velocity acts stabilizing or destabilizing. We show how both slab setups can produce growth rate regimes, which deviate from analytic scaling laws, such that systematic numerical spectroscopic studies are truly necessary, for a complete understanding of linear tearing behavior in flowing plasmas.

Three-dimensional Modeling of the Magnetothermal Evolution of Neutron Stars: Method and Test Cases

Abstract Neutron stars harbor extremely strong magnetic fields within their solid outer crust. The topology of this field strongly influences the surface temperature distribution and, hence, the star’s observational properties. In this work, we present the first realistic simulations of the coupled crustal magnetothermal evolution of isolated neutron stars in three dimensions accounting for neutrino emission, obtained with the pseudo-spectral code parody. We investigate both the secular evolution, especially in connection with the onset of instabilities during the Hall phase, and the short-term evolution following episodes of localized energy injection. Simulations show that a resistive tearing instability develops in about a Hall time if the initial toroidal field exceeds G. This leads to crustal failures because of the huge magnetic stresses coupled with the local temperature enhancement produced by dissipation. Localized heat deposition in the crust results in the appearance of hot spots on the star surface, which can exhibit a variety of patterns. Because the transport properties are strongly influenced by the magnetic field, the hot regions tend to drift away and get deformed following the magnetic field lines while cooling. The shapes obtained with our simulations are reminiscent of those recently derived from NICER X-ray observations of the millisecond pulsar PSR J0030+0451.

A fundamental understanding of the unstable eigenmodes of double tearing instabilities in a shear slab geometry

Two types of unstable eigenmodes of resistive tearing instabilities, namely, symmetric and anti-symmetric modes, in a double current sheet configuration are analyzed by means of both an eigenvalue solver and initial value simulation. It has been clearly identified that these two types of eigenmodes are different from the two independent single tearing modes even though the symmetric eigenmode in a double current sheet configuration shares the same properties of the single tearing mode near each current sheet. In the case with finite separation Δx between two current sheets, an arbitrary phase disturbance between two current sheets can lead to “phase instability,” i.e., the transition from the symmetric mode to the anti-symmetric mode. For a large Δx limit, both anti-symmetric and symmetric modes share the same properties of the single tearing mode. Thus, the superposition of two independent single tearing modes with arbitrary phases and arbitrary amplitudes at two current sheets can become the linear combination of symmetric and anti-symmetric eigenmodes. The same growth rate/eigenvalue of symmetric and anti-symmetric eigenmodes infers that an arbitrary superposition of two independent single tearing modes is still the eigenmode of the double current sheet configuration.

Relativistic HPIC-LBM and its application in large temporal-spatial turbulent magnetic reconnection. Part II. Role of turbulence in the flux rope interaction

