剪切流影响磁重联过程的几个现象研究
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摘要
磁场重联是等离子体物理研究的基本现象之一,它是许多重要空间物理现象和磁约束核聚变问题的重要理论基础。通过磁重联,磁场的几何拓扑发生了改变,并伴随磁场能量向粒子能量的转换,形成高速的等离子体束流喷射。自从磁重联理论提出以来,已经得到很多学者的不断完善。但是因为所讨论问题的复杂性,以及空间和实验室里目前的观测手段都十分有限,所以对某些很重要问题的理解还存在不少争议。由于能量原理很难处理稳态平衡剪切流存在时的不稳定性问题,因此大多数磁重联理论模型仍限于从静态平衡的初始条件出发。然而剪切流在磁场重联的过程中又是非常重要的,比如聚变装置中的稳定撕裂模和压制磁岛生长等过程。
数值模拟作为理论与实验观测之间的桥梁,对于解释复杂的非线性物理过程是一种非常行之有效的办法。本论文从磁流体动力学(MHD)模型出发,采用数值模拟的方法对磁场重联问题展开讨论。着重模拟了环向剪切流、极向剪切流对磁重联的影响,同时霍尔(Hall)效应和导向场也作为重要的因素被考虑其中,并得出了一些有意义的结论,尤其进行了不同情况下的Hall四极场的可观测性分析。
本论文由以下6部分组成。
第一章,介绍了磁重联的背景。包括问题的提出、来源、学科发展史以及目前国内外的研究概况。并从空间探测与实验室托克马克(Tokamak)装置两个方面简要阐述了磁重联研究的应用前景,面临的挑战以及亟待解决的问题。
第二章,主要介绍了本文在磁重联研究中使用的数值处理方法,着重介绍了MHD的模拟过程以及对模拟结果的解释与诊断。
在磁层和行星际等离子体中经常可以观测到垂直于反平行磁场重联平面的剪切流。第三章,我们采用电阻MHD模型模拟了受迫磁重联电流片的非线性演化,讨论了这种垂直磁重联平面的剪切流对磁重联的影响。模拟结果发现在不考虑Hall效应时这种剪切流可以产生双极或者四极结构的垂直平面磁场分布。这种四极结构与典型的Hall-MHD重联中平面内电子回流过程产生的四极结构极其相似。这个结果将对以往的对于空间等离子体的快速磁重联现象的卫星观测判据提出新的挑战和思路。
基于第三章的结论,为了更好的弄清楚重联过程中的这种剪切流效应,在第四章中,我们采用Hall-MHD模型研究了Hall效应与剪切流效应共同存在时的重联过程。通过模拟发现垂直平面的四极磁场分量可以由两种效应共同产生,并且能够互相叠加产生出新的磁场分布。
在第五章中讨论了一些与第三章和第四章相关的问题。
(1)研究了导向场的空间分布效应。在这一部分定义了两个作为比较的无量纲参数:导向场强度参数α和导向场剪切长度参数χ。通过模拟发现重联过程随着导向场的增强以及χ的增加而减慢。
(2)首先采用和可压缩Hall-MHD模型讨论了无力场近似下撕裂模不稳定性的非线性演化,并与Bian和Vekstein近期的线性理论结果进行了比较。
(3)研究了不同导向场分布下所能产生的四极结构分量。并讨论了卫星观测中,对于(2)和(3)情况下实际四极场的可观测性研究。
第六章,讨论了极向剪切流驱动Alfvén共振的问题及其应用。日冕加热问题近几十年一直是太阳物理和空间物理难以解决的问题。人们设想了欧姆加热和波加热等多种加热机制,试图来解释日冕加热现象。但无论哪种加热模型中,磁场的小尺度变化效应都是很重要的。如果此时剪切流足够强,就可能激发Alfvén共振并形成薄电流片。这样欧姆加热和电流片中的波加热都可以为日冕加热提供足够的加热来源。
最后以工作成果总结全文并对所研究领域提出前景展望。
Magnetic reconnection is a fundamental phenomenon in plasma physics. It provides a theoretical basis for many phenomena in space astrophysical and magnetic confinement fusion plasmas. Through reconnection, the magnetic field topology can be changed and high-speed plasma jets can be ejected. The theories of magnetic reconnection have been developed for many years. However, debates on many specific issues still outstand due to the complexity of the problem and the insufficient data. For example, most researches on magnetic reconnection are based on the static state equilibrium due to the difficulty in energy principle description for steady state equilibria with shear flows. Nevertheless, the effect of the shear flows on magnetic reconnection and related processes is important and sometimes crucial, such as for suppressing island growth and stabilizing the tearing mode in fusion devices.
