The local dayside reconnection rate for oblique interplanetary magnetic fields

We present an analysis of local properties of magnetic reconnection at the dayside magnetopause for various interplanetary magnetic field (IMF) orientations in global magnetospheric simulations. This has heretofore not been practical because it is difficult to locate where reconnection occurs for oblique IMF, but new techniques make this possible. The approach is to identify magnetic separators, the curves separating four regions of differing magnetic topology, which map the reconnection X-line. The electric field parallel to the X-line is the local reconnection rate. We compare results to a simple model of local two-dimensional asymmetric reconnection. To do so, we find the plasma parameters that locally drive reconnection in the magnetosheath and magnetosphere in planes perpendicular to the X-line at a large number of points along the X-line. The global magnetohydrodynamic simulations are from the three-dimensional Block-Adaptive, Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code with a uniform resistivity, although the techniques described here are extensible to any global magnetospheric simulation model. We find that the predicted local reconnection rates scale well with the measured values for all simulations, being nearly exact for due southward IMF. However, the absolute predictions differ by an undetermined constant of proportionality, whose magnitude increases as the IMF clock angle changes from southward to northward. We also show similar scaling agreement in a simulation with oblique southward IMF and a dipole tilt. The present results will be an important component of a full understanding of the local and global properties of dayside reconnection.Comment: 12 pages, 7 figures, 1 table, Submitted to Journal Geophysical Research Space Physics February 12, 2016; Revised April 28, 201

A New Electric Field in Asymmetric Magnetic Reconnection

We present a theory and numerical evidence for the existence of a previously unexplored in-plane electric field in collisionless asymmetric magnetic reconnection. This electric field, dubbed the "Larmor electric field," is associated with finite Larmor radius effects and is distinct from the known Hall electric field. Potentially, it could be an important indicator for the upcoming Magnetospheric Multiscale (MMS) mission to locate reconnection sites as we expect it to appear on the magnetospheric side, pointing Earthward, at the dayside magnetopause reconnection site.Comment: 5 pages, 3 figures, to be published in Physical Review Letter

Pressure-Strain Interaction: III. Particle-in-Cell Simulations of Magnetic Reconnection

How energy is converted into thermal energy in weakly collisional and collisionless plasma processes such as magnetic reconnection and plasma turbulence has recently been the subject of intense scrutiny. The pressure-strain interaction has emerged as an important piece, as it describes the rate of conversion between bulk flow and thermal energy density. In two companion studies, we presented an alternate decomposition of the pressure-strain interaction to isolate the effects of converging/diverging flow and flow shear instead of compressible and incompressible flow, and we derived the pressure-strain interaction in magnetic field-aligned coordinates. Here, we use these results to study pressure-strain interaction during two-dimensional anti-parallel magnetic reconnection. We perform particle-in-cell simulations and plot the decompositions in both Cartesian and magnetic field-aligned coordinates. We identify the mechanisms contributing to positive and negative pressure-strain interaction during reconnection. This study provides a roadmap for interpreting numerical and observational data of the pressure-strain interaction, which should be important for studies of reconnection, turbulence, and collisionless shocks.Comment: 18 pages, 7 figures, accepted to Physics of Plasma