Quantitatively analyzing the role of turbulence in the magnetic fluctuation-induced self-generating-organization region and the plasma turbulence-induced self-feeding-sustaining region, which is closely related to the evolution of null points and the magnetic helical structure, represents the key issues in understanding the magnetic energy release-conversion, plasma heating, and charged particles energization and acceleration in three-dimensional large temporal-spatial scale turbulent magnetic reconnection (3D LTSTMR). The first part of this two-paper series developed and validated the continuous kinetic-dynamic-hydro fully coupled temporal-spatial scale relativistic hybrid particle-in-cell and lattice Boltzmann (RHPIC-LBM) model and code for investigating the fine structure evolution of the 2.5D solar atmosphere LTSTMR activities. Based on the model and code developed in Part I, in this paper, we investigate the turbulence of the magnetic helical structure, current density vector fields, self-generating-organization magnetic potential vector fields, self-feeding-sustaining plasma motion, and the ion and electron acceleration of 3D LTSTMR with 100,000 CPU cores on the Tianhe-2 from National Supercomputer Center in Guang Zhou (NSCC-GZ). According to the simulation evidence, we discovered and confirmed the following results: (i) Slipping magnetic reconnection (MR) exists in the adjacent magnetic field lines (MFLs) during the compress-stretch-slip process on the quasi-separatrix layers (QSLs and MFLs drastically change and form a linkage span) and the adjacent MFLs’ break-rejoin MR exists on the separatrix surfaces (SLs). Both are consistent to observations; (ii) The slipping MR (defined as 1st type MR) and the MFLs’ break-rejoin MR (defined as 2nd type MR) are closely linked with the oblique and resistive tearing instabilities, respectively. In the 3D model, the 1st type MR forms O-type null points, while the 2nd type MR forms X-type null points. The magnetic energy conversion is dominated by turbulence-induced oblique instabilities in the 3D model instead of the resistive tearing instabilities in the 2D/2.5D model, which is consistent with the 3D observations; (iii) Magnetic energy conversion occurs in the interaction of the plasmoid-to-flux rope, plasmoid-to-plasmoid, and flux rope-to-flux rope. The turbulent acceleration is an independent acceleration mechanism in LTSTMR, induced by the interaction of waves-to-waves and waves-to-particles, which is different from the original hybrid acceleration mechanism (composed of parallel electric fields, betatron, shock and Fermi) ; (iv) Particles can be energized and accelerated at a longer time scale (−30 s) and can be accelerated to relativistic energies after being pre-accelerated by a Fermi-Betatron-shock wave acceleration process. These results are in agreement with the observations.

On the Hall-mediated resistive tearing instability of highly elongated current sheets

The present paper provides a comprehensive description of various regimes involved in the two-fluid model of resistive tearing instability. These include two novel regimes of this instability, which correspond to the long-wave modes that can develop in a highly elongated current sheet. This issue is relevant to the study of fast magnetic reconnection and magnetic turbulence in magnetohydrodynamic objects with a large value of the Lundquist number.

Generation Mechanism for Interlinked Flux Tubes on the Magnetopause

AbstractWe use a global magnetohydrodynamics simulation to analyze transient magnetic reconnection processes at the magnetopause. The solar wind conditions have been kept constant, and an interplanetary magnetic field with large duskward BY and southward BZ components has been imposed. Five flux transfer events (FTEs) with clear bipolar magnetic field signatures have been observed. We observed a peculiar structure defined as interlinked flux tubes (IFTs) in the first and fourth FTE, which had very different generation mechanisms. The first FTE originates as an IFTs and remains with this configuration until its final moment. However, the fourth FTE develops as a classical flux rope but changes its 3‐D magnetic configuration to that of IFTs. This work studies the mechanism for generating IFTs. The growth of the resistive tearing instability has been identified as the cause for the first IFTs formation. We believe that the instability has been triggered by the accumulation of interplanetary magnetic field at the subsolar point where the grid resolution is very high. The evidence shows that two new reconnection lines form northward and southward of the subsolar region. The IFTs have been generated with all the classical signatures of a single flux rope. The other IFTs detected in the fourth FTE developed as a result of magnetic reconnection inside its complex and twisted magnetic fields, which leads to a change in the magnetic configuration from a flux rope of twisted magnetic field lines to IFTs.

Verification of linear resistive tearing instability with gyrokinetic particle code VirtEx

Current-driven resistive tearing instability is verified using the newly developed global first-principles particle-in-cell code called VirtEx, which was coded from scratch in conformity with the C++'11 specifications. The tearing instability is first verified in the fluid limit in a cylinder geometry by ignoring the gyrokinetic effect of ions, and the numerical results agree well with the analytical predictions of the resistive tearing theory. Then, the effect of toroidicity on resistive tearing instability is investigated.

