Abstract
Kinetic simulations and spacecraft observations have documented strong anisotropy in the electron distribution function during magnetic reconnection. The level and role of electron pressure anisotropy is investigated for asymmetric geometries applicable to reconnection in the dayside magnetopause. A previously derived analytic model for the pressure anisotropy is generalized and is applied to the asymmetric geometry. In agreement with the results from a kinetic simulation, the generalized model predicts the strongest pressure anisotropy and parallel electric fields in the inflow region characterized by low electron pressure.
This work was funded in part by NASA grant NNX10AL11G, an NSF CAREER grant 0844620 at MIT and by the NASA Heliophysics Theory Program at LANL. The research of PLP was supported by NASA grant NNX08AM15G, and the asymmetric particle simulations were performed using resources of the National Energy Research Scientific Computing Center and the UCLA Dawson Cluster.
I. INTRODUCTION
II. REVIEW OF ELECTRON MODEL FOR SYMMETRIC RECONNECTION
III. ELECTRON DYNAMICS IN ASYMMETRIC RECONNECTION
A. Electrons in the inflow regions in asymmetric reconnection
B. Model for exhaust electrons
IV. KINETIC SIMULATION RESULTS FOR ANTIPARALLEL ASYMMETRIC RECONNECTION
V. PRESSURE ANISOTROPY IN SYMMETRIC VS. ASYMMETRIC RECONNECTION
VI. SUMMARY AND CONCLUSION
Key Topics
 Magnetic reconnection
 34.0
 Magnetosheath
 29.0
 Magnetic fields
 18.0
 Electric fields
 17.0
 Magnetic anisotropy
 16.0
Figures
(Color) Geometry of Magnetosheath reconnection.
(Color) Geometry of Magnetosheath reconnection.
(Color) Schematic illustration of how the acceleration potential, , causes the formation of a bidirectional beam distribution in the reconnection inflow region.
(Color) Schematic illustration of how the acceleration potential, , causes the formation of a bidirectional beam distribution in the reconnection inflow region.
(Color) Three dimensional sketch of the magnetic field line geometry typical of Hall reconnection. The reconnection electric field, E _{rec}, provides important contributions to Φ_{∥} because of the outofplane bending of the magnetic field lines.
(Color) Three dimensional sketch of the magnetic field line geometry typical of Hall reconnection. The reconnection electric field, E _{rec}, provides important contributions to Φ_{∥} because of the outofplane bending of the magnetic field lines.
(a) The acceleration potential, Φ_{∥}, evaluated as a function of n for B ∈{0.5, 1, 2}. The dashed line represents the Boltzmann scaling Φ_{∥} ∝ log(n). (b) The parallel pressure, p _{∥}, evaluated as a function of n for B ∈ {0.5, 1, 2}. The straight dashed line represents the Boltzmann scaling p = nT. (c) The perpendicular pressure, p _{⊥}, evaluated as a function of n for B/B _{∞} ∈ {0.5, 1, 2}. The Boltzmann scaling p = nT, coincides with p _{⊥} (n) for .
(a) The acceleration potential, Φ_{∥}, evaluated as a function of n for B ∈{0.5, 1, 2}. The dashed line represents the Boltzmann scaling Φ_{∥} ∝ log(n). (b) The parallel pressure, p _{∥}, evaluated as a function of n for B ∈ {0.5, 1, 2}. The straight dashed line represents the Boltzmann scaling p = nT. (c) The perpendicular pressure, p _{⊥}, evaluated as a function of n for B/B _{∞} ∈ {0.5, 1, 2}. The Boltzmann scaling p = nT, coincides with p _{⊥} (n) for .
(a) Magnetic geometry of asymmetric reconnection. Our notation for the ambient distributions and field strength, f _{ xx } and B _{ x }, are shown, where subscript 1 (2) denotes the magnetosheath (magnetosphere). North and south are indicated by subscripts N and S, respectively. The black bars at the upper and lower boundaries of the simulation box indicate the positions where we apply Φ_{∥} = 0. As indicated by the arrows, in the magnetosheath inflow the parallel electric fields generally point towards the reconnection region, while they are directed away from the reconnection region in the magnetospheric inflow. (b), (c) Form of the theoretically expected distributions for Φ_{∥} < 0 (magnetosheath) and Φ_{∥} > 0 (magnetosphere).
