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Instability at interface between reconnection jet and pre-existing plasma sheet
A& Space Res. Vol. 29, No. 7, pp. 1125-I 128.2002 Q 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved
Pergamon
Printed in Great Britain 0273- 1177/02 $22.00 + 0.00
www.elsevier.com/locatelasr
PII: SO273-1177(02)00032-7
INSTABILITY
AT INTERFACE
RECONNECTION
JET AND
PLASMA M.S. Nakamura’,
BETWEEN
PRE-EXISTING
SHEET
M. Fujimoto2,
and H. Matsumoto’
lRadio Science Center for Space and Atmosphere, h’yoto University, Gokasho, Uji 611-0011, JAPAN 2Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-l Ookayama, Meguro-ku, Tokyo 152-8551, JAPAN
ABSTRACT When a reconnection jet encounters a pre-existing plasma sheet standing ahead of it, the interface between the two where both plasma and magnetic field are compressed becomes unstable and develops a bubblelike structure. We have conducted three-dimensional hybrid simulations (ions as particles and electrons as massless charge neutralizing fluid) of this instability. We suggest that this instability generates a variety of plasma flows and field configurations which may have relevance to some magnetospheric phenomena. 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved. INTRODUCTION Magnetic reconnection is one of the most important processes in space plasmas. In the Earth’s magnetotail, magnetic reconnection produces not only change in the magnetic field topology but also converts magnetic energy stored in the lobe to plasma kinetic energy. Magnetic reconnection is considered to be initiated in a thin plasma sheet whose thickness is comparable to the relevant ion inertia length, which is frequently observed prior to substorm onsets (e.g. Sergeev et al., 1990). Since ion kinetic effects cannot be ignored in such a situation, two-dimensional hybrid simulations of the magnetic reconnection process in the plane including the lobe magnetic field have been extensively performed (e.g. Kuznetsova et al, 1996; Nakamura et al., 1998; Lottermoser et al., 1998). These simulations (as well as MHD simulations) show compression of plasma density and magnetic field component normal to the current sheet at the interface between the reconnection jet and the preexisting plasma sheet (PEPS). The compression is indeed observed in the magnetotail on the tailward side of the reconnection region (Fujimoto et al., 1996; Nagai et al., 1998). On the earthward side, the structure of the interface would be intimately related with the structure of fieldaligned currents generated in the course of substorms. These studies, however, lack the degree of freedom associated with the third dimension. In this paper, we report a new instability that grows at the interface between the reconnection jet and the PEPS, having wave-number vector in the dawn-dusk direction. SIMULATION MODEL AND RESULTS The three-dimensional simulation model used here is essentially the same as before with some modifications on the boundary conditions (Nakamura and Fujimoto, 1998, 2000). The coordinate system is the same as used conventionally (the x-, y-, and z-axis are directed to the earthward, duskward, and northward direction, respectively). Hereafter, simulation results are normalized as follows: Magnetic field by Bu (lobe magnetic field), density by nn (lobe density), velocity by VA (the AlfvCn velocity in the lobe), time scale by a;’ (the reciprocal of the ion cyclotron frequency in the lobe), spatial scale by X; = VAQ?‘, and magnitude of the resistivity by PO&VA, respectively. Using typical values, i.e. lobe density of 0.05 particle/cm3 and lobe magnetic field of 20 nT, the unit time and length are QF1 N 0.5 s and Xi 2: 1000 km, respectively. The size of the simulation box is 0 5 x 5 320, 0 5 y 5 56, and 0 2 .z < 32 with 400 x 70 x 64 cells. With the large simulation box, the boundary conditions have little effects. The symmetric boundary conditions are imposed at the x and z boundaries and the periodic boundary condition is imposed in the y direction. The 1125
1126
M. S. Nakamura et 01. 1.0 Bz T=lOO
0.0
56
T=120 56
0 Tzl4t-l
56
Y
0 0 Fig.
1. The
X B,
and density
plots on the z=O
160
0
plane at five different
160
X times,
T=lOO,
120,
140,
160, and T=180.
