Field lines visualized in 3D. The color represents the -component of the magnetic field. Two views are presented to help the viewer to imagine the true 3D structure. The top view is from above while the bottom view is frontal but slightly tilted.
Electron charge density of the background superimposed with the intersection of the magnetic surfaces (projection of the magnetic field lines on the page, computed as the contour lines of the out of plane vector potential). Only the electrons initially in the background plasma are contributing to the density shown. Note that the color scale is inverted with blue indicating the higher density in absolute value (the electron charge density is negative). Four times are shown. Simulation with , , , and .
Electron velocity normalized to the local thermal speed . Note that the figure shows only the central part of the domain to make the features more visible. The complete box size is (see Fig. 6 for the full domain).
Parallel electric field , normalized as . Note that the figure shows only the central part of the domain to make the features more visible. The complete box size is (see Fig. 6 for the full domain).
Electron parallel velocity normalized to the local electron thermal velocity and parallel electric field . Panel (a) shows the contour lines of and in false color. Vice versa in panel (b). The parallel electric field is normalized as . Only the top left quadrant of the computational domain is shown and the axes have been shifted to be centered with the center of the simulation box.
Electron background density , parallel electron velocity normalized to the local thermal velocity and parallel electric field for the three different mass ratios.
Detail of electron holes in the parallel electric field. Comparison of the case with [(a) and (d)], [(b) and (e)], and [(c) and (f)]. On the left [panels (a)–(c)] the blow up of the inset displayed in the right panels [(d)–(f)] is shown. The left panels are scaled to the respective initial electron skin depth computed based on the initial peak density in the Harris sheet. A red circle of the same size is added in each of the left panels. The size is chosen to be the same as that of the electron holes displayed, showing that the electron holes have the same size at all mass ratio and that this size is approximately that once rescaled to the local electron skin depth due to the reduced density in the cavities is or .
Local grid spacing (equal in both directions and ) measured in terms of the local electron skin depth . Run with .
Comparison of two box sizes ( on the left, on the right) for two runs with the standard parameter and mass ratio . The top panels show the electron flow speed normalized to the local thermal speed and the bottom panels show the parallel electric field. Note that for the larger box (right panels) only the central part of the simulation box is displayed.
Comparison of periodic (left panels) and semiopen boundary conditions (right panels) for two runs with the standard parameter and mass ratio . The top panels show the electron flow speed normalized to the local thermal speed and the bottom panels show the parallel electric field.
Mass ratio, time step, and grid resolution of the simulations.
Mass ratio study. Scaling of the Alfvén speed and gain obtained by the use of the implicit moment method. By comparison, in the real Earth magnetotail, the typical value of is around 300.
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