王曉， 黃燦

中國(guó)科學(xué)院近地空間環(huán)境重點(diǎn)實(shí)驗(yàn)室， 中國(guó)科學(xué)技術(shù)大學(xué)地球和空間科學(xué)學(xué)院， 合肥　230026

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磁島合并研究

王曉， 黃燦*

中國(guó)科學(xué)院近地空間環(huán)境重點(diǎn)實(shí)驗(yàn)室， 中國(guó)科學(xué)技術(shù)大學(xué)地球和空間科學(xué)學(xué)院， 合肥230026

摘要本文采用二維全粒子模擬來研究無碰撞等離子體中的磁島合并過程.結(jié)果表明，磁島合并分為兩個(gè)階段，在第一個(gè)階段，兩個(gè)磁島因同向電流絲之間的吸引力而緩慢地相互靠近，在這個(gè)過程中，合并線附近的電子被面外電場(chǎng)加速，形成薄電流片，同時(shí)電流片兩側(cè)形成磁場(chǎng)堆積.第二個(gè)階段為快速重聯(lián)階段，合并線附近的電磁場(chǎng)結(jié)構(gòu)和以Harris電流片為初態(tài)的重聯(lián)擴(kuò)散區(qū)的電磁場(chǎng)結(jié)構(gòu)很相似，其中最顯著的特點(diǎn)為面外磁場(chǎng)的四極型結(jié)構(gòu).

關(guān)鍵詞磁重聯(lián); 磁島; 磁島合并; 粒子模擬

1引言

磁重聯(lián)是空間等離子體中的一個(gè)基本過程，它提供了一種將磁場(chǎng)能量快速地轉(zhuǎn)化為等離子體動(dòng)能和熱能的有效機(jī)制(Vasyliunas, 1975; Wang and Lee, 1999; Biskamp, 2000; Priest and Forbes, 2000).因此，很多空間等離子體中的爆發(fā)現(xiàn)象都可以用磁重聯(lián)來解釋，如地球磁層亞暴和太陽耀斑(Masuda et al., 1994; Tsuneta et al., 1992; Cargill and Klimchuk, 1997; Nishida et al., 1978; Ge and Russell, 2006; Wesson, 1997; Angelopoulos et al., 2008).基于電阻MHD理論的磁重聯(lián)模型Sweet-Parker模型由于重聯(lián)率太低而無法解釋實(shí)際空間等離子體中的瞬時(shí)爆發(fā)現(xiàn)象(Sweet, 1958; Parker, 1957; Petschek, 1964)，然而，無碰撞磁重聯(lián)理論提供了一種磁場(chǎng)快速重聯(lián)的方式.研究表明，Hall效應(yīng)在無碰撞磁重聯(lián)中起著主導(dǎo)作用(Birn, 2001).同時(shí)，無碰撞磁重聯(lián)的擴(kuò)散區(qū)有著多層次的結(jié)構(gòu)，包括離子擴(kuò)散區(qū)和電子擴(kuò)散區(qū)(Sonnerup, 1979; Shay et al., 2001; Lu et al., 2010; Wang et al., 2010a, 2010b)，在離子慣性尺度以內(nèi)、電子慣性尺度以外的區(qū)域，電子仍然凍結(jié)在磁力線上，而離子可以橫越磁力線，因此，電子和離子的運(yùn)動(dòng)是分離的，這樣會(huì)產(chǎn)生面內(nèi)的Hall電流和面外的四極型磁場(chǎng)結(jié)構(gòu)，這部分區(qū)域即為離子擴(kuò)散區(qū).在電子慣性尺度以內(nèi)，電子和離子均不凍結(jié)在磁力線上，這部分區(qū)域?yàn)殡娮訑U(kuò)散區(qū)(Ma and Bhattacharjee, 2001; Pritchett, 2001; Fu et al., 2006; Lu et al., 2011).

