Force-free current sheets are local plasma structures with field-aligned electric currents and approximately uniform plasma pressures. Such structures, widely found throughout the heliosphere, are sites for plasma instabilities and magnetic reconnection, the growth rate of which is controlled by the structure's current sheet configuration. Despite the fact that many kinetic equilibrium models have been developed for one-dimensional (1D) force-free current sheets, their two-dimensional (2D) counterparts, which have a magnetic field component normal to the current sheets, have not received sufficient attention to date. Here, using particle-in-cell simulations, we search for such 2D force-free current sheets through relaxation from an initial, magnetohydrodynamic equilibrium. Kinetic equilibria are established toward the end of our simulations, thus demonstrating the existence of kinetic force-free current sheets. Although the system currents in the late equilibrium state remain field aligned as in the initial configuration, the velocity distribution functions of both ions and electrons systematically evolve from their initial drifting Maxwellians to their final time-stationary Vlasov state. The existence of 2D force-free current sheets at kinetic equilibrium necessitates future work in discovering additional integrals of motion of the system, constructing the kinetic distribution functions, and eventually investigating their stability properties.
We discuss a family of Vlasov-Maxwell equilibrium distribution functions for current sheet equilibria that are intermediate cases between the Harris sheet and the force-free (or modified) Harris sheet. These equilibrium distribution functions have potential applications to space and astrophysical plasmas. The existence of these distribution function had been briefly discussed in by Harrison and Neukirch 2009, but here it is shown that their approach runs into problems in the limit where the guide field goes to zero. The nature of this problem will be discussed and an alternative approach will …
Sub-ion scale current sheets in kinetic Alfvén wave turbulence
Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）；Victoria University of Wellington（惠灵顿维多利亚大学）；Charles University, Faculty of Mathematics and Physics（查理斯大学数学物理学院）
We present analysis of 17,043 proton kinetic-scale current sheets collected over 124 days of Wind spacecraft measurements in the solar wind at 11 Samples/s magnetic field resolution. The current sheets have thickness $λ$ from a few tens to one thousand kilometers with typical value around 100 km or from about 0.1 to 10$λ_{p}$ in terms of local proton inertial length $λ_{p}$. We found that the current density is larger for smaller scale current sheets, $J_0\approx 6\; {\rm nA/m^2} \cdot (λ/100\;{\rm km})^{-0.56}$ , but does not statistically exceed critical value $J_A$ corresponding to the drif…
Non-equilibrium ionization (NEI) is essentially required for astrophysical plasma diagnostics once the plasma status departs from ionization equilibrium assumptions. In this work, we perform fast NEI calculations combined with magnetohydrodynamic (MHD) simulations and analyze the ionization properties of a Petschek-type magnetic reconnection current sheet during solar eruptions. Our simulation reveals Petschek-type slow-mode shocks in the classical Spitzer thermal conduction models and conduction flux-limitation situations. The results show that under-ionized features can be commonly found in …
In this paper we study the scaling relations for the triggering of the fast, or "ideal", tearing instability starting from equilibrium configurations relevant to astrophysical as well as laboratory plasmas that differ from the simple Harris current sheet configuration. We present the linear tearing instability analysis for equilibrium magnetic fields which a) go to zero at the boundary of the domain and b) contain a double current sheet system (the latter previously studied as a cartesian proxy for the m=1 kink mode in cylindrical plasmas). More generally, we discuss the critical aspect ratio …
One of the most important problems of magnetotail dynamics is the substorm onset and the related instability of the magneotail current sheet. Since the simplest 2D current sheet configuration with monotonic $B_z$ was proven to be stable to the tearing mode, the focus of the instability investigation moved to more specific configurations, e.g. kinetic current sheets with strong transient ion currents and current sheets with non-monotonic $B_z$ (local $B_z$ minima or/and peaks). Stability of the latter current sheet configuration has been studied both within kinetic and fluid approaches, whereas…
The integration of kinetic effects in fluid models is important for global simulations of the Earth's magnetosphere. We use a two-fluid ten moment model, which includes the pressure tensor and has been used to study reconnection, to study the drift kink and lower hybrid drift instabilities. Using a nonlocal linear eigenmode analysis, we find that for the kink mode, the ten moment model shows good agreement with kinetic calculations with the same closure model used in reconnection simulations, while the electromagnetic and electrostatic lower hybrid instabilities require modeling the effects of…