Catastrophe Model for the Onset of Fast Magnetic Reconnection

Solar flares, magnetic substorms and sawtooth crashes in fusion devices are explosive events in which magnetic reconnection facilitates the rapid release of energy stored in stressed magnetic fields into the surrounding plasma. Much effort has gone into understanding how the energy is released so fast. Collisional (Sweet-Parker) reconnection, based on resistive magnetohydrodynamics (MHD), is a successful physical model but is far too slow to explain observed energy release rates. In collisionless (Hall) reconnection, dispersive waves introduced by the Hall effect lead to energy release rates fast enough to explain observations. However, the steady-state description does not address why reconnection is explosive. We present a fully nonlinear model for the dynamics of magnetic reconnection. Using scaling arguments and resistive Hall-MHD numerical simulations, we show that the Sweet-Parker solution only exists when the current sheet is thick enough, while the Hall solution only exists when the resistivity is small enough. Furthermore, we show that reconnection is bistable, i.e., both the Sweet-Parker and Hall solutions can exist for the same set of control parameters. The disappearance of steady-state solutions as a control parameter varies is interpreted as a saddle-node bifurcation. Three signatures of this model are verified with numerical simulations, including the existence of a heretofore unidentified unstable steady-state reconnection solution. We present a theoretical model motivating that the existence of saddle-node bifurcations is intimately related to the presence of dispersive waves caused by the Hall effect. This result has a potentially profound impact on the long-standing ``Onset Problem'', i.e., explaining how large amounts of free magnetic energy can be stored for a long time before being explosively released. During Sweet-Parker reconnection, magnetic energy accumulates because the energy release is very slow. When the thickness of the current sheet decreases past a critical value, the Sweet-Parker solution catastrophically disappears, causing a sudden transition to Hall reconnection which begins the fast release of the stored energy. We delineate scenarios for the catastrophic onset of Hall reconnection and discuss the impact of this model on observations of magnetic explosions, showing in particular that it is consistent with observations of reconnection events in the solar corona

Quantifying Energy Conversion in Higher Order Phase Space Density Moments in Plasmas

Weakly collisional and collisionless plasmas are typically far from local thermodynamic equilibrium (LTE), and understanding energy conversion in such systems is a forefront research problem. The standard approach is to investigate changes in internal (thermal) energy and density, but this omits energy conversion that changes any higher order moments of the phase space density. In this study, we calculate from first principles the energy conversion associated with all higher moments of the phase space density for systems not in LTE. Particle-in-cell simulations of collisionless magnetic reconnection reveal that energy conversion associated with higher order moments can be locally significant. The results may be useful in numerous plasma settings, such as reconnection, turbulence, shocks, and wave-particle interactions in heliospheric, planetary, and astrophysical plasmas.Comment: 16 pages, 3 figures, includes both main paper and supplementary materia

Scaling the Ion Inertial Length and Its Implications for Modeling Reconnection in Global Simulations

We investigate the use of artificially increased ion and electron kinetic scales in global plasma simulations. We argue that as long as the global and ion inertial scales remain well separated, (1) the overall global solution is not strongly sensitive to the value of the ion inertial scale, while (2) the ion inertial scale dynamics will also be similar to the original system, but it occurs at a larger spatial scale, and (3) structures at intermediate scales, such as magnetic islands, grow in a self‐similar manner. To investigate the validity and limitations of our scaling hypotheses, we carry out many simulations of a two‐dimensional magnetosphere with the magnetohydrodynamics with embedded particle‐in‐cell (MHD‐EPIC) model. The PIC model covers the dayside reconnection site. The simulation results confirm that the hypotheses are true as long as the increased ion inertial length remains less than about 5% of the magnetopause standoff distance. Since the theoretical arguments are general, we expect these results to carry over to three dimensions. The computational cost is reduced by the third and fourth powers of the scaling factor in two‐ and three‐dimensional simulations, respectively, which can be many orders of magnitude. The present results suggest that global simulations that resolve kinetic scales for reconnection are feasible. This is a crucial step for applications to the magnetospheres of Earth, Saturn, and Jupiter and to the solar corona.Key PointsThe effects of artificially increased kinetic scales are studied with MHD‐EPIC simulationsChanging the kinetic scales does not change the global solution significantlyIncreasing the kinetic scales makes global simulations with embedded kinetic regions feasiblePeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140018/1/jgra53815_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/140018/2/jgra53815.pd

Assessing the time dependence of reconnection with Poynting's theorem: MMS observations