Resistive tearing instability in electron MHD: application to neutron star crusts

We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the Electron-MHD limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as $\gamma \propto B^{2/3} \sigma^{-1/3}$ where $B$ is the magnetic field and $\sigma$ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane parallel configuration where the magnetic field polarity reverses, through simulations of systems initiating in Hall equilibrium with some superimposed perturbation. Following a transient phase, during which there is some minor rearrangement of the magnetic field, the perturbation grows exponentially. Once the instability is fully developed the magnetic field forms the characteristic islands and X-type reconnection points, where Ohmic decay is enhanced. We discuss the implications of this instability for the local magnetic field evolution in neutron stars' crusts, proposing that it can contribute to heating near the surface of the star, as suggested by models of magnetar post-burst cooling. In particular, we find that a current sheet a few meters thick, covering as little as $1\%$ of the total surface can provide $10^{42}~$erg in thermal energy within a few days. We briefly discuss applications of this instability in other systems where the Hall effect operates such as protoplanetary discs and space plasmas.

Investigation of the non-linear magnetic reconnection in solar chromosphere

برای مشاهده وقوع باز اتصالی مغناطیسی در کروموسفر خورشیدی، رفتار اختلالات غیرخطی در معادلات مغناطوهیدرودینامیکی (MHD) بررسی می‌شود. مطالعه عددی ناپایداری برشی مقاومتی در یک صفحه‌ی جریان با در نظر گرفتن چارچوب MHD معرفی می‌گردد. برای این منظور، مدل چهار میدان استفاده می‌شود. بر اساس شبیه سازی انجام شده نشان داده می‌شود که جملات غیرخطی باعث می‌شوند تا باز اتصالی سریعتر و در مقیاس زمانی طول عمر اسپیکول‌ها در کروموسفر اتفاق بیفتد.

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x-z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.

Density-shear instability in electron magneto-hydrodynamics

We discuss a novel instability in inertia-less electron magneto-hydrodynamics (EMHD), which arises from a combination of electron velocity shear and electron density gradients. The unstable modes have a lengthscale longer than the transverse density scale, and a growth-rate of the order of the inverse Hall timescale. We suggest that this density-shear instability may be of importance in magnetic reconnection regions on scales smaller than the ion skin depth, and in neutron star crusts. We demonstrate that the so-called Hall drift instability, previously argued to be relevant in neutron star crusts, is a resistive tearing instability rather than an instability of the Hall term itself. We argue that the density-shear instability is of greater significance in neutron stars than the tearing instability, because it generally has a faster growth-rate and is less sensitive to geometry and boundary conditions. We prove that, for uniform electron density, EMHD is “at least as stable” as regular, incompressible MHD, in the sense that any field configuration that is stable in MHD is also stable in EMHD. We present a connection between the density-shear instability in EMHD and the magneto-buoyancy instability in anelastic MHD.

Plasmoid formation in current sheet with finite normal magnetic component.

Current sheet configurations in natural and laboratory plasmas are often accompanied by a finite normal magnetic component that is known to stabilize the two-dimensional resistive tearing instability in the high Lundquist number regime. Recent magnetohydrodynamic simulations indicate that the nonlinear development of ballooning instability is able to induce the formation of X lines and plasmoids in a generalized Harris sheet with a finite normal magnetic component in the high Lundquist number regime where the linear two-dimensional resistive tearing mode is stable.

Alfvén resonance induced by two types of m/n = 2/2 MHD instabilities in a rotating cylindrical plasma

Alfvén resonances induced by two types of m/n = 2/2 magnetohydrodynamic (MHD) instabilities in rotating plasmas are investigated numerically using a cylindrical MHD model. It is shown that the m/n = 2/2 tearing mode is destabilized in the small rotation regime and stabilized in the sufficiently large rotation regime. The results are verified by previous theories on resistive tearing instabilities in flowing plasmas. Another unstable branch, i.e. the Kelvin–Helmholtz (KH) instability, can be excited by linearly sheared plasma rotation in the absence of an inflection point, which is generally required for driving the KH instability in an ordinary fluid. Both the m/n = 2/2 tearing mode and the m/n = 2/2 KH mode can induce Alfvén resonances. The resonance conditions and the radial profiles of the resonance currents are discussed in detail.

