Joachim Birn

Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge

The Geospace Environmental Modeling (GEM) Reconnection Challenge project is presented and the important results, which are presented in a series of companion papers, are summarized. Magnetic reconnection is studied in a simple Harris sheet configuration with a specified set of initial conditions, including a finite amplitude, magnetic island perturbation to trigger the dynamics. The evolution of the system is explored with a broad variety of codes, ranging from fully electromagnetic particle in cell (PIC) codes to conventional resistive magnetohydrodynamic (MHD) codes, and the results are compared. The goal is to identify the essential physics which is required to model collisionless magnetic reconnection. All models that include the Hall effect in the generalized Ohms law produce essentially indistinguishable rates of reconnection, corresponding to nearly Alfvenic inflow velocities. Thus the rate of reconnection is insensitive to the specific mechanism which breaks the frozen-in condition, whether resistivity, electron inertia, or electron thermal motion. The reconnection rate in the conventional resistive MHD model, in contrast, is dramatically smaller unless a large localized or current dependent resistivity is used. The Hall term brings the dynamics of whistler waves into the system. The quadratic dispersion property of whistlers (higher phase speed at smaller spatial scales) is the key to understanding these results. The implications of these results for trying to model the global dynamics of the magnetosphere are discussed.

Flow braking and the substorm current wedge

Recent models of magnetotail activity have associated the braking of earthward flow with dipolarization and the reduction and diversion of cross-tail current, that is, the signatures of the substorm current wedge. Estimates of the magnitude of the diverted current by Haerendel [1992] and Shiokawa et al. [1997, 1998] tend to be lower than results from computer simulations of magnetotail reconnection and tail collapse [Birn and Hesse, 1996], despite similar underlying models. An analysis of the differences between these estimates on the basis of the simulations gives a more refined picture of the diversion of perpendicular into parallel currents. The inertial currents considered by Haerendel [1992] and Shiokawa et al. [1997] contribute to the initial current reduction and diversion, but the dominant and more permanent contribution stems from the pressure gradient terms, which change in connection with the field collapse and distortion. The major effect results from pressure gradients in the z direction, rather than from the azimuthal gradients [Shiokawa et al., 1998], combined with changes in B y and B x . The reduction of the current density near the equatorial plane is associated with a reduction of the curvature drift which overcompensates changes of the magnetization current and of the gradient B drift current. In contrast to the inertial current effects, the pressure gradient effects persist even after the burst of earthward flow ends.

On the electron diffusion region in planar, asymmetric, systems

Particle-in-cell simulations and analytical theory are employed to study the electron diffusion region in asymmetric reconnection, which is taking place in planar configurations without a guide field. The analysis presented here focuses on the nature of the local reconnection electric field and on differences from symmetric configurations. Further emphasis is on the complex structure of the electron distribution in the diffusion region, which is generated by the mixing of particles from different sources. We find that the electric field component that is directly responsible for flux transport is provided not by electron pressure-based, “quasi-viscous,” terms but by inertial terms. The quasi-viscous component is shown to be critical in that it is necessary to sustain the required overall electric field pattern in the immediate neighborhood of the reconnection X line.

Two-satellite observations of substorm injections at geosynchronous orbit

Energetic particle and plasma measurements from three fairly closely spaced geosynchronous satellites are used to examine the simultaneous behavior of substorm particle injections at spatially separated locations. A total of 43 injection events are identified as dispersionless at two or more satellites. The observations confirm that the ion and electron injection regions are spatially offset in the azimuthal direction, as previously deduced statistically from single-satellite observations and revealed by test-particle trajectories in MHD simulations of geomagnetic tail reconnection. The two-spacecraft observations show further that the injection regions for both ions and electrons expand azimuthally in both the eastward and westward directions over a timescale of several minutes. The observed expansion rates are comparable to expansion rates derived from the test particle/MHD simulations, lending further support to the identification of such reconnection as the ultimate cause of substorm particle injections.

Three-dimensional magnetotail equilibria by numerical relaxation techniques

A numerical method to iteratively approach three-dimensional magnetostatic force equilibria is presented. The emphasis of the modeling is on the development of a suitable model of the Earths magnetotail, including a portion of the inner magnetosphere, i.e., on models which violate the “tail approximation” commonly employed in analytical models. The numerical approach will be discussed and compared to methods developed for laboratory plasma physics. The method is then applied, as a first example, to the magnetotail outside of 10 RE using Tsyganenkos (1987) model for the quiet magnetosphere as an initial condition. We discuss the changes of the magnetic field necessary to yield an equilibrium configuration and the resulting distribution of the self-consistently derived pressure. At last we will show that a self-consistent magnetotail equilibrium based on a close approximation to Tsyganenkos model requires a region 1 type current system which is not present in the initial configuration.

