TOWARDS THE UNDERSTANDING OF
MAGNETIC RECONNECTION:
SIMULATION AND SATELLITE OBSERVATIONS
M. HOSHINO
The Institute of Space and Astronautical Science (ISAS)
3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, JAPAN
1.
Introduction
Magnetic reconnection processes are thought to be important to understanding fundamental plasma phenomena in geophysical/astrophysical plasmas such as the earth's magnetosphere, solar and stellar ares, and the
astrophysical accretion disks. By virtue of the recent intensive plasma and
magnetic eld observations of the earth's magneotail by the ISEE, AMPTE,
and GEOTAIL satellites and the X ray observations of solar ares by the
YOHKOH satellite, it is getting to be possible to discuss self-consistently
detailed physical pictures of microscopic and macroscopic reconnection processes. The computer simulation study of magnetic reconnection also plays
an important role on understanding of non-linear time evolutions of reconnection.
Magnetohydrodynamic (MHD) description of reconnection so far adequately accounts for the hot and high speed plasma ows and the plasmoid
formation/ejection in both the solar corona and the Earth's magnetotail,
though the diculty is that the physics of the violation of the MHD approximation remains in doubt. From the recent satellite observations in
the Earth's magnetotail, it is now recognized that non-Maxwellian, ion
distribution functions are often observed [Lui et al., 1977; DeCoster and
Frank, 1979; Sarris and Axford, 1979, Mukai et al., 1996]. Moreover, the
distribution functions show sometimes non-gyrotropic behavior with several bunched structure in the velocity space [Frank et al., 1994, Hoshino et
al., 1997; Tu et al., 1997; Hoshino et al., 1998a]. Since those non-MHD, kinetic features appear in the macroscopic scale length such as the thickness
of the plasma sheet, the self-consistent understanding of both the macroscopic evolution of reconnection and the microscopic behavior seen in the
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M. HOSHINO
distribution functions becomes important in the reconnection modeling of
a sudden energy release mechanism.
We study the kinetic, collisionless reconnection processes beyond the
MHD reconnection picture, and discuss the electron and ion dynamics in the
magnetic reconnection region in terms of comparison between the particlein-cell simulation and the Geotail observations.
2.
Ion Dynamics in Magnetic Reconnection
An important step toward a collisionless reconnection model is, we believe,
the study of ion distribution functions in a thin plasma. The motion of thermal particles near the X-type neutral line is described by the meandering
motion [Sonnerup,
1971], and the unmagnetized particles are trapped in the
p
distance of rL , where is the thickness of the plasma sheet and rL is the
Larmor radius. Those particles contribute to the energy diusion by being
accelerated by the dawn-dusk electric eld during the nite transition in
the weak magnetic eld region [Laval and Pellat, 1968; Coppi et al., 1966].
On the other hand, the motion within a weakly magnetized plasma sheet
outside the meandering particle region is described by the Speiser motion
[Speiser, 1965]. Thermal particles remain within the current sheet for a
time comparable to the gyroperiod based on the normal magnetic eld Bz ,
and after the interaction of the particles with the dawn-dusk electric eld,
the particles are ejected from the plasma sheet along the strong magnetic
eld. This nite time interaction between particles and the electric eld in
the current sheet is also important as the origin of an eective conductivity
[Lyons and Speiser, 1982].
The meandering/Speiser motion can produce a unique signature in the
velocity space. If the thermalization time scale is slower than the dynamic
time scale, the bunched ion structure as the \memory" of the meandering/Speiser motion could be observed in the velocity space. Since the lobe
thermal energy is much smaller than the typical kinetic energy gain during
the interaction of particles with the dawn-dusk electric eld, the lobe origin plasma forms a coherent structure representing the meandering/Speiser
motion, and multi-component plasma populations could be found in the
velocity space. It is expected that the structure of the plasma velocity
distribution functions can provide very important information on the dynamical evolution of magnetic reconnection. From this point of view, we
study the structure of the plasma distribution functions seen in the typical
GEOTAIL observations during the passage of the plasmoid, and then we
compare the result with the numerical simulation result obtained by using
a two-dimensional, full particle-in-cell simulation.
Figure 1 shows the GEOTAIL plasmoid observations when the space-
RECONNECTION BEYOND ION INERTIA SCALE
10:15
10:20
UT
313
10:25
Figure 1.
