Initial profiles of the bulk flow velocity , transverse magnetic field component , convective electric field , and net charge density in the positive (upper) and negative (bottom) field-aligned vorticity (FAV) cases. The convective electric field directions are illustrated by arrows.
Density profiles at from the simulations for the ion-kinetic scale shear layer case, in which . Upper (bottom) panels show the results from the positive (negative) FAV case. Density of particles which initially exist in the region are shown separately. Solid (dashed) lines show the ion (electron) density.
Ion velocity distribution functions in the middle of the shear layer at in the positive (left) and negative (right) FAV cases. Black and white lines show contour lines of an equal count level at and (initial), respectively.
Profiles at of the component in the positive (upper) and negative (bottom) FAV cases. Solid (dashed) lines are of ions (electrons). Shaded regions show the initial velocity shear layer.
(Upper) Illustration of representative orbits of ions, one crossing and the other moving toward the center of the shear layer, from the initial state until a quarter of ion gyroperiod in the negative FAV case (red solid arrows) and no shearing flow case (black dashed arrows). (Below) Profiles at (a quarter of ion gyroperiod) of ion density (b), difference between ion and electron densities (c), and electric field component (d) in the and negative FAV case. Narrow lines in Figs. 5(c) and 5(d) show initial profiles of and , respectively.
Thickness at of the broadened shear layer vs the initial thickness for 24 cases in which changed are the initial shear layer thickness , shearing flow speed , and ion thermal speed are changed. Solid lines show the results from and cases including the results discussed in Secs. III A and III B. Dashed lines show the and cases, and dotted lines show the and cases. Both and are in Fig. 6(a) (b) are normalized by the ion inertial length [the modified ion gyroradius ; see Eq. (7)].
Growth rate of the KHI vs the wave number normalized by the initial half thickness of the shear layer (a) and the broadened half thickness of the shear layer (b) for , 1.0, and 0.5 cases. Left (right) panels show the results from the positive (negative) FAV cases. Square marks show the growth rates calculated from compressible MHD simulations using the same fluid parameters as the particle simulations, and dashed lines show the rate from the linear incompressible MHD theory for discontinuous velocity profile (Ref. 4).
for the fastest growing KH mode in Fig. 7 as a function of time for and 0.5 cases. Upper (bottom) panel shows the results from the positive (negative) FAV cases. Solid (dashed) lines show the ion (electron) vortices.
Difference as a function of time in the positive FAV (left) and negative FAV (right) cases. (a) The vortex size dependence in which , 1.0, and 0.5 cases are compared for . (b) The shearing flow speed dependence in which and 0.5 cases are compared for . Dotted lines show the theoretical values obtained from Eq. (10).
Density contour at for ions which initially exist at in the positive FAV and case. Black lines show the ion streamlines. The white solid line shows a streamline passing through point A2 where and have a maximum value. At point A1, the white streamline crosses . The white dashed line is an ellipse passing through both A1 and A2 points, an approximation of the white streamline.
Density contours at the saturation time of the fastest growing KH mode for ions (left panels) and electrons (right panels) which initially exist at . The upper and lower panels show the positive and negative FAV cases, respectively, for . Solid (dashed) white lines show the most bulging edges in the Y-direction of the ion (electron) vortex. The edge is marked by the line where the density is half of the peak value near the vortex edge.
The same contours as Fig. 11 but for .
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