initial magnetic field is a Harris type model, B = [&(z), 0, 01, w h ere B,(z) = Bu tanh(z/D) for 0 5 z < 16 and B,(z) = -Bu tanh((z - 32)/D) for 16 5 z 5 32. Here, D=2 is the half-thickness of the initial plasma sheet. Current-carrying hot plasma sheet ions modeled by a drifting Maxwellian, whose thermal pressure balances the magnetic pressure, are added to uniform cold lobe ions. The symmetry about z=O artificially excludes the tail-KH mode (e.g., Nakamura and Fujimoto, 2000) and an instability that produces a wavy structure within the jet (Lottermoser et al., 1998). Sixty-four ion particles in a cell represent unit density. Electrons are at rest initially and their temperature is fixed to zero for simplicity. Anomalous resistivity is located at one corner of the simulation box with the form q(~,z) = vu [exp(-(x/IcZ)2 - (z/k=)“) + 0.011, where qe=2.0 and k,=k,=D. The resistive region is aligned to the y-axis and is two-dimensional, unlike our previous studies where three-dimensionally localized resistivity, rather short in the y direction, is assumed to
Three-DimensionalMagnetotailReconnection:Ion Signatures
1127
1.0
Bx -1 .o 16
16
16
16
2
Z
Z
Z
-16
-16 0
Y
56
-16 0
Y
56
-16 0
Y
56
0
Y
56
Fig. 2. The B,, density, B,, and B, plots on the cc=60 plane at T=180.
induce three-dimensional dynamics. Magnetic reconnection is initiated by the resistivity and a reconnection jet accelerated maximally up to 0.7 is ejected away from the resistive region in the x direction. The jet collides with the PEPS and the interface between the two develops. The evolution of the instability at the jet-PEPS interface is shown by several snap shots of the B, and density plots on the z=O plane from T=lOO to T=180 in Figure 1. At T=lOO both B, and density are compressed at the interface with the density peak located slightly ahead of the peak of B, and on its shoulder. The signature of the instability becomes visible at T=120 when both B, and density begin to show three islands of enhancements (one wavelength N 18) within the interface. Then the interface becomes wavy and eventually a bubble-like structure emerges (T=140 - 180). This is brought about by higher B, regions moving faster in the x direction. The higher B, regions move also slowly in the +y direction. By the time bubbles are formed, clear pattern in the density is lost and it becomes difficult to relate it with the B, pattern. Figure 2 shows the B,, B,, B,, and density plots on the x=60 plane at T=180. For convenience, symmetric lower half portions (z
of the mode properties (growth rates, and temperature of the current sheet, doubled (D=4) show the wavelength is D as institutionally expected in MHD. this stage, we are not in a position to
M. S. Nakamura et al.
56
Fig. 3. The
B,,
density,
V,, and V, plots on the z=O plane at T=300.
complete this task. Instead, here we list up some possible candidates: K-H instability driven by the gradient drift of ions at the interface, the Rayleigh-Taylor instability driven by the +x directed magnetic tension on the z=O plane, and, Richtmyer-Meshkov instability (Wu, 2000). The first candidate requires the current thickness to be small while the others do not. The second candidate is purely a three-dimensional instability while others are two-dimensional. In addition to this line of research in an idealized geometry, a more realistic simulation of the instability in the magnetotail requires a dipole-like field at the earthward end of
the simulation box. ACKNOWLEDGEMENTS Numerical simulations
are performed
on VPP at NUCC via STE Lab. Simulation
Promotion
Program.
REFERENCES Fujimoto, M, M.S. Nakamura, T. Nagai, T. Mukai, T. Yamamoto, et al., New kinetic evidence for the near-Earth reconnection, Geophys. Res. Lett., 23, pp. 2533-2536, 1996. Kuznetsova, M. M., M. Hesse, and D. Winske, Ion dynamics in a hybrid simulation of magnetotail reconnection, J. Geophys. Res., 101,pp. 27,351-27,373, 1996. Lottermoser, R.-F, M. Scholer, and A. P. Matthews, Ion kinetic effects in magnetic reconnection: Hybrid simulations, J. Geophys. Res., 103, pp. 4547-4559, 1998. Nagai T., M. Fujimoto, MS. Nakamura, R. Nakamura, Y. Saito, et al., A large southward magnetic field of -23.5 nT in the January 10, 1995, plasmoid, J. Geophys. Res., 103, pp. 4441-4451, 1998. Nakamura, MS., M. Fujimoto, and K. Maezawa, Ion dynamics and resultant velocity space distributions in the course of magnetotail reconnection, J. Geophys. Res., 103, pp. 4531-4546, 1998. Nakamura, M.S. and M. Fujimoto, A three-dimensional hybrid simulation of magnetic reconnection, Geophys. Res. Lett., 25, pp. 2917-2920, 1998.
Nakamura, MS., and M. Fujimoto, 3-D hybrid simula!ions of magnetic reconnection sheet, Adv. Space Res., 26, pp. 431-434,200O.
in a thin current
Sergeev, V. A., P. Tanskanen, K. Mursula, A Korth, and R.C. Elphic, Current sheet thickness in the near-Earth plasma sheet during substorm growth phase, J. Geophys. Res., 95, pp. 3819-3822, 1990. Wu, C. C., Shock wave interaction with the magnetopause, J. Geophys. Res., 105,pp. 7533-7543, 2000.