高能電子的產(chǎn)生是無碰撞磁重聯(lián)的一個(gè)重要特征(Wang et al., 2008, 2010a, 2010b, 2014; Lin and Hudson, 1971; Savrukhin, 2001; Guo et al., 2005).高能電子的激發(fā)不僅發(fā)生在重聯(lián)擴(kuò)散區(qū)(Guo et al., 2005; Hoshino et al., 2001; Hoshino, 2005)，收縮的磁島(Drake et al., 2006; Huang et al., 2013)以及磁偶極化鋒面(dipolarization front，簡(jiǎn)稱DF)區(qū)(Wu et al., 2013; Huang et al., 2015)也可以產(chǎn)生大量高能電子.最近，有學(xué)者提出磁島合并的過程中也可以觀察到明顯的電子加速，Pritchett(2008)利用二維particle-in-cell(PIC)模擬研究了多個(gè)磁島相互合并的過程，發(fā)現(xiàn)當(dāng)多個(gè)磁島最終合并成為一個(gè)大磁島的過程中，產(chǎn)生了大量高能電子.另外，Oka等(2010a, 2010b)和Tanaka等(2010, 2011) 也發(fā)現(xiàn)了磁島合并中高能離子的顯著增多，是由細(xì)長(zhǎng)的薄電流片中的撕裂模不穩(wěn)定性所引起.近年來的磁島合并研究大多只是單純地關(guān)注高能電子的產(chǎn)生，對(duì)磁島合并過程中流場(chǎng)以及電磁場(chǎng)位形的演化并沒有詳細(xì)涉及.本文利用二維PIC模擬，以磁島鏈為初態(tài)討論了磁島合并中電磁場(chǎng)結(jié)構(gòu)的演化，整個(gè)過程分為兩個(gè)階段：在第一個(gè)階段，合并線附近會(huì)形成磁場(chǎng)堆積并產(chǎn)生一個(gè)薄電流片；在第二個(gè)階段，兩個(gè)磁島快速合并成一個(gè)大磁島.

2計(jì)算方法

本文采用二維PIC全粒子模擬程序來研究?jī)蓚€(gè)磁島的合并過程.在此次模擬中，電磁場(chǎng)隨時(shí)間的演化通過蛙跳格式求解Maxwell方程得到，并且分配在固定的網(wǎng)格系統(tǒng)上，電子和離子是分開來處理的.本文采用的初始平衡態(tài)為x-z平面內(nèi)的磁島鏈位形, 初始磁場(chǎng)為

其中B0為電流片兩側(cè)無限遠(yuǎn)處的磁場(chǎng)，L為初始電流片半寬度，ε決定了初始磁島的半寬度，即Zi/L=cosh-1(1+2ε)，本次模擬中我們?nèi)ˇ?0.7，同時(shí)，我們還加了一個(gè)小擾動(dòng)來使系統(tǒng)快速達(dá)到磁島合并階段. 模擬區(qū)域x方向?yàn)橹芷谛赃吔鐥l件，z方向?yàn)榉瓷湫赃吔鐥l件.相應(yīng)的密度分布為

其中nb為背景均勻等離子體密度，n0為電流片中心等離子體密度.初始的電子和離子滿足Maxwell速度分布，隨機(jī)分布在網(wǎng)格中.初始等離子體只有y方向上的宏觀漂移速度，滿足Vi0/Ve0=-Ti0/Te0(其中Vi0和Ve0分別為離子和電子的初始漂移速度，Ti0和Te0為離子和電子的初始溫度).在本次模擬中，我們?nèi)囟缺葹門i0/Te0=5，密度比n0=5ne，光速取為c=15vA(其中vA為基于B0和n0的阿爾芬速度)，離子和電子的質(zhì)量比取為mi/me=25.模擬區(qū)域大小為L(zhǎng)x×Lz=25.6c/ωpi×25.6c/ωpi，網(wǎng)格總數(shù)為Nx×Nz=512×512，每個(gè)網(wǎng)格平均大約有100個(gè)粒子，初始電流片半寬L=Lx/4π，計(jì)算時(shí)間步長(zhǎng)為ΩiΔt=0.001，其中Ωi=eB0/mi為離子回旋頻率.

3模擬結(jié)果

圖1列出了兩磁島中心的間距，磁島中心O點(diǎn)和合并點(diǎn)X點(diǎn)之間的磁通量差值，以及由重聯(lián)電場(chǎng)表征的重聯(lián)率分別隨時(shí)間的演化過程.可以從圖中看出，磁島合并開始于Ωit=20，結(jié)束于Ωit=41，這段時(shí)間內(nèi)，兩磁島中心距離以及O點(diǎn)和X點(diǎn)間磁通量差值一直在不斷快速減小，這個(gè)過程中，重聯(lián)率不斷增大，到Ωit=38時(shí)達(dá)到最大值Ey/vAB0～0.27.

