Abstract
Kinetic simulations of magnetic reconnection provide detailed information about the electric and magnetic structure throughout the simulation domain, as well as high resolution profiles of the essential fluid parameters including the electron and ion densities, flows, and pressuretensors. However, the electron distribution function,f(v), within the electron diffusion region becomes highly structured in the three dimensional velocity space and is not well resolved by the data available from the particleincell(PIC) simulations. Here, we reconstruct the electron distribution function within the diffusion region at enhanced resolution. This is achieved by tracing electron orbits in the fields taken from PIC simulations back to the inflow region where an analytic form of the magnetized electron distribution is known. For antiparallel reconnection, the analysis reveals the highly structured nature of f(v), with striations corresponding to the number of times electrons have been reflected within the reconnection current layer, and exposes the origin of gradients in the electron pressuretensor important for momentum balance. The structure of the reconnection region is strongly tied to the pressureanisotropy that develops in the electrons upstream of the reconnection region. The addition of a guide field changes the nature of the electron distributions, and the differences are accounted for by studying the motion of single particles in the field geometry. Finally, the geometry of small guide field reconnection is shown to be highly sensitive to the ion/electron mass ratio applied in the simulation.
We gratefully acknowledge support from NASA (National Aeronautics and Space Administration) through Grant NNX10AL11G, and National Science Foundation (NSF) CAREER Grant 0844620 (both at MIT) and by the NASA Heliophysics Theory Program at LANL. Simulations were carried out using LANL institutional computing resources and the Pleiades computer at NASA.
I. INTRODUCTION
II. ORBIT TRACING METHOD
III. ANTIPARALLEL RECONNECTION
A. Role of and in determining the structure of f
IV. RECONNECTION WITH SMALL GUIDE FIELDS
A. Mass ratio 400 simulations
B. Mass ratio 1836 simulations
V. SUMMARY AND CONCLUSION
Key Topics
 Diffusion
 18.0
 Magnetic fields
 14.0
 Magnetic reconnection
 14.0
 Particleincell method
 11.0
 Space vehicles
 6.0
Figures
Time slice from an openboundary PIC simulation of antiparallel reconnection. (a) Acceleration potential . (b) Magnetic field strength B. (c) Pressure anisotropy . (d) Out of plane current density (normalized to ). (e) Distribution function just upstream of the electron diffusion region at the point marked with circles. The color plot shows data from the PIC code, while the black contour lines are from the analytic form of f in Appendix.
Time slice from an openboundary PIC simulation of antiparallel reconnection. (a) Acceleration potential . (b) Magnetic field strength B. (c) Pressure anisotropy . (d) Out of plane current density (normalized to ). (e) Distribution function just upstream of the electron diffusion region at the point marked with circles. The color plot shows data from the PIC code, while the black contour lines are from the analytic form of f in Appendix.
Plots of reconstructed distribution function along a cut at . Velocity units are in terms of c. (a) Distribution function averaged over , and , where is the Lorentz factor. (b) Moments of the electron distribution for a cut along the z axis passing through the xline. From left to right, the density, fluid velocity, diagonal, and offdiagonal components of the pressure tensor are plotted. The dashed lines show the data from the PIC simulation while the solid lines show the reconstructed moments. Density and pressure components are normalized to and the value of outside the layer.
Plots of reconstructed distribution function along a cut at . Velocity units are in terms of c. (a) Distribution function averaged over , and , where is the Lorentz factor. (b) Moments of the electron distribution for a cut along the z axis passing through the xline. From left to right, the density, fluid velocity, diagonal, and offdiagonal components of the pressure tensor are plotted. The dashed lines show the data from the PIC simulation while the solid lines show the reconstructed moments. Density and pressure components are normalized to and the value of outside the layer.
Electron distribution within neutral sheet. (a) Isosurface of the distribution at xline. The different colors correspond to the number of times the electrons are reflected in the layer. (b) Electron orbits from xline with 0, 1, and 2 reflections. Color plot is inplane electric field , with contours of inplane projection of magnetic field lines.
Electron distribution within neutral sheet. (a) Isosurface of the distribution at xline. The different colors correspond to the number of times the electrons are reflected in the layer. (b) Electron orbits from xline with 0, 1, and 2 reflections. Color plot is inplane electric field , with contours of inplane projection of magnetic field lines.
(a) and (b) Isosurfaces of the distribution at above and below xline at (x, z) = (206.25, 200). The red region lies in , the blue in . Note the relative displacement in of the red and blue surfaces as z increases, causing a gradient in . (c) and (d) Isosurfaces of the distribution at to the left and right of the xline. Rotation of the distribution along the layer causes the gradient in . (e) and (f) distribution of particles taken from PIC simulation at . (g) and (h) The distributions in (a), (b) after integrating over and , showing the and contributions separately (making the displacement in clearer). Vertical axis units are arbitrary. The red line represents , while the blue is for .
