Stratified Current Sheet During Plasma Sheet Thinning

STRATIFIED CURRENT SHEET DURING PLASMA SHEET THINNING M. Hoshino 1

1 University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033 Japan

ABSTRACT

The c u r r e n t sheet s t r u c t u r e during the plasma sheet compression is studied for a one-dimensional Harris-type c u r r e n t sheet. We find t h a t a stratified s t r u c t u r e embedded in a thick p l a s m a sheet is formed by taking into account the non-MHD effect. The global (smoothed) current density is enhanced during the plasma sheet compression, but the n e u t r a l sheet current does not necessarily increase. The c u r r e n t density can be reduced t h a n the initial state before the plasma sheet compression. This kinetic c u r r e n t sheet s t r u c t u r e may play an i m p o r t a n t role on the onset m e c h a n i s m of substorms in magnetotail.

INTRODUCTION The onset of substorms in the earth's magnetotail is the most i m p o r t a n t unresolved issue in space plasma. It is believed t h a t the plasma sheet is one of the key elements for u n d e r s t a n d i n g the dynamic p h e n o m e n a in the earth's magnetosphere. The modern satellite explorations of last decade showed that the plasma sheet has a stratified s t r u c t u r e in which a thin c u r r e n t sheet is embedded in a thick plasma sheet. The thickness of the thin c u r r e n t sheet may become as thin as the t h e r m a l ion gyro-radius during the active m a g n e t o s p h e r e [e.g. Fairfield, 1984: McComas et al., 1986; Mitcheel et al., 1990]. Mukai et al. [1998] found a super thin current sheet during the substorm growth phase, which thickness is estimated to be less t h a n the ion gyroradius. It is now recognized t h a t the formation of the thin current sheet (TCS) is occurring in a wide region of magnetotail [e.g., Sergeev et la., 1993; S a n n y et al., 1994; Pulkkinen et al., 1994; Asano et al. 2002]. In such a thin current sheet plasmas begin to behave in a nonadiabatic motion resulting in non-MHD effects, and both ion and electron dynamics become important. Since the configuration of TCS has a large a m o u n t of the free energy, it is favorable for various kinetic plasma instabilities. The onset of magnetic energy release in magnetotail is believed to be strongly coupled with the formation of TCS. It is expected t h a t TCS seems to be formed when the solar wind energy is stored into the m a g n e t o s p h e r e and the lobe magnetic field is increasing. In order to study the relationship between the lobe magnetic field and the central current sheet density, it is necessary to investigate the p l a s m a diamagnetic current self-consistently coupled to the -108-

magnetic field profile. Furthermore, since the thickness of TCS becomes of the order of the ion gyro-radius, the non-MHD effects such as the inertia effect, a finite gyro-radius motion etc. should be taken into account. We study the nonlinear time evolution of the plasma sheet by using a particle-in-cell simulation code. EVOLUTION OF CURRENT SHEET: SIMULATION STUDY We consider the general problem of the plasma sheet evolution by compressing the plasma sheet. For simplicity, a one-dimensional, Harris current sheet configuration is assumed as an initial state, and the lobe magnetic field is allowed to increase at the outer boundary of the system to be time dependent. The magnetic field profiled is B x =B o tanh(Z/~) at t=0. The induced dawn-dusk electric field from the outer boundary starts to penetrate into the plasma sheet with the magnetosonic speed, which results Fig 1. Evolution of the magnetic field in the formation of a thin current sheet. and electric current in a plasma sheet. We study the time evolution of the Note that the electric current increases plasma sheet by using a full with increasing the lobe magnetic field at particle-in-cell simulation, and we the outer boundary. discuss the plasma dynamics on the formation of TCS. The simulation box size is 1200 girds corresponding to 10k, and 106 particles for both ions and electron are used. In the present case, the mass ratio of ion to electron is assumed to be M/m=100, and the ion to electron temperature ratio is taken to be TIoNfrELE=4.2 in the initial state. The ion diamagnetic drift velocity is set to be 0.2 of the ion thermal velocity. Figure 1 shows the profiles of the electric current Jz and the magnetic field Bx at t=0 and 45, where the time is normalized by the Alfven transit time, Zh. One can find t h a t the "global" electric current is intensified with increasing the lobe magnetic field, but the current sheet shows a specific stratified structure in the vicinity of the neutral sheet at Z=0. Let us first discuss the relationship between the "global" (smoothed) electric current and the lobe magnetic field. In an MHD framework where the plasma is frozen into the magnetic field, the magnitude of Jz at the neutral sheet can be expressed as a function of the lobe magnetic field B1 at the outer boundary (Drake et al., 1981), Jz(t)cC(Bl(t)/Bo) 4/v cx=(Bl(t)/B0)2, -109-

