Out-of-plane electron currents in magnetic islands formed during collisionless magnetic reconnection【推荐论文】 .doc

精品论文Out-of-plane electron currents in magnetic islands formed during collisionless magnetic reconnection5HUANG Can, LU Quanming, WU Mingyu, LU San, WANG Shui(CAS Key Laboratory of Geospace Environment, Department of Geophysics and PlanetarySciences, University of Science and Technology of China, Hefei, 230026)Abstract: Secondary islands are considered to play a crucial role in collisionless magnetic reconnection. Based on 2-D particle-in-cell simulations, we investigate the characteristics of the10out-of-plane electron currents in magnetic islands formed during collisionless magnetic reconnectionwith an initial guide field. In a primary island (formed simultaneously with the appearance of the Xlines), due to the acceleration of the trapped electrons, the direction of the formed out-of-plane electron current is reverse to the original one. In the secondary island (formed in the vicinity of the X-line), theout-of-plane electron current is generated due to the accelerated electrons by the reconnection electric15field in the vicinity of the X line. In such a way, the direction of the out-of-plane electron current in a secondary island is found to be opposite to that in a primary island. Such characteristics are found to berelated to the evolution of the magnetic islands and then electron dynamics in the islands, which are proposed in this paper to be a possible criterion to identify a secondary island formed duringcollisionless magnetic reconnection, especially in the magnetotail.20Key words: space physics; magnetic island; collisionless magnetic reconnection0IntroductionAs a fundamental physical process in plasma, magnetic reconnection is often invoked to25explain the rapid conversion of magnetic energy into plasma kinetic and thermal energies1.Therefore, magnetic reconnection is believed to be the major driving mechanism for many explosive phenomena in solar atmosphere2, the Earths magnetosphere3, laboratory experiments4, and even the magnetotail of a non-magnetized planet5. The characteristics of the ion diffusion region are considered to be the key point to understand the fast rate of30collisionless magnetic reconnection, which is determined by the Hall effects caused by ion-electron decoupling6.Recently, numerical studies have shown that the diffusion region is unstable and secondary magnetic islands may be formed in the vicinity of the X line. An extended electron current sheet is found to be formed in the vicinity of the X line in two-dimensional (2-D)35particle-in-cell (PIC) simulations of anti-parallel magnetic reconnection with open boundary condition, where a secondary island may be produced and then ejected out7. A new secondary island may be generated again and ejected out again, and such a process occurs periodically. Daughton et al.8 further found that secondary islands may also be generated in Sweet-Parker reconnection layers when the Lundquist number is sufficiently large. The40extension of the electron current sheet and the formation of secondary islands have also been found in guide field reconnection, although now the current sheet becomes tilted because the accelerated electrons in the vicinity of the X line stream outward along only two of the four separatrices9. The resulting in secondary islands not only can affect the reconnection rate in both anti-parallel and guide field reconnection7, 10, but can also enhance the electron45acceleration efficiency greatly in magnetic reconnection11. Therefore, it is crucial for us toknow the characteristics of secondary islands. In this paper, based on 2-D PIC simulationFoundations: Ph.D. Programs Foundation of Ministry of Education of China (No. 20123402120010) Brief author introduction:HUANG Can (1985-), Male, Associate Researcher, Space plasmas Correspondance author: Lu quanming (1969-), Male, Professor, Space plasmas. E-mail: qmluustc.edu.cn- 9 -results, we investigate the formation of out-of-plane electron currents in magnetic islands, especially the evolution of the primary islands, which makes it eventually distinct from the secondary ones. It is proposed that the direction of the out-of-plane electron currents may50provide a feasible observation criterion to identify a secondary island in collisionless magnetic reconnection.1Simulation Model2-D PIC simulations are employed in this paper. In the PIC