圖1　磁島中心O點(diǎn)和合并點(diǎn)X之間的磁通量差值ψωpi/cB0 (黑線)，兩磁島中心O點(diǎn)的距離Lsep/L0(藍(lán)線，其中L0為初始距離)，重聯(lián)率-Ey/vAB0(紅線隨時(shí)間的演化Fig.1　The time evolution of the magnetic flux difference between the X and O points ψωpi/cB0 (the black line), the distance between the two island O points Lsep/L0 (the blue line, where L0 is the initial distance), and the reconnection rate -Ey/vAB0 (thered line)

圖2所示為面外電場(chǎng)Ey/vAB0(圖2a—2e)、面內(nèi)極化電場(chǎng)Ex/vAB0(圖2f—2j)、面外磁場(chǎng)By/B0(圖2k—2o)的等值線圖，圖中實(shí)線為磁力線.可以看出，隨著磁島合并的開始，By在擴(kuò)散區(qū)呈現(xiàn)出典型的四極型分布，并且當(dāng)磁島合并結(jié)束后這種結(jié)構(gòu)仍然持續(xù)一段時(shí)間.與此同時(shí)，合并中心區(qū)附近出現(xiàn)負(fù)值的面外電場(chǎng)Ey，兩邊的正電場(chǎng)是磁島運(yùn)動(dòng)所引起，平面內(nèi)Ex在X點(diǎn)兩側(cè)呈現(xiàn)出對(duì)稱的月牙形分布.這種擴(kuò)散區(qū)的電磁場(chǎng)結(jié)構(gòu)與Harris電流片重聯(lián)的電磁場(chǎng)結(jié)構(gòu)非常相似，均是由于電子和離子的運(yùn)動(dòng)分離所引起(Sonnerup, 1979; Shay et al., 2001; Lu et al., 2010; Ma and Bhattacharjee, 2001; Pritchett, 2001; Fu et al., 2006; Oka et al., 2010b).圖3所示為電子和離子在Ωit=35時(shí)的流場(chǎng)圖，可以很明顯看到，在離子擴(kuò)散區(qū)中，電子和離子運(yùn)動(dòng)分離，并且離子速度遠(yuǎn)小于電子速度，電子從分離線內(nèi)側(cè)流入，經(jīng)電子擴(kuò)散區(qū)加速后，從分離線外側(cè)流出.

圖2　面外電場(chǎng)Ey/vAB0(a—e)，面內(nèi)極化電場(chǎng)Ex/vAB0(f—j)，面外磁場(chǎng)By/B0(k—o)隨時(shí)間的演化，實(shí)線為磁力線Fig.2　The time evolution of the out-of-plane electric field Ey/vAB0 (a—e), the electric field in the x direction Ex/vAB0 (f—j), and the out-of-plane magnetic field By/B0 (k—o) at Ωit=0, 17, 27, 37 and 42. The in-plane magnetic field lines are also represented

圖3　離子(a)和電子(b)的流場(chǎng)分布，實(shí)線為磁力線，Ωit=35Fig.3　The flow pattern of the ions (a) and electrons (b) at Ωit=35. The in-plane magnetic field lines are also represented for reference

圖4　z=0剖線上(a)z方向磁場(chǎng)Bz/B0，(b)y方向總電流密度Jy/en0vA，(c)y方向電場(chǎng)Ey/vAB0， (d) 電子流體參考系下的電子電流密度和電場(chǎng)的點(diǎn)積·E*隨時(shí)間的演化，實(shí)線為磁力線Fig.4　The time evolution of (a) the magnetic field in the z direction Bz/B0, (b) the total out-of-plane current density Jy/en0vA, (c) the out-of-plane electric field Ey/vAB0, (d) the dot product of the electron current density and the electric field in the electron frame ·E* along the cut z=0. The in-plane magnetic field lines are also represented

圖5　z=0剖線上y方向電子電流密度Jey/en0vA(黑線)和漂移電子電流密度eneEx/Bz(紅線)沿x方向的分布，Ωit=39Fig.5　The profiles of the electron out-of-plane current Jey/en0vA (the black line) and the electron drift current eneEx/Bz (the red line) along the cut z=0 at Ωit=39