where we assumed the equation of state T oc N ~- 1 with y=2 (i.e., two -dimensional heating perpendicular to the magnetic field). In order to compare the simulation result with the above MHD theory, we first estimate the current intensity in our simulation result by fitting the curve of sech2(Z/z*), which is depicted in the dashed lines in Figure 1. The fitting curve differs 2.2 i ................... near the neutral sheet, but the curve shows the "global" current sheet profile quite well. In Figure 2, the open circles are the Jz(z-0) estimated from the simulation result as a function of -.jz 1 . 6 the lobe magnetic field Bl, while the 2" 1.4 ....... ; Jns = B (It ) " 8 5 dashed curve is the least-square fit for z a power-law function of Jz(t) oc (Bl(t)/B0) p. We obtained p=1.85, which 1.0~ is close to the adiabatic MHD theory with p-2. This is suggestive of the ~ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 quasi-adiabatic compression for the B~( t ) / B ~ ( O ) global current sheet structure. To further confirm the quasi-adiabatic Fig 2. Relationship between the neutral compression, we examine the density sheet current JNs(t) and the lobe magnetic and temperature relation at the field at the outer boundary Bl(t). neutral sheet. Figure 3 shows ion and electron temperatures as a function of the plasma density. Both ion and electron temperatures are normalized mi on(O)/mle(O ) --4. 2 . . . . . ! . . . . . .! . . . . . ! d,I ' ' by each initial temperatures. The 2.5 .............. ' ............... ' ................ ' .............. 9.......... : ~, G - - ~ open circles and open squares are the i 9 T -N 266 -,'" simulation data of ion and electron, i ele 4a~ respectively, while the solid curves i show a power-law function fitting of T -o- ~ 2.0 .......... i . . . . . . . . . . . . . . . ~. . . . . .~. . .". . .i. . . . . .... . . . . . . . ocN ~ i. We obtained y=2.29 for ion ' ~: T. - N ~29 and y=3.66 for electron. These results . _ . - 0"!lOll :: suggest that the ion heating is almost two-dimensional compression, while the non-adiabatic electron heating is occurring in the current sheet. Since 1.o :; ; the initial electron temperature is 1.0 1.1 1.2 1.3 1.4 assumed to be 4.2 times smaller t h a n N(t)/N(0) the ion one, the electron contribution to the total temperature is still Fig 3. Relationship between the plasma negligible. Therefore, the temperature TNs(t) and the plasma temperature and density relation is density N(t) at the neutral sheet. Note almost consistent with the Jz-B1 that the initial ratio of the ion to electron relation in Figure 2. temperature TION]TELE=4.2.

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Our essential aim it to u n d e r s t a n d the current sheet structure embedded in the thick p l a s m a sheet. Figure 4 shows the ion and electron current densities at t=0 (blue) and t=45 (red). The ion and electron currents are shown in positive and negative velocities, respectively. At t=45, we can clearly find t h a t both ion and electron current profiles near the neutral sheet depart from the global current profile described by the sech2(Z/z *) curve fit. The absolute value of the electron current increases with approaching toward the neutral sheet, and its peak current becomes 10 times larger t h a n the initial electron current. However, the current quickly decreases inside Z/k < 0.2, and the current shows a positive value. For the ion current, the spatial profile is not so different from the initial current, but one can find the reduction of the current density n e a r the neutral sheet as well. The above fine structure of the electric current may be understood by virtue of the polarization electric field produced by the inertia effect of electrons and ions. The dawn-dusk electric field induced from the outer b o u n d a r y t r a n s p o r t s both ions and electrons toward the neutral sheet, but the ions start to be unmagnetized inside the ion inertia layer near the neutral sheet, while the magnetized electrons Fig 4. Ion and electron current profile in can be still effectively t r a n s p o r t e d toward the neutral sheet. Then the the nonlinear evolution of the plasma Hall electric field Ey directed toward sheet. Double current sheet can be found the n e u t r a l sheet is induced in the ion for both ions and electrons. inertia layer. Therefore, the Ey x Bx drift motion for electrons can enhance the J y current, while the effect of the Ey x Bx motion for ions makes the ion Jy current weaken in the ion meandering width. The ions, however, are almost unmagnetized in the layer and this effect is smaller t h a n that for electrons. Inside the electron inertia length, the electric field Ey i n d u c e d b y the electron pressure seems to play an i m p o r t a n t role. Note t h a t we discussed t h a t a strong electron heating near the plasma sheet in Figure 2, and we found t h a t various plasma waves are excited in the plasma sheet driven by the plasma compression (not shown here). The driven force from the outer b o u n d a r y seems to be the source of the plasma waves t h a t contribute to the electron heating. By assuming the Boltman-Maxwell state in the thin layer of the electron inertia scale, we can expect the outward Ey from the neutral sheet in a quasi-steady state, which in t u r n decelerates the meandering electron in the vicinity of the neutral sheet. The thickness of the electron meandering width can be e s t i m a t e d (mTELE/MTIoN)I/4(~i~ ) 1 / 2 ... 0.1~ in our simulation parameter. We can find t h a t the thickness of the electron thin current layer in Figure 4 is of the order of 0.1~. -111-

