Search

We develop a first-principles scaling theory of the spreading of three-dimensional (3D) magnetic reconnection of finite extent in the out of plane direction. This theory addresses systems with or without an out of plane (guide) magnetic field, and with or without Hall physics. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory. New results include the following: (1) reconnection spreads in a particular direction if an x-line is induced at the interface between reconnecting and non-reconnecting regions, which is controlled by the out of plane gradient of the electric field in the outflow direction. (2) The spreading mechanism for anti-parallel collisionless reconnection is convection, as is known, but for guide field reconnection it is magnetic field bending. We confirm the theory using 3D two-fluid and resistive-magnetohydrodynamics simulations. (3) The theory explains why anti-parallel reconnection in resistive-magnetohydrodynamics does not spread. (4) The simulation domain aspect ratio, associated with the free magnetic energy, influences whether reconnection spreads or convects with a fixed x-line length. (5) We perform a simulation initiating anti-parallel collisionless reconnection with a pressure pulse instead of a magnetic perturbation, finding spreading is unchanged rather than spreading at the magnetosonic speed as previously suggested. The results provide a theoretical framework for understanding spreading beyond systems studied here and are important for applications including two-ribbon solar flares and reconnection in Earth's magnetosphere.

Using kinetic particle-in-cell (PIC) simulations, we simulate reconnection conditions appropriate for the magnetosheath and solar wind, i.e., plasma beta (ratio of gas pressure to magnetic pressure) greater than 1 and low magnetic shear (strong guide field). Changing the simulation domain size, we find that the ion response varies greatly. For reconnecting regions with scales comparable to the ion Larmor radius, the ions do not respond to the reconnection dynamics leading to ''electron-only'' reconnection with very large quasi-steady reconnection rates. The transition to more traditional ''ion-coupled'' reconnection is gradual as the reconnection domain size increases, with the ions becoming frozen-in in the exhaust when the magnetic island width in the normal direction reaches many ion inertial lengths. During this transition, the quasi-steady reconnection rate decreases until the ions are fully coupled, ultimately reaching an asymptotic value. The scaling of the ion outflow velocity with exhaust width during this electron-only to ion-coupled transition is found to be consistent with a theoretical model of a newly reconnected field line. In order to have a fully frozen-in ion exhaust with ion flows comparable to the reconnection Alfv\'en speed, an exhaust width of at least several ion inertial lengths is needed. In turbulent systems with reconnection occurring between magnetic bubbles associated with fluctuations, using geometric arguments we estimate that fully ion-coupled reconnection requires magnetic bubble length scales of at least several tens of ion inertial lengths.

Magnetic island equilibria resulting from reconnection in magnetohydrodynamic (MHD) simulations are explored in a two-dimensional slab geometry. Magnetic islands are evolved to finite amplitude with a nonzero resistivity. The resistivity and flows are then set to zero and the system is allowed to relax toward equilibrium. A y-type singular current layer in the equilibrium state is identified for all but systems with the smallest values of the tearing mode stability parameter Δ′. It is shown that the length of the equilibrium y line tracks the length of the Sweet–Parker current layer that develops during reconnection. This suggests that the formation of Sweet–Parker current layers during magnetic reconnection in the resistive MHD model is a consequence of the presence of a singularity in post-reconnection state. A threshold in Δ′ for singular behavior is also identified.

The scaling of the reconnection rate is examined in situations in which the equilibrium current supporting a reversed magnetic field has a spatial scale length that is much greater than all nonmagnetohydrodynamic (non-MHD) kinetic scales. In this case, denoted as embedded reconnection, the narrow non-MHD region around the x-line where dissipation is important is embedded inside of a much larger equilibrium current sheet. In this system, the magnetic field just upstream of this non-MHD region, Bd, changes significantly during the reconnection process. This wide equilibrium current sheet is contrasted with the very thin equilibrium current sheets of width c/ωpi used in previous simulations to establish the importance of the Hall term in Ohm’s law in allowing fast reconnection in large scale collisionless systems. In the present study we lay out a procedure for determining Bd directly from simulation data and use this value to renormalize the reconnection rate using Sweet–Parker-like scaling arguments. Using two-dimensional two-fluid simulations, we find that the time evolution of the reconnection process can be broken into two phases: A developmental phase that is quite long and strongly dependent on system size and presumably the dissipation mechanisms, and a fast asymptotic phase in which the flow velocity into the x-line is on the order of 0.1 of the Alfven speed based on Bd. The reconnection rate during the asymptotic phase is independent of system size and the majority of island growth and flux reconnection occurs during this phase. The time to reconnect a significant amount of magnetic flux is roughly consistent with solar flare timescales.