simulations, ions and electrons are treated as individual particles, and their trajectories are followed by integrating the Newton55equation. The electromagnetic fields are defined in the grids, and can be known by solving the Maxwell equations with a full explicit algorithm. Periodic boundary conditions are assumed in the x direction, and the particles leave one boundary will re-enter the other boundary. The ideal conducting boundary conditions for electromagnetic fields are employed in the z direction. The1-D Harris current sheet is used as the initial configuration in the present simulations12, and60profile of the magnetic field isB0 ( z) = B0 tanh（z d）e x + By0e y ,(1)whereB0 and d are the asymptotical magnetic field and the initial half-width of the currentsheet, respectively. Here,By 0is the amplitude of the initial guide field, set to beBy 0 = -B0 inour simulations. The corresponding profile of the number density is65n( z) = nb + n0 sech2（z d ）, (2)where nbrepresents the density of the uniform, background plasma while n0is the peak Harrisdensity. The distributions of ions and electrons are assumed to be satisfied the Maxwellian function. The background plasma is non-drifting, while the drift speeds in the y direction of theHarris plasma satisfyVi 0Ti 0 = -Ve0Te0(whereTi 0andTe 0are the initial ion and electron70temperatures, whileVi 0andVe 0are the initial ion and electron drift speeds). In our simulations,the initial density ratio is set to ben0 = 5nb . We choosed = 0.5c wpi(wherec wpiis the ioninertial length based on the peak Harris densityn0 ). The mass ratio is set to bemi me =100(where miis the mass of the ion, and meis the rest mass of the electron), and the light speed isc = 15vA , where v Ais the Alfven speed based onB0 andn0 . Two simulation cases (Runs 175and 2) are performed in this paper. The initial temperature ratio is set to beRuns 1 and 2, respectively.Ti 0Te0 = 4and 0.5 inThe computation is carried out in a rectangular domain in the ( x, z)plane. The simulationbox employed in this paper has a size ofLx = 51.2 c wpiin the x direction and a sizeLz = 12.8 c wpiin the z direction withNx ´ Nz = 1024 ´ 256grids, so the spatial resolution is80Dx = Dz = 0.05c wpi = 0.5c wpe(wherec wpeis the electron inertial length based on the peakHarris densityn0 ). The time step is set toWi Dt = 0.001 , whereWi = eB0 miis the iongyrofrequency. More than 300 particles per cell, on average, are employed in the simulations. An initial flux perturbation is introduced in order to make the system reach the stage of a rapid growth of the reconnection rate quickly.852Simulation ResultsIn Run 1,Ti 0Te0 = 4 , and the initial current in the Harris current sheet is mainly carried byions. Figure 1 shows the contour of the out-of-plane electron currentJ eyat Wi t = 0, 10, 20, 27,and 32 for Run 1. The magnetic field lines are also plotted in the figure for reference. Initially the electron current is positive, and it is along the y direction. This is a multiple X line reconnection.90With the proceeding of the reconnection, two X lines are formed at aboutx = 0andx = 26 c wpi , and two magnetic islands are formed between them. Here we define a magnetic island, which is formed simultaneously with the appearance of the X lines, as a primary island.The width of the primary island will increase in the z direction, and it is about 6 c wpiat thesaturation stage. At the same time, the electrons in the vicinity of the X lines are accelerated along95the - ydirection by the reconnection electric field. Then an electron current sheet, where thecurrent is carried mainly by the electrons, is formed. We can find that the electron current sheet inthe vicinity of the X line, which is aroundx = 26 c wpi , is extended in the x direction. It is100unstable to the tearing instability and a secondary island is then formed. Here, an island, which is formed in the vicinity of the X line, is called as a secondary island. Obviously, the out-of-plane electron current in the primary islands is negative, and the electron flow is along the + y direction.In the secondary island, the out-of-plane electron current is positive, and the electron flow is alongthe - ydirection.Fig. 1 The time evolution of the out-of-plane electron current densityJ eyat Wi t = 0, 10, 20, 27, and 32 for Run1051. The solid lines represent the in-plane magnetic field lines.The characteristics of the out-of-plane electron currents in the primary and secondary