Pergamon
Printed in Great Britain 0273- 1177/02 $22.00 + 0.00
www.elsevier.com/locatelasr
PII: SO273-1177(02)00032-7
INSTABILITY
AT INTERFACE
RECONNECTION
JET AND
PLASMA M.S. Nakamura’,
BETWEEN
PRE-EXISTING
SHEET
M. Fujimoto2,
and H. Matsumoto’
lRadio Science Center for Space and Atmosphere, h’yoto University, Gokasho, Uji 611-0011, JAPAN 2Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-l Ookayama, Meguro-ku, Tokyo 152-8551, JAPAN
ABSTRACT When a reconnection jet encounters a pre-existing plasma sheet standing ahead of it, the interface between the two where both plasma and magnetic field are compressed becomes unstable and develops a bubblelike structure. We have conducted three-dimensional hybrid simulations (ions as particles and electrons as massless charge neutralizing fluid) of this instability. We suggest that this instability generates a variety of plasma flows and field configurations which may have relevance to some magnetospheric phenomena. 0 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved. INTRODUCTION Magnetic reconnection is one of the most important processes in space plasmas. In the Earth’s magnetotail, magnetic reconnection produces not only change in the magnetic field topology but also converts magnetic energy stored in the lobe to plasma kinetic energy. Magnetic reconnection is considered to be initiated in a thin plasma sheet whose thickness is comparable to the relevant ion inertia length, which is frequently observed prior to substorm onsets (e.g. Sergeev et al., 1990). Since ion kinetic effects cannot be ignored in such a situation, two-dimensional hybrid simulations of the magnetic reconnection process in the plane including the lobe magnetic field have been extensively performed (e.g. Kuznetsova et al, 1996; Nakamura et al., 1998; Lottermoser et al., 1998). These simulations (as well as MHD simulations) show compression of plasma density and magnetic field component normal to the current sheet at the interface between the reconnection jet and the preexisting plasma sheet (PEPS). The compression is indeed observed in the magnetotail on the tailward side of the reconnection region (Fujimoto et al., 1996; Nagai et al., 1998). On the earthward side, the structure of the interface would be intimately related with the structure of fieldaligned currents generated in the course of substorms. These studies, however, lack the degree of freedom associated with the third dimension. In this paper, we report a new instability that grows at the interface between the reconnection jet and the PEPS, having wave-number vector in the dawn-dusk direction. SIMULATION MODEL AND RESULTS The three-dimensional simulation model used here is essentially the same as before with some modifications on the boundary conditions (Nakamura and Fujimoto, 1998, 2000). The coordinate system is the same as used conventionally (the x-, y-, and z-axis are directed to the earthward, duskward, and northward direction, respectively). Hereafter, simulation results are normalized as follows: Magnetic field by Bu (lobe magnetic field), density by nn (lobe density), velocity by VA (the AlfvCn velocity in the lobe), time scale by a;’ (the reciprocal of the ion cyclotron frequency in the lobe), spatial scale by X; = VAQ?‘, and magnitude of the resistivity by PO&VA, respectively. Using typical values, i.e. lobe density of 0.05 particle/cm3 and lobe magnetic field of 20 nT, the unit time and length are QF1 N 0.5 s and Xi 2: 1000 km, respectively. The size of the simulation box is 0 5 x 5 320, 0 5 y 5 56, and 0 2 .z < 32 with 400 x 70 x 64 cells. With the large simulation box, the boundary conditions have little effects. The symmetric boundary conditions are imposed at the x and z boundaries and the periodic boundary condition is imposed in the y direction. The 1125
1126
M. S. Nakamura et 01. 1.0 Bz T=lOO
0.0
56
T=120 56
0 Tzl4t-l
56
Y
0 0 Fig.
1. The
X B,
and density
plots on the z=O
160
0
plane at five different
160
X times,
T=lOO,
120,
140,
160, and T=180.
