Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
History of electromagnetic theory wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Magnetic monopole wikipedia , lookup
Field (physics) wikipedia , lookup
Condensed matter physics wikipedia , lookup
State of matter wikipedia , lookup
Lorentz force wikipedia , lookup
Plasma (physics) wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Electromagnet wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
The Lower-Hybrid Drift Instability in Harris Current Sheet: Particle dynamics GUO Fan (郭帆),LU Quan-Ming (陆全明) Magnetic reconnection is a fundamental plasma physical process in solar corona, Earth’s magnetosphere and laboratory plasma experiments [1]. It leads to topological changes of magnetic field and rapidly converts magnetic energy into plasma kinetic energy. On the other hand, current sheets with thickness of the order of ion scale are unstable to a variety of instabilities, e.g. lower-hybrid drift instability [2]. These instabilities are long thought to be central important in the onset and nonlinear development of magnetic reconnection. However, while this topic has been studied for several decades, its influence to the onset and development of magnetic reconnection is still unclear. The lower-hybrid drift instability (LHDI) is driven by the diamagnetic current in the presence of inhomogeneities in the density and magnetic field [4]. According to linear theory, the fastest growing modes are primarily electrostatic with k B 0 and wavelength on electron scale. In the past the LHDI has been generally considered as a possible candidate to provide anomalous resistivity needed in classic reconnection model. Unfortunately, while enhanced fluctuations are required in the central region of current sheet to produce enough anomalous resistivity, linear theory predicts the fastest growing modes are localized on the edge region due to finite beta effects [3]. Thus it is impossible for the LHDI provide any significant anomalous resistivity inside the current sheet. This conclusion is also confirmed by observations in the magnetosphere [5], and laboratory experiments [6]. Although previous theory considers LHDI as an unimportant mode, recently some new results begin to challenge the former conclusion. First, although the fastest growing modes are on the electron scale, the LHDI is unstable over a broad range of wavelengths and frequencies, the electromagnetic modes with longer wavelength can penetrate into the central region even though the fastest growing modes are confined to the edge [7]. Second, LHDI can strongly modify the structure of current sheet, and causes anisotropic heating of electrons [8-9]. These effects will efficiently enhance the growth rate of collisionless tearing mode [10], therefore may play an important role in the onset of and nonlinear development of magnetic reconnection. However, the effect of LHDI on the dynamics of individual species of particles and its importance in evolution of current sheet is still unclear. In this paper, we discuss the dynamics of electrons and protons in Harris current sheets with 2-D full particle simulation. Our results show that due to the effect of LHDI, the dynamical features of electrons and ions are strongly distinct and depend on different physical mechanism. While electrons perform drift motion in the influence of excited LH waves, the protons are mainly governed by a direct electrostatic field created by accumulation of ions at the edge of current sheet. Their possible effects on the evolution of current sheet are also discussed. A two-dimensional full particle code is used to study the evolution of the Harris current sheet [11]. In this code, the electromagnetic fields are defined on the grids and are updated by solving the Maxwell equations with a full explicit algorithm. Both the ions and electrons are advanced self-consistently in the electromagnetic fields. The simulation box (y, z) is 12.8c / pi 6.4c / pi and the time step is tce 0.1, the spatial grid is 512×256. Harris current sheet equilibrium is considered initially, in which an initial magnetic field is given by B0 ( z) B0 tanh( z / L)ex (1) and a plasma density is given by n 0 ( z ) n 0 sec h 2 ( z / L) (2) In the simulation we employ about three million particles to represent the ions and electrons individually in Harris current sheet. The distribution functions for the ions and electrons are Maxwellian, and their drift speed in the direction of y satisfy Vi0 / Ve0 Ti0 / Te0 , in which the temperature ratio is set to be Ti0 / Te0 5 , ‘i’ and ‘e’ for ions and electrons respectively. The diamagnetic current is J 0 (z) en 0 (z)(Vi0 Ve0 ) . The mass ratio is mi / me 180 , which is large enough to suppress the drift-kink instability (DKI) [12]. The current sheet thicknesses L 0.5c / pi is considered, where c / pi is the ion inertial length defined using the peak Harris density n 0 , and c is the light speed in vacuum and is set to be c=15VA, where VA is the Alfven speed defined based on B0 and n0. No background plasma is introduced, since the presence of background