Dissipation of plasma turbulent energy is a phenomenon having significant implications for the heating of the solar corona and solar wind. While processes involving linear wave damping, stochastic heating, and reconnection have been postulated as contributors to heating mechanisms, the relative role that they play is not currently understood. In this manuscript, we establish a theoretical framework for applying reconnection heating predictions to turbulent systems. Kinetic particle-in-cell (PIC) simulations are used to study heating due to reconnection, and these results are then adapted to a turbulent medium. First, the factors controlling the heating of plasmas in reconnection exhausts are examined using laminar reconnection simulations; predictions for heating are determined which require only the plasma conditions just upstream of the reconnection diffusion region as input. The laminar predictions are then applied to PIC simulations of turbulence. Key assumptions are: (1) the plasma conditions just up...

Electron bulk heating during magnetic reconnection with symmetric inflow conditions is examined using kinetic particle-in-cell (PIC) simulations. The degree of electron heating is well correlated with the inflowing Alfv\'en speed $c_{Ar}$ based on the reconnecting magnetic field through the relation $\Delta T_e = 0.033 \,m_i\,c_{Ar}^2$, where $\Delta T_{e}$ is the increase in electron temperature. For the range of simulations performed, the heating shows almost no correlation with inflow total temperature $T_{tot} = T_i + T_e$ or plasma $\beta$. An out-of-plane (guide) magnetic field of similar magnitude to the reconnecting field does not affect the total heating, but it does quench perpendicular heating, with almost all heating being in the parallel direction. These results are qualitatively consistent with a recent statistical survey of electron heating in the dayside magnetopause, which also found that $\Delta T_e$ was proportional to the inflowing Alfv\'en speed. The net electron heating varies very little with distance downstream of the x-line. The simulations show at most a very weak dependence of electron heating on the ion to electron mass ratio. In the antiparallel reconnection case, the largely parallel heating is eventually isotropized downstream due a scattering mechanism such as stochastic particle motion or instabilities. The study highlights key properties that must be satisfied by an electron heating mechanism: (1) Preferential heating in the parallel direction; (2) Heating proportional to $m_i\,c_{Ar}^2$; (3) At most a weak dependence on electron mass; and (4) An exhaust electron temperature that varies little with distance from the x-line., Comment: 27 pages, 1 table, 7 figures. Submitted to Physics of Plasmas

An unsolved problem in plasma turbulence is how energy is dissipated at small scales. Particle collisions are too infrequent in hot plasmas to provide the necessary dissipation. Simulations either treat the fluid scales and impose an ad hoc form of dissipation (e.g., resistivity) or consider dissipation arising from resonant damping of small amplitude disturbances where damping rates are found to be comparable to that predicted from linear theory. Here, we report kinetic simulations that span the macroscopic fluid scales down to the motion of electrons. We find that turbulent cascade leads to generation of coherent structures in the form of current sheets that steepen to electron scales, triggering strong localized heating of the plasma. The dominant heating mechanism is due to parallel electric fields associated with the current sheets, leading to anisotropic electron and ion distributions which can be measured with NASA's upcoming Magnetospheric Multiscale mission. The motion of coherent structures also generates waves that are emitted into the ambient plasma in form of highly oblique compressional and shear Alfven modes. In 3D, modes propagating at other angles can also be generated. This indicates that intermittent plasma turbulence will in general consist of both coherent structures and waves. However, the current sheet heating is found to be locally several orders of magnitude more efficient than wave damping and is sufficient to explain the observed heating rates in the solar wind.

