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A review of pressure anisotropy caused by electron trapping in collisionless plasma, and its implications for magnetic reconnection
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View: Figures


Image of FIG. 1.
FIG. 1.

(a) Illustration of the VTF open cusp experimental configuration. (b)Guiding center trajectory of a particle in the linear magnetic cusp. (c)Experimentally measured in-plane electrostatic potential during magnetic reconnection in VTF. (d) Theoretically calculated pressure anisotropy during slow reconnection in a linear magnetic cusp.

Image of FIG. 2.
FIG. 2.

(a) Gyrophase averaged electron distribution, , measured by the Wind spacecraft on 1 April 1999 during an encounter with a reconnection region in the deep magnetotail. (b) Distribution from a numerical model that reproduces the Wind observations. The match can only be obtained with the assumption that a parallel acceleration potential of 1 kV is present at the location of the measurement. (c) Example of the acceleration potential computed from the electric and magnetic configuration of kinetic simulation. The overlaid trapped electron trajectory is typical for the reconnection region.

Image of FIG. 3.
FIG. 3.

Illustration of a flux tube expanding in time while being fed by “half Maxwellian” distributions from both ends of the tube. The distribution shown below the tube is representative for the electrons inside the tube, where the green area represents the contributions in velocity space from trapped electrons. Trapping can result from a local minimum in or be caused by electric fields parallel to the flux tube as associated with a parallel acceleration potential, .

Image of FIG. 4.
FIG. 4.

Contour plots of the distribution in Eq. (16) , for . In (a), is evaluated with , whereas in (b) . The gray areas characterized by straight contours correspond to the trapped regions in velocity space with boundaries expressed in Eq. (17) .

Image of FIG. 5.
FIG. 5.

Color contours of the electron distribution measured by Wind, also displayed above in Fig. 2(a) . The overlaid black contours represent in Eq. (16) , evaluated with and .

Image of FIG. 6.
FIG. 6.

PIC simulation results: (a) Out-of-plane current density , (b) magnetic field strength with points used in Fig. 9 , where (white) and (black), and (c) plasma density . Dashed lines represent in-plane magnetic field lines. Simulation electron distribution functions with theoretical level lines superimposed along the cut right of the X line at the locations indicated in (a) ((d) , (e) , (f) , and (g) ).

Image of FIG. 7.
FIG. 7.

Possible profiles of as a function of the position along the flux tube. The model in Eq. (15) is valid for the profiles in (a) with no local minimum in and (b) with one local minimum. For cases like that in (c) local trapping can occur, which causes changes to the distribution function not accounted for by Eq. (15) .

Image of FIG. 8.
FIG. 8.

(a) The acceleration potential, , evaluated as a function of for . The dashed line represents the Boltzmann scaling . (b) The parallel pressure, , evaluated as a function of for . The straight dashed line represents the Boltzmann scaling  = . (c) The perpendicular pressure, , evaluated as a function of for . The Boltzmann scaling , coincides with for .

Image of FIG. 9.
FIG. 9.

Comparison of the analytical equations of state in Eqs. (30) and (31) against PIC data from points marked in Fig. 6(b) .

Image of FIG. 10.
FIG. 10.

Contours of out of plane current density as observed in (a) a fluid simulation with isotropic pressure, (b) a fluid simulation applying our new anisotropic equations of state, and (c) a fully kinetic simulation.

Image of FIG. 11.
FIG. 11.

(a) Classification of simulation runs for in space of mass ratio and guide field . The red lines in the symbols represent the observed elongated electron current channels. (b) Classification of simulation runs for in space of electron beta , and mass ratio . (c) Out-of-plane current, , in a fluid simulation with anisotropic electron pressure carried out with and .

Image of FIG. 12.
FIG. 12.

(a) Electron anisotropic pressure ratio from a kinetic simulation of anti-parallel reconnection (see Ref. for more details). (b) Typical trapped electron orbit, which passes repeatedly through the region of weak magnetic field (blue areas) in the outflow.

Image of FIG. 13.
FIG. 13.

Electron distribution within neutral sheet. (a) Isosurface of the distribution at X line. The different colors correspond to the number of times the electrons are reflected in the layer. (b) Color plot is in-plane electric field , with contours of in-plane projection of magnetic field lines. Electron orbits are shown traced back in time from the X line and characterized by 0 (red), 1 (blue), and 2 (magenta) reflections. The black ×-symbols identify where the value of for each trajectory is obtained using a relativistic version of Eq. (16) as the boundary condition.

Image of FIG. 14.
FIG. 14.

(a) and the difference predicted by the equations of state and directly from the PIC codes as functions of along a cut through the X line. (b)-(d) Predicted dependence on the upstream electron beta of various quantities along with PIC simulation results. (b) Characteristic Hall magnetic field strength normalized to upstream reconnecting field. (c) Maximum pressure ratio . (d) Maximum upstream acceleration potential normalized to electron temperature, .

Image of FIG. 15.
FIG. 15.

Contours of and from a kinetic simulations of asymmetric anti-parallel reconnection. The left-hand inflow region is characterized by , whereas for the right hand inflow region .

Image of FIG. 16.
FIG. 16.

The (a) acceleration potential and (b) parallel electron pressure near the X line formed by two merging plasmoids.

Image of FIG. 17.
FIG. 17.

(Top panel) Contours of constant in a kinetic simulation of anti-parallel reconnection. (Middle panels) Electron distributions for the points marked in the top panel. The magenta lines indicate the trapped passing boundaries. (Bottom panels) Electron distributions recorded by Cluster 1 spacecraft in a separator crossing. The magenta dots indicate the locations of measurements in velocity space. The simulated distributions in the middle panels qualitatively match these experimental distributions.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A review of pressure anisotropy caused by electron trapping in collisionless plasma, and its implications for magnetic reconnection