(a) Magnetic geometry of asymmetric reconnection. Our notation for the ambient distributions and field strength, f _{ xx } and B _{ x }, are shown, where subscript 1 (2) denotes the magnetosheath (magnetosphere). North and south are indicated by subscripts N and S, respectively. The black bars at the upper and lower boundaries of the simulation box indicate the positions where we apply Φ_{∥} = 0. As indicated by the arrows, in the magnetosheath inflow the parallel electric fields generally point towards the reconnection region, while they are directed away from the reconnection region in the magnetospheric inflow. (b), (c) Form of the theoretically expected distributions for Φ_{∥} < 0 (magnetosheath) and Φ_{∥} > 0 (magnetosphere).
(Color) (a) Magnetic flux tube of the northern exhaust (straightened out). The parallel electric and magnetic forces on the electrons generally accelerate electrons towards the magnetosheath. Electron trajectories are divided into four types. p _{1N }: passing electrons injected at the magnetosheath, wr: electrons injected at the magnetosheath that w ill r eflect, r: reflected electrons injected at and returning to the magnetosheath, and p _{2N }: passing electrons originating from the magnetosphere. (b) and (c) Distributions expected in the exhaust. In the limit considered here with no trapped trajectories, these will be nearly isotropic.
(Color) (a) Magnetic flux tube of the northern exhaust (straightened out). The parallel electric and magnetic forces on the electrons generally accelerate electrons towards the magnetosheath. Electron trajectories are divided into four types. p _{1N }: passing electrons injected at the magnetosheath, wr: electrons injected at the magnetosheath that w ill r eflect, r: reflected electrons injected at and returning to the magnetosheath, and p _{2N }: passing electrons originating from the magnetosphere. (b) and (c) Distributions expected in the exhaust. In the limit considered here with no trapped trajectories, these will be nearly isotropic.
(Color) Contours of constant B, n, E _{∥}, and eΦ_{∥}/T _{ e }. In the magnetosheath inflow and exhaust we generally have Φ_{∥} < 0, whereas Φ_{∥} > 0 in the magnetospheric inflow. Three field lines are selected for the analysis in Fig. 8. In addition 9 points are selected in (d) for which the electron distributions are displayed in Fig. 9.
(Color) Contours of constant B, n, E _{∥}, and eΦ_{∥}/T _{ e }. In the magnetosheath inflow and exhaust we generally have Φ_{∥} < 0, whereas Φ_{∥} > 0 in the magnetospheric inflow. Three field lines are selected for the analysis in Fig. 8. In addition 9 points are selected in (d) for which the electron distributions are displayed in Fig. 9.
(Color) The three columns of subfigures display various quantities evaluated along the three field lines selected in Fig. 7. The quantities are shown as a function of l, where l is the inplane distance measured along the respective field lines. (a), (d), (g) Magnetic field strength, B, and acceleration potential, Φ_{∥}. (b), (e), (h) Number density n and the isotropic approximation, , where n _{∞} is the value of n and where the Φ_{∥} = 0 boundary condition is applied. (c), (f), (i) Parallel and perpendicular pressure.
(Color) The three columns of subfigures display various quantities evaluated along the three field lines selected in Fig. 7. The quantities are shown as a function of l, where l is the inplane distance measured along the respective field lines. (a), (d), (g) Magnetic field strength, B, and acceleration potential, Φ_{∥}. (b), (e), (h) Number density n and the isotropic approximation, , where n _{∞} is the value of n and where the Φ_{∥} = 0 boundary condition is applied. (c), (f), (i) Parallel and perpendicular pressure.
The three columns of subfigures display the electron distributions observed at three points for each of the three field lines selected in Fig. 7. The classes of electron trajectories are indicated by the notation introduced in Fig. 6.
The three columns of subfigures display the electron distributions observed at three points for each of the three field lines selected in Fig. 7. The classes of electron trajectories are indicated by the notation introduced in Fig. 6.
(Color) Comparison between the profiles of Φ_{∥} and p _{∥}/p _{∥} observed in asymmetric reconnection (a) and (b) versus symmetric reconnection (c) and (d). Note that the coordinates used in (a) and (b) are representative for the magnetopause, whereas the coordinates used in (c) and (d) are representative for symmetric magnetotail reconnection.
(Color) Comparison between the profiles of Φ_{∥} and p _{∥}/p _{∥} observed in asymmetric reconnection (a) and (b) versus symmetric reconnection (c) and (d). Note that the coordinates used in (a) and (b) are representative for the magnetopause, whereas the coordinates used in (c) and (d) are representative for symmetric magnetotail reconnection.
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