We perform a systematic study of the effect of inflow density on reconnection diffusion regions using a 2.5-D particle-in-cell code. The diffusion region structures are analyzed at times when all simulations have reconnected the same amount of magnetic flux. We find that reducing the inflow density from 1 to 1/100th of the current sheet density dramatically increases the diffusion region physical size and the reconnection rate. The width of the diffusion region scales with the upstream ion inertial length systematically. Consistent with the presence of counter-streaming inflowing ion beams near the x-line, the ion meandering width in the diffusion region also scales with the ion inertial length. The aspect ratio of the ion diffusion region remains a constant, independent of the inflow density. The quadrupole Hall magnetic field is reduced. The upstream magnetic field deviates from its asymptotic value by ∼50% at the lowest simulated inflow density. The downstream ion outflow velocity scales linearly with ...

The effect of driving frequency on the efficiency of turbulence generation through magnetic forcing is studied using kinetic hybrid simulations with fully kinetic ions and fluid electrons. The efficiency of driving is quantified by examining the energy input into magnetic field as well as the thermal energy for various driving frequencies. The driving is efficient in exciting turbulence and heating the plasma when the time period of the driving is larger than the nonlinear time of the system. For driving at faster time scales, the energy input is weak and the steady state energy is much lower. The heating of the plasma is correlated with intermittent properties of the magnetic field, which are manifested as non-Gaussian statistics. Implications for turbulence in solar corona are discussed.

The structure in space and time of a driven turbulent magnetoplasma is analyzed using kinetic simulations. For a two dimensional case with a strong uniform out-of-plane magnetic field, large scale driving produces a turbulent state that spans fluid scales to kinetic proton scales. There are fluid electrons in this hybrid representation. In near steady conditions, spectral analysis shows an almost complete absence of discrete point spectral features that would be associated with a dispersion relation and wave activity. While there is indication of a low level of wave activity, the results show that the dynamics are dominated by nonlinear activity. Implications for understanding plasma cascade, dissipation, and heating are discussed.

It was recently shown that magnetic reconnection exhibits bistability, where the Sweet–Parker (collisional) and Hall (collisionless) reconnection solutions are both attainable for the same set of system parameters. Here, a dynamical model based on saddle-node bifurcations is presented which reproduces the slow to fast transition. It is argued that the properties of the dynamical model are a result of the Hall effect and the dispersive physics associated with it. Evidence from resistive two-fluid and Hall magnetohydrodynamics simulations are presented that show that the time evolution agrees with the dynamical model, the outflow speed is correlated with the dispersive physics due to the Hall effect, and bistability persists in the absence of electron inertia.

Sweet–Parker (collisional) magnetic reconnection at high Lundquist number is modified by secondary islands. Daughton et al. [Phys. Rev. Lett. 103, 065004 (2009)] suggested the Sweet–Parker model governs the fragmented current sheet segments. If true, the reconnection rate would increase by the square root of the number of secondary islands. High Lundquist number resistive magnetohydrodynamic simulations are presented which agree, in a time-averaged sense, with the predicted scaling. This result may have important implications for energy storage before a solar eruption and its subsequent release.

The comment by Semenov et al. has called into question our derivation of the outflow velocity in asymmetric magnetic reconnection. We present three reasons that the analysis presented in the comment is incorrect. Most importantly, the authors of the comment have incorrectly applied results from one-dimensional shock theory to the problem of conservation through a two-dimensional dissipation region. For completeness, we compare their predictions to numerical simulation results, finding that their theory does not describe the data. We conclude the analysis in the comment is without merit.

The results of large-scale, particle-in-cell simulations are presented on the role of Hall electric and magnetic fields on the structure of the electron dissipation region and outflow exhaust during the collisionless magnetic reconnection of antiparallel fields. The simulations reveal that the whistler wave plays the key role in driving the electrons away from the magnetic x-line. Further downstream the electron outflow exhaust consists of a narrow super-Alfvenic jet, which remains collimated far downstream of the x-line, flanked by a pedestal whose width increases monotonically with increasing distance downstream. The open outflow exhaust, which is required for fast reconnection in large systems, is driven by the Hall electric and magnetic fields. Finally, it is the whistler that ultimately facilitates fast reconnection by diverting the electrons flowing toward the current layer into the outflow direction and thereby limiting the length of this layer. The results are contrasted with reconnection in an electron-positron plasma where the Hall fields are absent. The consequence of the expanding outflow exhaust is that, consistent with recent observations, the extended super-Alfvenic electron outflow jet carries a smaller and smaller fraction of the outflowing electrons with increasing distance downstream of the x-line. The results suggest that the structure of the electron current layer and exhaust in simulations might be sensitive to boundary conditions unless the simulation boundary along the outflow direction is sufficiently far from the x-line.