We investigate the time dependence of electromagnetic-field-to-plasma energy conversion in the electron diffusion region of asymmetric magnetic reconnection. To do so, we consider the terms in Poynting's theorem. In a steady state there is a perfect balance between the divergence of the electromagnetic energy flux $\nabla \cdot \vec{S}$ and the conversion between electromagnetic field and particle energy $\vec{J} \cdot \vec{E}$. This energy balance is demonstrated with a particle-in-cell simulation of reconnection. We also evaluate each of the terms in Poynting's theorem during an observation of a magnetopause reconnection region by Magnetospheric Multiscale (MMS). We take the equivalence of both sides of Poynting's theorem as an indication that the errors associated with the approximation of each term with MMS data are small. We find that, for this event, balance between $\vec{J}\cdot\vec{E}=-\nabla\cdot\vec{S}$ is only achieved for a small fraction of the energy conversion region at/near the X-point. Magnetic energy was rapidly accumulating on either side of the current sheet at roughly three times the predicted energy conversion rate. Furthermore, we find that while $\vec{J}\cdot\vec{E}>0$ and $\nabla\cdot\vec{S}<0$ are observed, as is expected for reconnection, the energy accumulation is driven by the overcompensation for $\vec{J}\cdot\vec{E}$ by $-\nabla\cdot\vec{S}>\vec{J}\cdot\vec{E}$. We note that due to the assumptions necessary to do this calculation, the accurate evaluation of $\nabla\cdot\vec{S}$ may not be possible for every MMS-observed reconnection event; but if possible, this is a simple approach to determine if reconnection is or is not in a steady-state.Comment: Resubmitted to GRL after minor rev. on 1 February 201

The Importance of Heat Flux in Quasi-Parallel Collisionless Shocks

Collisionless plasma shocks are a common feature of many space and astrophysical systems and are sources of high-energy particles and non-thermal emission, channeling as much as 20\% of the shock's energy into non-thermal particles. The generation and acceleration of these non-thermal particles have been extensively studied, however, how these particles feed back on the shock hydrodynamics has not been fully treated. This work presents the results of self-consistent hybrid particle-in-cell simulations that show the effect of self-generated non-thermal particle populations on the nature of collisionless, quasi-parallel shocks. They contribute to a significant heat flux density upstream of the shock. Non-thermal particles downstream of the shock leak into the upstream region, taking energy away from the shock. This increases the compression ratio, slows the shock down, and flattens the non-thermal population's spectral index for lower Mach number shocks. We incorporate this into a revised theory for the Rankine-Hugoniot jump conditions that include this effect and it shows excellent agreement with simulations. The results have the potential to explain discrepancies between predictions and observations in a wide range of systems, such as inaccuracies of predictions of arrival times of coronal mass ejections and the conflicting radio and x-ray observations of intracluster shocks. These effects will likely need to be included in fluid modeling to accurately predict shock evolution.Comment: 7 pages, 3 figures, a lot of appendi

Scale Filtering Analysis of Kinetic Reconnection and its Associated Turbulence

Previously, using an incompressible von K\'arm\'an-Howarth formalism, the behavior of cross-scale energy transfer in magnetic reconnection and turbulence was found to be essentially identical to each other, independent of an external magnetic (guide) field, in the inertial and energy-containing ranges (Adhikari et al., Phys. Plasmas 30, 082904, 2023). However, this description did not account for the energy transfer in the dissipation range for kinetic plasmas. In this letter, we adopt a scale-filtering approach to investigate this previously unaccounted-for energy transfer channel in reconnection. Using kinetic particle-in-cell (PIC) simulations of antiparallel and component reconnection, we show that the pressure-strain (PS) interaction becomes important at scales smaller than the ion inertial length, where the nonlinear energy transfer term drops off. Also, the presence of a guide field makes a significant difference in the morphology of the scale-filtered energy transfer. These results are consistent with kinetic turbulence simulations, suggesting that the pressure strain interaction is the dominant energy transfer channel between electron scales and ion scales

Higher-order nonequilibrium term: Effective power density quantifying evolution towards or away from local thermodynamic equilibrium

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A forefront research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here, we introduce the ``higher-order non-equilibrium term'' (HORNET) effective power density that quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, namely magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, $\rm{Pi-D}$, and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8\% and 35\% for electrons and ions, respectively, for reconnection; up to 67\% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed.Comment: 19 pages (including references), 7 figure