islands can be demonstrated more clearly in Figure 2, which shows the profiles of the total current (solid lines), ion current (dashed lines) and electron current (dotted lines) in (a) the secondary island and(b) the primary island atWi t = 27 for Run 1. The profiles of the currents in the secondary and110primary islands are obtained along the linesx = 27 c wpiandx = 39 c wpi, respectively.115Obviously, in the secondary island, the out-of-plane current, which is mainly carried by electrons, is positive with the peak about 3.0 en0vA , while the contribution of ions is almost negligible. In the primary island, the contributions of ions and electrons to the out-of-plane currents are comparable, and the out-of-plane electron current is negative with the peak about 1.3 en0vA . We also can findthat the at the edge of the primary island, the out-of-plane current is positive.Fig. 2 The profiles of the total current (solid lines), ion current (dashed lines) and electron current (dotted lines) in(a) the secondary island and (b) the primary island atWi t = 27 for Run 1.In the vicinity of the X line, the electrons are accelerated along the- y direction by the120reconnection electric field. Therefore, it is easy to understand that the out-of-plane electron current in a secondary island is positive, since a secondary island is formed in the extended electroncurrent sheet. Figure 3 shows a typical electron trajectory in the ( x, z ) plane and the evolution ofthe velocity in the y direction fromWi t = 30to Wi t = 34 for Run 1, the electron is at lasttrapped in the secondary island. The magnetic field lines and the reconnection electric field E y125are also plotted in the figure for reference. The electron is accelerated in the - ydirection by thereconnection electric field when it enters the vicinity of the X line. At the same time, the secondary island is formed in the vicinity of the X line, and the electron is trapped by thesecondary island.The trapped electron has a large velocity in the- y direction. In this way, theformed out-of-plane electron current in the secondary island has a positive value.130Fig. 3 A typical electron trajectory in the ( x, z ) plane during (a)30 £ Wi t £ 32.2, (b)32.2 £ Wi t £ 34, and theevolution of the velocity in the y directionveyfor Run 1. The magnetic field lines (dotted contours) and thereconnection electric field E y(filled contours) atWi t = (a) 30 and (b) 33.5 are also plotted in the figure for135reference.The formation of the out-of-plane electron current in a primary island can also be understood by following the electron trajectories. Figure 4 shows a typical electron trajectory in the primary island for Run 1. Figure 4(a) and 4(b) exhibit the electron trajectory in the ( x, z ) plane and theevolution of the gyrocenter velocity in the y direction ( vGy ), respectively. In the calculation, afixed electromagnetic field, which is obtained from the simulations atWi t = 27, is used. The140magnetic field lines are also plotted in the figure for reference.Initially, the electron is located atA. The electron can be obviously accelerated in the y direction at the two ends of the island,which is during the period from B to C and D to E. During the period from B to C, the velocity ofthe electron gyrocenter in the y direction is accelerated from about 6.5 v Ato about 8.7 v A . Then,the electron drifts along the - xdirection during the period from C to D. During the period from145D to E, the velocity of the electron gyrocenter in the y direction gets further accelerated to about9.3 v A . Therefore, the electrons in the primary island are accelerated in the + y direction, which leads to a negative electron currents in the island. The particle is accelerated at the two ends of theprimary island due to the existence of the electric field in these regions. According to a two-fluidvemodel for the plasma, the electric field can be expressed asE = -V ´ B - Ñ× Pe - me dVe . Inenee dt150general, the electron inertial term- me dVee dtis negligible. While in these regions, the electricfield is determined mainly by the electron motion term-Ve ´ B , which is demonstrated in Figure5. Figure 5 plots the profiles of the electric field (a) E yand , (b) Ezalongz = 0in theprimary island atWi t = 27 for Run 1. The electric fieldEx is much smaller than E yandEz ,and we don't plot it in the figure. Obviously, in the primary island, the electric field is determined155mainly by the elec