A Sweet-Parker-type scaling analysis for asymmetric antiparallel reconnection (in which the reconnecting magnetic field strengths and plasma densities are different on opposite sides of the dissipation region) is performed. Scaling laws for the reconnection rate, outflow speed, the density of the outflow, and the structure of the dissipation region are derived from first principles. These results are independent of the dissipation mechanism. It is shown that a generic feature of asymmetric reconnection is that the X-line and stagnation point are not colocated, leading to a bulk flow of plasma across the X-line. The scaling laws are verified using two-dimensional resistive magnetohydrodynamics numerical simulations for the special case of asymmetric magnetic fields with symmetric density. Observational signatures and applications to reconnection in the magnetosphere are discussed.

It was recently shown that the slow (collisional) Sweet-Parker and the fast (collisionless) Hall magnetic reconnection solutions simultaneously exist for a wide range of resistivities; reconnection is bistable [Cassak, Shay, and Drake, Phys. Rev. Lett., 95, 235002 (2005)]. When the thickness of the dissipation region becomes smaller than a critical value, the Sweet-Parker solution disappears and fast reconnection ensues, potentially explaining how large amounts of magnetic free energy can accrue without significant release before the onset of fast reconnection. Two-fluid numerical simulations extending the previous results for anti-parallel reconnection (where the critical thickness is the ion skin depth) to component reconnection with a large guide field (where the critical thickness is the thermal ion Larmor radius) are presented. Applications to laboratory experiments of magnetic reconnection and the sawtooth crash are discussed.

This paper presents two-fluid simulations of forced magnetic reconnection with finite electron inertia in a collisionless three-dimensional (3D) cube with periodic boundaries in all three directions. Comparisons are made to analogous two-dimensional (2D) simulations. Reconnection in this system is driven by a spatially localized forcing function that is added to the ion momentum equation inside the computational domain. Consistent with previous results in similar, but larger forced 2D simulations [B. Sullivan, B. N. Rogers, and M. A. Shay, Phys. Plasmas 12, 122312 (2005)], for sufficiently strong forcing the reconnection process is found to become Alfvenic in both 2D and 3D, i.e., the inflow velocity scales roughly like some fraction of the Alfven speed based on the upstream reconnecting magnetic field, and the system takes on a stable configuration with a dissipation region aspect ratio on the order of 0.15.

We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we calculate kinetic entropy in two forms -- the ``combinatorial'' form related to the logarithm of the number of microstates per macrostate and the ``continuous'' form related to $f \ln f$, where $f$ is the particle distribution function. We discuss the advantages and disadvantages of each and discuss subtleties about implementing them in PIC codes. Using collisionless PIC simulations that are two-dimensional in position space and three-dimensional in velocity space, we verify the implementation of the kinetic entropy diagnostics and discuss how to optimize numerical parameters to ensure accurate results. We show the total kinetic entropy is conserved to three percent in an optimized simulation of anti-parallel magnetic reconnection. Kinetic entropy can be decomposed into a sum of a position space entropy and a velocity space entropy, and we use this to investigate the nature of kinetic entropy transport during collisionless reconnection. We find the velocity space entropy of both electrons and ions increases in time due to plasma heating during magnetic reconnection, while the position space entropy decreases due to plasma compression. This project uses collisionless simulations, so it cannot address physical dissipation mechanisms; nonetheless, the infrastructure developed here should be useful for studies of collisional or weakly collisional heliospheric, planetary, and astrophysical systems. Beyond reconnection, the diagnostic is expected to be applicable to plasma turbulence and collisionless shocks., 20 pages, 7 figures