Emergence and Detection of Electron-Scale Current Sheets in Turbulence with MMS Observations and fully kinetic 3D simulations
University of Hawaii, Manoa（夏威夷大学马诺阿分校）；Univ Orleans（奥尔良大学）；Laboratory for Atmospheric and Space Physics, University of Colorado Boulder（科罗拉多大学博尔德分校大气与空间物理实验室）；University of Iowa（爱荷华大学）；Columbia University（哥伦比亚大学）
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Since kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless te…
A detailed investigation of the properties of a Vlasov-Maxwell equilibrium for the force-free Harris sheet
本文详细讨论了Harrison和Neukirch（Phys. Rev. Lett. 102，135003，2009）。将给出分布函数的推导和其一般性质及其对分布函数参数的依赖性的讨论。特别是，分布函数在两个速度分量中可以是单峰或多峰的，可能对稳定性有影响。将研究分布函数的形状对其参数值的依赖性，并讨论与宏观量（如当前板厚度）的关系。
Sweet-Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it forms. Formation can occur due to sheared, sub-Alfvénic incompressible flows which narrow the sheet. Standard tearing theory (Furth et al. 1963; Coppi et al. 1976; Rutherford 1973) is not immediately applicable to such forming sheets for two reasons: first, because the flow introduces terms not present in the standard calculation; second, because the changing equ…
Using fully kinetic simulations, we study the suppression of asymmetric reconnection in the limit where the diamagnetic drift speed >> Alfven speed and the magnetic shear angle is moderate. We demonstrate that the slippage between electrons and the magnetic flux facilitates reconnection, and can even result in fast reconnection that lacks one of the outflow jets. Through comparing a case where the diamagnetic drift is supported by the temperature gradient with a companion case that has a density gradient instead, we identify a robust suppression mechanism. The drift of the x-line is slowed dow…
Intermittency of heating in weakly collisional plasma turbulence is an active subject of research, with significant potential impact on understanding of the solar wind, solar corona and astrophysical plasmas. Recent studies suggest a role of vorticity in plasma heating. In magnetohydrodynamics small scale vorticity is generated near current sheets and this effect persists in kinetic plasma, as demonstrated here with hybrid and fully kinetic Particle-In-Cell (PIC) simulations. Furthermore, vorticity enhances local kinetic effects, with a generalized resonance condition selecting sign-dependent …
Many in-situ spacecraft observations have demonstrated that magnetic reconnection in the Earth's magnetotail is largely controlled by the pre-reconnection current sheet configuration. One of the most important thin current sheet characteristics is the preponderance of electron currents driven by strong polarized electric fields, which are commonly observed in the Earth's magnetotail well before the reconnection. We use particle-in-cell simulations to investigate magnetic reconnection in the 2D magnetotail current sheet with a finite magnetic field component normal to the current sheet and with…
Particle distributions in weakly collisional environments such as the magnetosphere have been observed to show deviations from the Maxwellian distribution. These can often be reproduced in kinetic simulations, but fluid models, which are used in global simulations of the magnetosphere, do not necessarily capture any of this. We apply the maximum entropy fluid closure of Levermore, which leads to well posed moment equations, to reconstruct particle distributions from a kinetic simulation in a reconnection region. Our results show that without information other than the moments, the model can re…
We present statistical analysis of 11,200 proton kinetic-scale current sheets (CS) observed by Parker Solar Probe during 10 days around the first perihelion. The CS thickness $λ$ is in the range from a few to 200 km with the typical value around 30 km, while current densities are in the range from 0.1 to 10\;$μ{\rm A/m^2}$ with the typical value around 0.7\;$μ{\rm A/m^2}$. These CSs are resolved thanks to magnetic field measurements at 73--290 Samples/s resolution. In terms of proton inertial length $λ_{p}$, the CS thickness $λ$ is in the range from about $0.1$ to $10λ_{p}$ with the typical va…
Magnetic reconnection can explosively release magnetic energy when opposing magnetic fields merge and annihilate through a current sheet, driving plasma jets and accelerating non-thermal particle populations to high energy, in plasmas ranging from space and astrophysical to laboratory scales. Through laboratory experiments and spacecraft observations, significant experimental progress has been made in demonstrating how fast dissipation and reconnection occurs in narrow, kinetic-scale current sheets. However, a challenge has been to demonstrate what triggers reconnection and how it proceeds rap…
Magnetic reconnection associated with the tearing instability occurring in double-current sheet systems is investigated within the framework of reduced resistive magnetohydrodynamics (MHD) in a two-dimensional Cartesian geometry. The explosive non linear phase is particularly explored using the adaptive finite-element FINMHD code. The critical aspect ratio, that is defined as the minimum $L/x_s$ ratio (with $L$ and $x_s$ being the periodic system length and half-distance between the two current layers respectively) necessary for non linear destabilization after the linear and early non linear …