plasma is strongly stabilizing to the LHDI and adds complexity to the simulation results. The periodic boundary conditions are used along the y direction. The ideal conducting boundary conditions for electromagnetic fields are employed in the z direction, and particles are reflected if they reach the boundaries. Fig. 1 (a) shows the fluctuations in the magnetic field B x excited the growth of LHDI at time i t 1.8 . In this figure, the initial magnetic field in Eq. (1) has been subtracted to show the magnetic fluctuation. It is observed that the magnetic fluctuations are mainly localized on the edge of the current sheet meanwhile propagate in the direction of y, with a wavelength approximately 0.7c / pi . Fig. 1 (b) displays the electric field E y , the fluctuation of electric field is excited in a larger region than that of magnetic field. These features of excited waves are correspondent well with linear theory [3] and previous simulations [7]. The excited waves will make electrons perform E B drift motion and generate electron vortices which move in the direction of y. These electron vortices will strongly reduce cross-field current and dissipate the magnetic field [13]. The electric field E z is plotted in Fig. 1 (c). It is shown that there is a large scale electric field point out of the current sheet in simulation plane. This electric field is primarily electrostatic and formed due to the accumulation of ions on the edge of the current sheet. Fig. 2 (a) and Fig. 2 (b) illustrate the z-component velocities of electrons and ions, respectively. In Fig. 2 (a), clear wave-like structures are formed in the region of 1 z 1 , which is consistent with the electric field E y . This result demonstrates the electrons perform E B drift motion in the influence of LH waves. The y-component (current direction) electron velocity can also be interpreted as drift motion due to the influence of z-component electric field [8]. The electron drift motion will strongly modify the current profile and may have significant roles in nonlinear development of Harris current sheet [9]. On the other hand, the proton motion shown in Fig. 2 (b) is consistent well with E z in Fig. 1 (c). This indicates that protons are accelerated in the direction of z due to direct electric field. Thus the motions of electrons and protons perform very distinct feature and are dependent on different physical mechanism. Because of the large separation between protons scale and electrons scale due to large mass ratio, the dynamics of protons and electrons usually show very different features in current sheet with thickness on the order of ion inertial scale. In this condition, ions decouple from the magnetic field and electrons still perform a rotation motion in the current sheet. In this work we report the effect of LHDI on the dynamics of ions and electrons, the results show that due to the different motions of ions and electrons, the dynamics of individual particles depends on two different physical mechanisms and shows distinct features. First, the acceleration of electrons in current sheet is primarily E B drift, in which the electric field is from the LH waves excited by LHDI. Second, the acceleration of protons in Harris current sheet is mostly direct electric field acceleration. This electric field is created by accumulation of ions on the edge of Harris current sheet due to the nonlinear effect of LHDI. Last, when the electromagnetic component of LHDI penetrates into the current sheet, the gradient magnetic drift will dominate motion of electrons, and may result in the kink of current sheet. This effect may result in important nonlinear consequences. It is needed to note that our simulation results are only 2-D and can not reveal the full pictures of the motion of particles parallel to the magnetic field. In order to reveal the full features of LHDI and its importance in reconnection physics, one should implement a full 3-D simulation with high spatial resolution, which beyond the computation current available. [1] Wang S. and Lee L. C. 1999 Magnetic Reconnection (Hefei: Anhui Education Press) (in Chinese) [2] Coppi B., Laval G., and Pellat R., Phys. Rev. Lett. 16, 1207 (1966) [3] Huba J.D., Drake J.F., and Gladd N.T., Phys. Fluids 23, 552 (1980) [4] Davidson R.C., Gladd N.T., Wu C.S., and Huba J.D., Phys. Fluids 20, 301 (1977) [5] Bale S.D., Mozer F.S. and Phan T., Geophys. Res. Lett. 29, 2180 (2002) [6] Carter T., Ji H., Trintchouk F., Yamada M. and Kulsrud R., Phys. Rev. Lett. 88, 015001 (2002) [7] Daughton W., Phys. Plasmas 10, 3103 (2003) [8] Daughton W., Lapenta G., and Ricci P., Phys. Rev. Lett. 93, 105004 (2004) [9] Ricci P., Brackbill J.U., Daughton W., and Lapenta G., Phys. Plasma 12, 055901 (2005). [10] Karimabadi H., Daughton W., and Quest, K.B., Geophys. Res. Lett. 31, L18801 (2004). [11] Fu X. R., Lu Q. M., and Wang S., Phys. Plasma 13, 012309 (2006) [12] Daughton W., J. Geophys. Res. 103, A12, 29429-29444 [13] Shinohara I., Suzuki H., Fujimoto M., and Hoshino M., Phys. Rev. Lett. 87, 095001(2001) Fig. 1a Fig. 1b Fig, 1c Fig. 2a Fig. 2b Fig. 3a Fig. 3b Fig. 4