initial magnetic field is a Harris type model, B = [&(z), 0, 01, w h ere B,(z) = Bu tanh(z/D) for 0 5 z < 16 and B,(z) = -Bu tanh((z - 32)/D) for 16 5 z 5 32. Here, D=2 is the half-thickness of the initial plasma sheet. Current-carrying hot plasma sheet ions modeled by a drifting Maxwellian, whose thermal pressure balances the magnetic pressure, are added to uniform cold lobe ions. The symmetry about z=O artificially excludes the tail-KH mode (e.g., Nakamura and Fujimoto, 2000) and an instability that produces a wavy structure within the jet (Lottermoser et al., 1998). Sixty-four ion particles in a cell represent unit density. Electrons are at rest initially and their temperature is fixed to zero for simplicity. Anomalous resistivity is located at one corner of the simulation box with the form q(~,z) = vu [exp(-(x/IcZ)2 - (z/k=)“) + 0.011, where qe=2.0 and k,=k,=D. The resistive region is aligned to the y-axis and is two-dimensional, unlike our previous studies where three-dimensionally localized resistivity, rather short in the y direction, is assumed to
Three-DimensionalMagnetotailReconnection:Ion Signatures
1127
1.0
Bx -1 .o 16
16
16
16
2
Z
Z
Z
-16
-16 0
Y
56
-16 0
Y
56
-16 0
Y
56
0
Y
56
Fig. 2. The B,, density, B,, and B, plots on the cc=60 plane at T=180.
induce three-dimensional dynamics. Magnetic reconnection is initiated by the resistivity and a reconnection jet accelerated maximally up to 0.7 is ejected away from the resistive region in the x direction. The jet collides with the PEPS and the interface between the two develops. The evolution of the instability at the jet-PEPS interface is shown by several snap shots of the B, and density plots on the z=O plane from T=lOO to T=180 in Figure 1. At T=lOO both B, and density are compressed at the interface with the density peak located slightly ahead of the peak of B, and on its shoulder. The signature of the instability becomes visible at T=120 when both B, and density begin to show three islands of enhancements (one wavelength N 18) within the interface. Then the interface becomes wavy and eventually a bubble-like structure emerges (T=140 - 180). This is brought about by higher B, regions moving faster in the x direction. The higher B, regions move also slowly in the +y direction. By the time bubbles are formed, clear pattern in the density is lost and it becomes difficult to relate it with the B, pattern. Figure 2 shows the B,, B,, B,, and density plots on the x=60 plane at T=180. For convenience, symmetric lower half portions (z
of the mode properties (growth rates, and temperature of the current sheet, doubled (D=4) show the wavelength is D as institutionally expected in MHD. this stage, we are not in a position to
M. S. Nakamura et al.
56
Fig. 3. The
B,,
density,
V,, and V, plots on the z=O plane at T=300.
complete this task. Instead, here we list up some possible candidates: K-H instability driven by the gradient drift of ions at the interface, the Rayleigh-Taylor instability driven by the +x directed magnetic tension on the z=O plane, and, Richtmyer-Meshkov instability (Wu, 2000). The first candidate requires the current thickness to be small while the others do not. The second candidate is purely a three-dimensional instability while others are two-dimensional. In addition to this line of research in an idealized geometry, a more realistic simulation of the instability in the magnetotail requires a dipole-like field at the earthward end of
the simulation box. ACKNOWLEDGEMENTS Numerical simulations
are performed
on VPP at NUCC via STE Lab. Simulation
Promotion
Program.
REFERENCES Fujimoto, M, M.S. Nakamura, T. Nagai, T. Mukai, T. Yamamoto, et al., New kinetic evidence for the near-Earth reconnection, Geophys. Res. Lett., 23, pp. 2533-2536, 1996. Kuznetsova, M. M., M. Hesse, and D. Winske, Ion dynamics in a hybrid simulation of magnetotail reconnection, J. Geophys. Res., 101,pp. 27,351-27,373, 1996. Lottermoser, R.-F, M. Scholer, and A. P. Matthews, Ion kinetic effects in magnetic reconnection: Hybrid simulations, J. Geophys. Res., 103, pp. 4547-4559, 1998. Nagai T., M. Fujimoto, MS. Nakamura, R. Nakamura, Y. Saito, et al., A large southward magnetic field of -23.5 nT in the January 10, 1995, plasmoid, J. Geophys. Res., 103, pp. 4441-4451, 1998. Nakamura, MS., M. Fujimoto, and K. Maezawa, Ion dynamics and resultant velocity space distributions in the course of magnetotail reconnection, J. Geophys. Res., 103, pp. 4531-4546, 1998. Nakamura, M.S. and M. Fujimoto, A three-dimensional hybrid simulation of magnetic reconnection, Geophys. Res. Lett., 25, pp. 2917-2920, 1998.
Nakamura, MS., and M. Fujimoto, 3-D hybrid simula!ions of magnetic reconnection sheet, Adv. Space Res., 26, pp. 431-434,200O.
in a thin current
Sergeev, V. A., P. Tanskanen, K. Mursula, A Korth, and R.C. Elphic, Current sheet thickness in the near-Earth plasma sheet during substorm growth phase, J. Geophys. Res., 95, pp. 3819-3822, 1990. Wu, C. C., Shock wave interaction with the magnetopause, J. Geophys. Res., 105,pp. 7533-7543, 2000.