(a) and (b) Isosurfaces of the distribution at above and below xline at (x, z) = (206.25, 200). The red region lies in , the blue in . Note the relative displacement in of the red and blue surfaces as z increases, causing a gradient in . (c) and (d) Isosurfaces of the distribution at to the left and right of the xline. Rotation of the distribution along the layer causes the gradient in . (e) and (f) distribution of particles taken from PIC simulation at . (g) and (h) The distributions in (a), (b) after integrating over and , showing the and contributions separately (making the displacement in clearer). Vertical axis units are arbitrary. The red line represents , while the blue is for .
(a) Electron distributions averaged over at the xline from simulations in which the force of on the electrons is modified. In the left plot, there is no elongation due to the absence of . The center plot shows the distribution in the unmodified simulation, while there is increased electron acceleration in the final plot, where has been effectively doubled. (b) Comparison of the reconstructed distribution using (from simulation data) and 0 (assuming only magnetic trapping). The importance of the parallel potential in determining the length of the fingers is evident. Note that the data in (a) and (b)come from two different sets of simulations.
(a) Electron distributions averaged over at the xline from simulations in which the force of on the electrons is modified. In the left plot, there is no elongation due to the absence of . The center plot shows the distribution in the unmodified simulation, while there is increased electron acceleration in the final plot, where has been effectively doubled. (b) Comparison of the reconstructed distribution using (from simulation data) and 0 (assuming only magnetic trapping). The importance of the parallel potential in determining the length of the fingers is evident. Note that the data in (a) and (b)come from two different sets of simulations.
Changes in the reconnection geometry as the guide field is increased from 0 to . The left column shows the inplane electric field , while the right column shows the electron flow velocity (in this figure, the xaxis is shifted such that the xline is located at ). The electron Alfvén speed is 0.3c, so electrons in the jets are moving at this velocity.
Changes in the reconnection geometry as the guide field is increased from 0 to . The left column shows the inplane electric field , while the right column shows the electron flow velocity (in this figure, the xaxis is shifted such that the xline is located at ). The electron Alfvén speed is 0.3c, so electrons in the jets are moving at this velocity.
Electron distributions at the xline from simulations of reconnection with increasing guide fields. From left toright, , and . At the largest guide field, the elongated electron jet is no longer present and the field geometry is different.
Electron distributions at the xline from simulations of reconnection with increasing guide fields. From left toright, , and . At the largest guide field, the elongated electron jet is no longer present and the field geometry is different.
(a) Isosurfaces of the electron distribution at the xline for . Colors show the number of times an electron is reflected before reaching the xline. (b) Trajectory of an electron reaching the point marked (b) in velocity space from the left and exiting from the right. Likewise for (c).
(a) Isosurfaces of the electron distribution at the xline for . Colors show the number of times an electron is reflected before reaching the xline. (b) Trajectory of an electron reaching the point marked (b) in velocity space from the left and exiting from the right. Likewise for (c).
Four different views of isosurfaces of the electron distribution at the xline for . Colors show the number of times an electron is reflected before reaching the xline, and only regions with electrons with 0, 1, and 2 reflections are shown.
Four different views of isosurfaces of the electron distribution at the xline for . Colors show the number of times an electron is reflected before reaching the xline, and only regions with electrons with 0, 1, and 2 reflections are shown.
A demonstration of the evolution of the velocity space positions of electrons in the fingers. Electrons from the zeroreflection finger in (a) follow the trajectories in (c) until they reach the onereflection finger at the xline (b). The distribution in (a) is taken from the average x position of the crossings of the three trajectories.
A demonstration of the evolution of the velocity space positions of electrons in the fingers. Electrons from the zeroreflection finger in (a) follow the trajectories in (c) until they reach the onereflection finger at the xline (b). The distribution in (a) is taken from the average x position of the crossings of the three trajectories.
Electron distributions at the xline from full mass ratio simulations. From left to right, the (antiparallel), , and . The antiparallel distribution has the same structure as in the mass ratio 400 antiparallel simulation, while the cases are similar to larger guide field simulations at mass ratio 400.
Electron distributions at the xline from full mass ratio simulations. From left to right, the (antiparallel), , and . The antiparallel distribution has the same structure as in the mass ratio 400 antiparallel simulation, while the cases are similar to larger guide field simulations at mass ratio 400.
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