Typical plasmoid event observed by Geotail on September 18, 1993. Top and
bottom panels show the ion distribution functions, and the magnetic eld and the plasma
moments data are shown in the middle panel. (color gure in CD-ROM)
craft was situated in the night side magnetotail, about 70 Re from the
Earth. A ground-based magnetometer at Kakioka station detected a Pi-2
onset at 1014UT. The top and bottom corners shows four typical distribution functions during the plasmoid passage, and the center gure shows time
series of three components of the magnetic eld, bulk ow velocities, ion
temperature, and plasma density. The time series of magnetic variations
showed a north-south bipolar signature in the Bz magnetic eld around
1018UT. Associated with the bipolar signature, the tailward plasma ows
are enhanced, and plasma density and temperature increases. Prior to the
northward turning of the Bz magnetic eld at 1017:47 UT, the tailward
high speed ion of 2500km=s is observed in the plasma sheet boundary
layer (PSBL). The vertical and horizontal axes are respectively aligned to
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M. HOSHINO
Vb
0
-2
-2
Z/λ
4
0
V⊥
nongyrotropic
0
-2
-2
2
0
V⊥
2
0
-4
2
Vb
2
PSBL
-8
-4
0
X/λ
2
CSI
Vb
Vb
2
0
-2
-2
0
V⊥
2
4
8
Maxwellian
0
-2
-2
0
V⊥
2
Particle-in-cell simulation result. Ion ow vectors, magnetic eld lines, and
plasma density in color contour are shown in the middle panel. Ion distribution functions
obtained in the simulation are shown in top and bottom panels. (color gure in CD-ROM)
Figure 2.
the directions of the magnetic eld and the plasma convection. The small
black spot situated in the center corresponds to the cold lobe ions, and the
high-speed component owing into the direction opposite that of the magnetic eld is the PSBL ion beam. The ion distribution inside the plasmoid
at the time interval of 1018:11-1018:23 UT is characterized by two cold ion
components parallel to the magnetic eld [Mukai et al., 1996]. Around the
turning point of the Bz polarity, namely at the time interval of 1018:231018:35 UT, an almost thermal ion distribution function is observed. Just
after the passage of the plasmoid at the time interval of 1020:11-1020:23UT,
we observe two main ion components bunched perpendicular to the magnetic eld. Together with another slice of the three-dimensional distribution
function, we nd that the ion distribution function is characterized by nongyrotropic behavior [Hoshino et al., 1998a]. We found several other similar
non-gyrotropic ion events when GEOTAIL is located in a weak Bx magnetic
eld region after the passage of plasmoids.
Figure 2 shows the particle simulation result. The center shows a snapshot of magnetic eld lines and plasma density in a color contour of a
RECONNECTION BEYOND ION INERTIA SCALE
315
reconnecting current sheet. The red and blue regions correspond to high
and low density regions, respectively. Four typical ion distribution functions obtained in this simulation box are shown in the top and bottom
four panels. The distribution shows a slice of a three-dimensional distribution function in a plane including the magnetic eld and the convection
vectors. The velocity scale is normalized by the Alfven velocity which is
dened by the lobe magnetic eld and the plasma sheet density. By comparing the behavior of those ion velocity distribution functions obtained
by the kinetic reconnection simulation with the distributions observed by
the Geotail satellite, we nd that most of ion dynamics observed in the
earth's magnetotail can be well reproduced by the two-dimensional kinetic
simulation.
Hoshino [1998b] have discussed that the plasma mixing under the action
of the meandering/Speiser particles accelerated in the current sheet play an
important role on the formation of a wide variety of distribution functions.
It has been discussed that those kinds of distributions are strongly coupled with the magnetic diusion process around an X-type region, and the
macroscopic evolution of the plasma sheet is also aected by the formation
mechanism of non-Maxwellian distributions.
3.
Electron Dynamics in Magnetic Reconnection
In the thin plasma sheet where the plasma sheet thickness becomes comparable to the ion inertia length (or ion Larmor radius), the electric eld
appears in the reconnection plane and aects on the dynamics of electrons
as well as of ions.
The origin of the electric eld can be understood as follows: In the lobe
region outside of the plasma sheet, the characteristic scale length is much
larger than the ion inertia length, the both ions and electrons follow the
motion of magnetic eld line. Inside the plasma sheet, however, the plasma
sheet thickness becomes comparable to the ion inertia length, ions start to
be unmagnetized and cannot follow the motion of the magnetic eld line,
while electrons are still magnetized until the scale size becomes less than
the electron inertia length. Therefore the electric elds in the reconnection
plane are excited in order to maintain the charge neutrality [Hoh 1966;
Dobrowolny 1968; Hoshino, 1987], as long as the evolution of magnetic
reconnection is slower than the Alfven transit time of the plasma sheet.