CONCLUSIONS We discussed how a thin current sheet can be formed during the plasma sheet compression, i.e., the energy loading stage in magnetotail. We showed that the kinetic plasma effects play a significant role on the thin current sheet formation, and the double current sheet can be form in consequence of the plasma sheet thinning. The electric current at the neutral sheet does not necessarily increase during the plasma sheet thinning. This study assumed one-dimensional, slab geometry of the plasma sheet, and many important plasma modes such as lower-hybrid-drift instability and tearing instability are not included. Our objective is to investigate the current sheet profile just before the onset of the magnetic reconnection or the current disruption etc., where the effects of such plasma instabilities do not emerge. However, we believe that this paper has important implications for understanding the dynamics on the onset of substorms in the earth's magnetotail.

REFERENCES Asano, Y., T. Mukai, M. Hoshino, Y. Saito, H. Hayakawa, and T. Nagai, Evolution of the thin current sheet in a substorm observed by Geotail, submitted to J. Geophys. Res. (2002) Drake, J. F., N. T. Gladd, and J. D. Huba, Magnetic field diffusion and dissipation in reversed-field plasmas, Phys. Fluids 24, 78 (1981) Fairfield, D. H., Magneotail energy storage and the variability of the magnetotail current sheet, Magnetic Reconnection in Space and Laboratory Plasmas, AGU/Geophys. Mono., W. Hones, Jr. Ed., 30, 168 (1984) McComas, D. J., C. T. Russel, R. C. Elphic, and S. J. Bame, The near-earth cross-tail current sheet: Detailed ISEE 1 and 2 case studies, J. Geophys. Res., 91, 4287 (1986) Mitchell, D. G., D. J. Williams, C. Y. Huang, L. A. Frank, and C. T. Russell, Current carriers in the near-earth cross-tail sheet during substorm growth phase, Geophys. Res. Lett., 17, 583 (1990) Mukai, T., M. Hoshino, Y. Saito, I. Shinohara, T. Yamamoto, T. Nagai, and S. Kokubun, Pre-Onset and Onset Signatures for Substroms in the Near-Tail Plasma Sheet: GEOTAIL Observations, Substorms-4, S. Kokubun and Y. Kamide, Eds., Terra Sci. Publ., pp.131-136 (1998). Pulkkinen, T. I., D. N. Baker, D. G. Mitchell, R. L. McPherron, C. Y. Huang, and L. A. Frank, Thin current sheets in the magnetotail during substorms: CDAW 6 revisited, J. Geophys. Res., 99, 5793 (1994) Sergeev, V. A., D. G. Mitchell, C. T. Russell, and D. J. Williams, Structure of the tail plasma/current sheet at -~llRe and its changes in the course of a substorm, J. Geophys. Res., 98, 17345 (1993) Sanny, J., R. L. McPherron, C. T. Russell, D. N. Baker, T. I Pulkkinen, and A. Nishida, Growth-phase thinning of the near-Earth current sheet during the CDAW 6 substorm, J. Geophys. Res., 99, 5805 (1994) -112-