MHD simulations of magnetic reconnection in a skewed three‐dimensional tail configuration

Using our three-dimensional MHD code we have studied the dynamic evolution of a non-symmetric magnetotail configuration, initiated by the sudden occurrence of (anomalous) resistivity. The initial configuration included variations in all three space dimensions, consistent with average tail observations. In addition, it was skewed due to the presence of a net cross-tail magnetic field component ByN with a magnitude as typically observed, so that it lacked commonly assumed mirror symmetries around the midnight meridian and the equatorial planes. The field evolution was found to be very similar to that of a symmetric configuration studied earlier (e.g., Birn and Hones, 1981), indicating plasmoid formation and ejection. The most noticeable new feature in the evolution of the individual field components is a reduction of By on the reconnected dipole-like field lines earthward from the reconnection region. The topological structure of the magnetic field, however, defined by the field line connections, shows remarkable differences from the symmetric case, consistent with conclusions by Hughes and Sibeck (1987) and Birn et al. (1989). The plasmoid, which is a magnetically separate entity in the symmetric case, becomes “open”, connected initially with the Earth, but getting gradually connected with the interplanetary field, as reconnection of lobe field lines proceeds from the midnight region to the flanks of the tail. The separation of the plasmoid from the Earth is thus found to take a finite amount of time. When the plasmoid begins to separate from the Earth, a filamentary structure of field connections develops, not present in the spatial variation of the fields; this confirms predictions by Birn et al. (1989). A localization of the electric field parallel to the magnetic field is found consistent with conclusions on general magnetic reconnection (Schindler et al., 1988a,b; Hesse and Schindler, 1988). The effect of E∥, integrated along field lines, is found to be maximal on field lines near the plasma sheet/lobe interface. The “footprints” of these regions at the near-Earth boundary show a clottiness, reflecting the filamentary structure of the field connections, but not present in the spatial structure of the field itself.

The solar wind electric field does not control the dayside reconnection rate

Working toward a physical understanding of how solar wind/magnetosphere coupling works, four arguments are presented indicating that the solar wind electric field vsw × Bsw does not control the rate of reconnection between the solar wind and the magnetosphere. Those four arguments are (1) that the derived rate of dayside reconnection is not equal to solar wind electric field, (2) that electric field driver functions can be improved by a simple modification that disallows their interpretation as the solar wind electric field, (3) that the electric field in the magnetosheath is not equal to the electric field in the solar wind, and (4) that the magnetosphere can mass load and reduce the dayside reconnection rate without regard for the solar wind electric field. The data are more consistent with a coupling function based on local control of the reconnection rate than the Axford conjecture that reconnection is controlled by boundary conditions irrespective of local parameters. Physical arguments that the solar wind electric field controls dayside reconnection are absent; it is speculated that it is a coincidence that the electric field does so well at correlations with geomagnetic indices.

Hybrid and Hall-MHD simulations of collisionless reconnection: Dynamics of the electron pressure tensor

In this study we compare the results of two-dimensional hybrid (particle ions, massless fluid electrons) and Hall-MHD simulations of collisionless reconnection in a thin current sheet. Both calculations include the full electron pressure tensor (instead of a localized resistivity) in the generalized Ohms law to initiate reconnection, and in both an initial perturbation to the Harris equilibrium is applied. As in the recent Geospace Environment Modeling (GEM) reconnection challenge studies, we find overall agreement between the two calculations in both the reconnection rate and the global configuration. Results of this study show that in addition to providing the reconnection electric field at the X point the divergence of the electron pressure tensor leads to in-plane electric fields that exert drag forces on the ions as they enter and exit the near-X-point region. The in-plane electric fields are enhanced in regions of small transverse scale along the edge of the sheet, and the resulting narrow electron current layers are demonstrated clearly. The possibility of improving magnetotail reconnection models by embedding a Hall-MHD calculation using the electron pressure tensor model inside a large-scale MHD simulation is suggested.

Kinetic model of electric potentials in localized collisionless plasma structures under steady quasi-gyrotropic conditions

Localized plasma structures, such as thin current sheets, generally are associated with localized magnetic and electric fields. In space plasmas localized electric fields not only play an important role for particle dynamics and acceleration but may also have significant consequences on larger scales, e.g., through magnetic reconnection. Also, it has been suggested that localized electric fields generated in the magnetosphere are directly connected with quasi-steady auroral arcs. In this context, we present a two-dimensional model based on Vlasov theory that provides the electric potential for a large class of given magnetic field profiles. The model uses an expansion for small deviation from gyrotropy and besides quasineutrality it assumes that electrons and ions have the same number of particles with their generalized gyrocenter on any given magnetic field line. Specializing to one dimension, a detailed discussion concentrates on the electric potential shapes (such as “U” or “S” shapes) associated with ...

The role of compressibility in energy release by magnetic reconnection

Using resistive compressible magnetohydrodynamics, we investigate the energy release and transfer by magnetic reconnection in finite (closed or periodic) systems. The emphasis is on the magnitude of energy released and transferred to plasma heating in configurations that range from highly compressible to incompressible, based on the magnitude of the background β (ratio of plasma pressure over magnetic pressure) and of a guide field in two-dimensional reconnection. As expected, the system becomes more incompressible, and the role of compressional heating diminishes, with increasing β or increasing guide field. Nevertheless, compressional heating may dominate over Joule heating for values of the guide field of 2 or 3 (in relation to the reconnecting magnetic field component) and β of 5–10. This result stems from the strong localization of the dissipation near the reconnection site, which is modeled based on particle simulation results. Imposing uniform resistivity, corresponding to a Lundquist number of 103...