圖6　z=0剖線上(a)z方向磁場(chǎng)在不同時(shí)刻的分布，Ωit=20, 22, 24, 26, 28, 30, 32, 34, 36(顏色從黑到紅)，藍(lán)色陰影部分為Ωit=39時(shí)的電流片寬度，(b)dBz/dt (其中d/dt為電子流體坐標(biāo)系下的隨體導(dǎo)數(shù))和電流片寬度隨時(shí)間的演化Fig.6　The demonstration of magnetic flux pileup. (a) Cuts of the magnetic field in the z direction along z=0 at Ωit=20, 22, 24, 26, 28, 30, 32, 34, 36 (the colors from the black to the red), the thickness of the current sheet in the x direction at Ωit=39 is also presented (the blue shadow). (b) The time evolution of dBz/dt (here d/dt is the material derivative in the electron frame) and the thickness of current sheet from Ωit=18 to Ωit=41 along the cut z=0

4結(jié)論

本文利用二維PIC模擬來研究無碰撞等離子體中兩個(gè)磁島的合并過程，結(jié)果顯示合并過程可分為兩個(gè)階段：在第一個(gè)階段，隨著兩個(gè)磁島的相互靠近，合并線附近的電子在y方向被電場(chǎng)加速，形成一個(gè)薄電流片，同時(shí)，電流片兩側(cè)磁場(chǎng)開始堆積；在第二個(gè)階段，電流片變得很薄，發(fā)生快速重聯(lián)，擴(kuò)散區(qū)電磁場(chǎng)結(jié)構(gòu)與Harris電流片的重聯(lián)擴(kuò)散區(qū)結(jié)構(gòu)非常相似.另外，從MHD的觀點(diǎn)上看，重聯(lián)的發(fā)生是撕裂模不穩(wěn)定性發(fā)展的一個(gè)必然結(jié)果.電流片中撕裂模的發(fā)展，是系統(tǒng)磁自由能降低，讓系統(tǒng)趨于較低能量態(tài)的要求.雖然本文的初態(tài)為兩個(gè)磁島結(jié)構(gòu)，但相對(duì)于合并后的終態(tài)還是處于一個(gè)較高能量的狀態(tài)，圖7所示為系統(tǒng)的總磁場(chǎng)能量隨時(shí)間的演化，可以看出，隨著第二個(gè)階段磁島快速合并的進(jìn)行，磁場(chǎng)能量很快下降了約10%，轉(zhuǎn)化為等離子體的動(dòng)能與熱能.

圖7　系統(tǒng)磁場(chǎng)能量隨時(shí)間的演化， 其中Fig.7　Time evolution of magnetic field energy,

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(本文編輯胡素芳)

doi:王曉， 黃燦. 2016. 磁島合并研究. 地球物理學(xué)報(bào)，59(7):2356-2361,10.6038/cjg20160703. 10.6038/cjg20160703 中圖分類號(hào)P353

基金項(xiàng)目國(guó)家自然科學(xué)基金項(xiàng)目(41331067,41474125,11235009,41274144,41121003)，國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃(973計(jì)劃)(2012CB825602)，中國(guó)科學(xué)院重點(diǎn)研究項(xiàng)目(KZZD-EW-01-4)資助.

作者簡(jiǎn)介王曉，男，博士研究生，主要從事磁場(chǎng)重聯(lián)方面的研究.E-mail:wangx998@mail.ustc.edu.cn *通訊作者黃燦，男，副教授，主要從事磁場(chǎng)重聯(lián)方面的研究. E-mail:canhuang@mail.ustc.edu.cn

收稿日期2015-12-11，2016-02-19收修定稿

The process of the coalescence of magnetic islands

WANG Xiao, HUANG Can*

KeyLaboratoryofGeospaceEnvironment,ChineseAcademyofSciences,SchoolofEarthandSpaceScience,UniversityofScienceandTechnologyofChina,Hefei230026,China

AbstractIn this paper, two-dimensional (2D) particle-in-cell (PIC) simulations are performed to investigate the coalescence process of magnetic islands in collisionless plasma. We find that the merging of magnetic islands have two stages: In the first stage, the two islands approach each other slowly due to the attractive force between the homodromous currents. The electrons around the merging line are accelerated by the out-of-plane electric field, and then a thin current sheet is formed, where the magnetic field is also piled up. In the second stage, the fast magnetic reconnection occurs in the thin current sheet around the merging line, and the resulted electromagnetic structures around the merging line are similar to those in reconnection diffusion region formed in a Harris current sheet, where the most characteristic is the quadrupole structure of the out-of-plane magnetic field.

KeywordsMagnetic reconnection; Magnetic island; Island coalescence; Particle simulation

Wang X, Huang C. 2016. The process of the coalescence of magnetic islands. Chinese J. Geophys. (in Chinese),59(7):2356-2361,doi:10.6038/cjg20160703.