In a linear growing stage of the tearing mode instability, the electric eld
parallel to the magnetic eld is roughly given by Ek kui =Ey ; where k is
the wave number of the tearing mode, ui is the ion drift velocity, and is the
linear growth rate. The large parallel electric eld may play an important
role on the electron dynamics in the reconnection region, because of the
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M. HOSHINO
V⊥,z/Ve
6
neutral sheet
boundary
0
-6
-6
0
6
0
Vb/Ve
4
Ζ/λ
lobe
6
0
6
Electron
0
-4
Ζ/λ
4
Ion
0
-4
-12.8
0
X/λ
12.8
Figure 3.
Particle-in-cell simulation result. From top to bottom, electron distribution
functions, electron ow vectors superposed with the magnetic eld lines, and ion ow
vectors are shown. (color gure in CD-ROM)
magnitude of kui = 1 in a thin plasma sheet.
Figure 3 shows the snapshot of the magnetic reconnection simulation.
The plasma parameters used in this simulation are almost same as that
shown in Figure 2, but the spatial resolution has been improved in order to
study the electron dynamics. Three electron distribution functions across
the boundary region are shown in the top panel. The middle and bottom
panels are respectively the electron ow vectors with magnetic eld lines
and the ion ow vectors. The ion ow vectors direct from the lobe toward
the plasma sheet, and then ions are ejected from an X-type region to an Otype region. On the other hand, we can nd the electron ow vectors have
the opposite directions along the boundary region between the lobe and the
plasma sheet. The dierence of ion and electron ows produces the Hall
electric current in the reconnection plane [Sonnerup, 1979; Terasawa 1983].
The location of the electron distribution functions are indicated by the box
in the electron ow vector panel. The distributions are a slice of a threedimensional distribution function in a plane including the magnetic eld
and the convection ow vectors perpendicular to the magnetic eld. The
velocity scale is normalized by the initial electron thermal velocity. Inside
the plasma sheet, a hot and isotropic Maxwellian distribution can be found,
RECONNECTION BEYOND ION INERTIA SCALE
317
while in the lobe region the distribution is described as a cold Maxwellian
distribution. The distributions obtained in the boundary region between
the lobe and the plasma sheet, however, show the deformed distribution
from the Maxwellian. The middle distribution shows the non-Maxwellian
distribution in which a cold component ows toward the parallel to the
magnetic eld, that is, toward the X-type region, and a hot component
ows away from the X-type region. By tracing the position of particles
backward in time, we found that the hot electron component comes from
the X-type region after the current sheet acceleration, which is the similar
process to the ion beam population observed in PSBL. On the other hand,
the cold component can be understood as a result of the Hall electric eld
acceleration given in the above equation.
The electron distributions similar to the above electron dynamics have
been already observed by the Geotail satellite [Tu et al.,1997; Fujimoto et
al.,1997]. The electron distributions composed with the cold core and the
hot component escaping from an X-type region are often observed near the
plasma sheet boundary. Although there remains uncertainty in the electric
eld measurement, we think that a strong parallel electric eld is produced
during the magnetic reconnection by virtue of the similarity of the distribution functions obtained by both the Geotail satellite and the numerical
simulation study. The electric eld produces the Hall electric current in
the reconnection plane, and we nd that the electrons are the main carrier of the eld aligned electric current which could propagate toward the
ionosphere in the form of the kinetic Alfven waves.
4.
Discussion and Conclusions
We have discussed both ion and electron dynamics beyond ion inertia length
in the magnetotail. A wide variety of non-Maxwellian ion distribution functions in the magnetotail have been observed in the thin plasma sheet. These
observations suggest that the ion inertia length becomes comparable to the
thickness of plasma sheet, namely, ion starts to be demagnetized and electron is still magnetized. These distributions are produced by non-adiabatic
ion motions in such region as a result of the plasma mixing between the
cold lobe ions and the hot plasma sheet plasmas. On the other hand, electron distributions observed by the Geotail satellite are almost gyrotropic
with respect to the magnetic eld, but the counter streaming electrons
which components have the dierent temperature are sometimes observed
near the boundary between the plasma sheet and the lobe. These ion and
electron distributions have provided very important information about the
microscopic transportation coecients such as electric conductivity, viscosity, and thermal conduction.
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M. HOSHINO
The studies of electron dynamics beyond electron inertia length should
be important to know the reconnection physics, because the nal breakdown of the frozen-in condition is controlled by the electrons. It will be
possible, in a near feature technology, to observe the velocity distribution
function within the time resolution of the order of 10 mil second, and the
electron inertia scale would be resolved. Kinetic electron behavior will provide variable information on plasma heating, mixing, and non-thermal particle acceleration. Our theoretical and observational study is only a rst
step to understanding more complete collisionless reconnection physics.
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