The stability of electron current sheets embedded within the reconnection exhaust is studied with a 3D fully kinetic particle-in-cell simulation. The electron current layers studied here form self-consistently in a reconnection regime with a moderate guide field, are supported by electron pressure anisotropy with the pressure component parallel to the magnetic field direction larger than the perpendicular components, and extend well beyond electron kinetic scales. In 3D, in addition to drift instabilities common to nearly all reconnection exhausts, the regime considered also exhibits an electr…
We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner (Phys. Plasmas 20, 102117, 2013) to allow for non-uniform density and temperature profiles. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al. (Phys. Plasmas 22, 112902, 2015). In one limit of the parameters, we recover the model of Kolotkov et al., while another limit gives a linear force-free …
Although turbulence has been conjectured to be important for magnetic reconnection, still very little is known about its role in collisionless plasmas. Previous attempts to quantify the effect of turbulence on reconnection usually prescribed Alfvénic or other low-frequency fluctuations or investigated collisionless kinetic effects in just two-dimensional configurations and antiparallel magnetic fields. In view of this, we analyzed the kinetic turbulence self-generated by three-dimensional guide-field reconnection through force-free current sheets in frequency and wavenumber spaces, utilizing 3…
We attempt to model magnetic reconnection during the two-ribbon flare in the gravitationally stratified solar atmosphere with the Lundquist number of $S=10^6$ using 2D simulations. We found that the tearing mode instability leads to the inhomogeneous turbulence inside the reconnecting current sheet (CS) and invokes the fast phase of reconnection. Fast reconnection brings an extra dissipation of magnetic field which enhances the reconnection rate in an apparent way. The energy spectrum in the CS shows the power-law pattern and the dynamics of plasmoids governs the associated spectral index. We …
Magnetic reconnection is thought to be the dynamical mechanism underlying many explosive phenomena observed both in space and in the laboratory, though the question of how fast magnetic reconnection is triggered in such high Lundquist ($S$) number plasmas has remained elusive. It has been well established that reconnection can develop over timescales faster than those predicted traditionally once kinetic scales are reached. It has also been shown that, within the framework of resistive Magnetohydrodynamics (MHD), fast reconnection is achieved for thin enough sheets via the onset of the so-call…
Plasmoid solutions of the Hahm--Kulsrud--Taylor equilibrium model
The Hahm-Kulsrud（HK）[T. S. Hahm和R. M. Kulsrud，Phys. Fluids { \bf 28}，2412（1985）]，由共振周期边界扰动驱动的磁剪切等离子体板的解示出了完全屏蔽（电流片）和完全重连（磁岛）响应。在全球范围内，重联涉及解决磁流体动力学（MHD）平衡问题。在具有连续对称性的系统中，这种MHD平衡通常通过求解Grad-Shafranov方程来找到，而在平板几何中，该方程中的椭圆算子是2-D拉普拉斯算子。因此，假设适当的压力和极向电流分布，保角映射方法可以用来将一个解决方案转化为另一个不同的边界条件，给出一个连续的解决方案序列的形式部分重新连接的磁岛（等离子体团）分离的Syrovatsky电流片。这两个HK解决方案似乎是特殊情况。
Ion-Scale Current Sheets Embedded in Reconnection Jet Shear Layer of the Near-Sun Heliospheric Current Sheet
Chungbuk National University（忠北国立大学）；University of California, Berkeley（加州大学伯克利分校）；New Mexico Consortium（新墨西哥联盟）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
In a weakly collisional, low-electron-beta plasma, large-scale Alfvén turbulence transforms into inertial kinetic-Alfvén turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tend to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale $a$ in the plane per…
Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov-Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to anti-parallel reconnection happens as the system evolves. The…
Revisiting the MRX Electron Current Sheet Width with Semi-Collisional Kinetic Simulations at Hydrogen Mass Ratio
Princeton University（普林斯顿大学）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Korea Institute of Fusion Energy（韩国聚变能源研究所）
Magnetic flux ropes with helical field lines and strong core field are ubiquitous structures in space plasmas. Recently, kinetic-scale flux ropes have been identified by high-resolution observations from Magnetospheric Multiscale (MMS) spacecraft in the magnetosheath, which have drawn a lot of attention because of their non-ideal behavior and internal structures. Detailed investigation of flux rope structure and dynamics requires development of realistic kinetic models. In this paper, we generalize an equilibrium model to reconstruct a kinetic-scale flux rope previously reported via MMS observ…
The NASA Magnetospheric Multiscale mission has made in situ diffusion region and kinetic-scale resolution measurements of asymmetric magnetic reconnection for the first time, in the Earth's magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type magnetic field but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions…