Comment on “Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability” [Phys. Plasmas 19, 072519 (2012)

Ahedo and Ramos [Phys. Plasmas 19, 072519 (2012)] revisited what they called the supersonic regime of the Hall-mediated resistive tearing instability and arrived to results that disagree with the previously known ones (Fruchtman and Strauss [Phys. Fluids B 5, 1408 (1993)], Bian and Vekstein [Phys. Plasmas 14, 072107 (2007)]). The present Comment aims to clarify the origin of this disagreement and to confirm in this way the validity of the earlier findings.

Response to “Comment on ‘Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability’” [Phys. Plasmas 20, 014703 (2013)

The Comment by Vekstein and Kusano repeats conclusions of Bian and Vekstein [Phys. Plasmas 14, 072107 (2007)] which were inferred from order of magnitude estimates and missed crucial fine details of the problem. The Comment does not show any actual solution to substantiate them, therefore we do not deem that it provides a valid clarification or counterargument to our mathematically proven result, which covers a parametric range down to β=0.

Supersonic regime of the Hall-magnetohydrodynamics resistive tearing instability

An earlier analysis of the Hall-magnetohydrodynamics (MHD) tearing instability [E. Ahedo and J. J. Ramos, Plasma Phys. Controlled Fusion 51, 055018 (2009)] is extended to cover the regime where the growth rate becomes comparable or exceeds the sound frequency. Like in the previous subsonic work, a resistive, two-fluid Hall-MHD model with massless electrons and zero-Larmor-radius ions is adopted and a linear stability analysis about a force-free equilibrium in slab geometry is carried out. A salient feature of this supersonic regime is that the mode eigenfunctions become intrinsically complex, but the growth rate remains purely real. Even more interestingly, the dispersion relation remains of the same form as in the subsonic regime for any value of the instability Mach number, provided only that the ion skin depth is sufficiently small for the mode ion inertial layer width to be smaller than the macroscopic lengths, a generous bound that scales like a positive power of the Lundquist number.

MOMENTUM TRANSPORT FROM CURRENT-DRIVEN RECONNECTION IN ASTROPHYSICAL DISKS

Current-driven reconnection is investigated as a possible mechanism for angular momentum transport in astrophysical disks. A theoretical and computational study of angular momentum transport from current-driven magnetohydrodynamic instabilities is performed. It is found that both a single resistive tearing instability and an ideal instability can transport momentum in the presence of azimuthal Keplerian flow. The structure of the Maxwell stress is examined for a single mode through analytic quasilinear theory and computation. Full nonlinear multiple mode computation shows that a global Maxwell stress causes significant momentum transport.

Effects of line tying on resistive tearing instability in slab geometry

The effects of line tying on resistive tearing instability in slab geometry are studied within the framework of reduced magnetohydrodynamics [B. B. Kadomtsev and O. P. Pogutse, Sov. Phys. JETP 38, 283 (1974); H. R. Strauss, Phys. Fluids 19, 134 (1976)]. It is found that line tying has a stabilizing effect. The tearing mode is stabilized when the system length L is shorter than a critical length Lc, which is independent of the resistivity η. When L is not too much longer than Lc, the growth rate γ is proportional to η. When L is sufficiently long, the tearing mode scaling γ∼η3/5 is recovered. The transition from γ∼η to γ∼η3/5 occurs at a transition length Lt∼η−2/5.

Two-fluid regimes of the resistive and collisionless tearing instability

The two-fluid (electrons and ions) plasma description is used to investigate spontaneous magnetic reconnection (tearing instability) in a sheared force-free magnetic configuration. The study includes both collisional (resistive) and collisionless (electron inertia) reconnection mechanisms. Together with the Hall effect, this yields various instability regimes, which can be identified by the magnitude of the four nondimensional parameters: Lundquist number S⪢1, electron/ion mass ratio μ≡me∕mi⪡1, plasma β, and the scaled ion inertial skin-depth di=c∕(ωpil), with l being the shear length of the magnetic field. The role of the electron gyroviscosity in the collisionless case is also clarified.