Numerical simulation is a powerful method to describe complicated, particularly nonlinear, physical processes and a bridge between theory and observation. Therefore, in this thesis, we apply MHD models numerically for magnetic reconnection studies. Thus, both toroidal and poloidal shear flows, as well as Hall effects and guide fields can be taken into consideration and certain important results, particularly the observability of the Hall quadrupolar field in different cases, are obtained.
The thesis then is organized as follows.
In Sec.1, a brief review of magnetic reconnection studies is introduced, including the origin, the basis and current achievements and progresses. We then discuss the applications and prospects, as well as challenges and outstanding issues that need to be resolved in both space physics exploration and magnetic confinement fusion.
In Sec.2, the applied numerical method is presented, especially the MHD simulation code. Then the diagnostic methods of the results are also introduced.
Sheared flows perpendicular to the anti-parallel reconnecting magnetic field are often observed in magnetosphere and interplanetary plasmas. In Sec. 3, we apply the reduced resistive MHD model for compressible plasmas to investigate the nonlinear evolution of the reconnection current sheet with such flows. Our study finds that the shear flows can generate bipolar or quadrupolar out-of-plane magnetic field perturbations in a two-dimensional resistive MHD reconnection without Hall effects. The quadrupolar structure has otherwise been thought a typical Hall MHD reconnection feature caused by the in-plane electron convention. The results will challenge the conventional understanding and satellite observations of the signature of reconnection evidence in space plasmas.
To further understand the effect investigated in Sec.3 on reconnection processes, we develop a Hall-MHD Model with the shear flows. In Sec.4 we have studied the effects of toroidal shear flows on magnetic reconnection with Hall effects exist and found that the quadrupolar out-of-plane magnetic field components generated both by the Hall effects and the shear flows can be added up and new reconnection patterns are formed.
In Sec.5, several problems relevant to our discussions in Sections 3 and 4 are discussed:
(1) First, the effect of spatial variation of the guide field is investigated. We defineαas the intensity and x as the typical length for the spatial variation of the guide field and find that the spatial variation of the guide field slows the reconnection process as x increases.
(2) We use the compressible Hall-MHD model to discuss the nonlinear evolution of the tearing modes in force-free field approximation, in compare with Bian & Vekstein's recent work in questioning if the quadrupolar structure during such reconnection processes is solely due to the effect.
(3) We also study the effect of the guide field of different profiles on magnetic reconnection generated quadrupole field components. And then the observability of the quadrupole field by satellite observations in the cases of (2) and (3) is discussed.
In Sec. 6, Alfven resonance generated by the poloidal sheared flows are studied for coronal heating application. Coronal heating has been an outstanding problem difficulty to solve for years. There are two categories of heating models: current sheet heating and wave heating. To both kinds of models however, small scale effect of the magnetic field is important. If the sheared flows are big enough, Alfvén resonance can be excited and a thin current sheet can be formed. The both the Ohmic dissipation and wave resonance on the current can provide the heating sources for the corona.
Finally, a brief summary and conclusion are given to complete the thesis.
数值模拟作为理论与实验观测之间的桥梁,对于解释复杂的非线性物理过程是一种非常行之有效的办法。本论文从磁流体动力学(MHD)模型出发,采用数值模拟的方法对磁场重联问题展开讨论。着重模拟了环向剪切流、极向剪切流对磁重联的影响,同时霍尔(Hall)效应和导向场也作为重要的因素被考虑其中,并得出了一些有意义的结论,尤其进行了不同情况下的Hall四极场的可观测性分析。
本论文由以下6部分组成。
第一章,介绍了磁重联的背景。包括问题的提出、来源、学科发展史以及目前国内外的研究概况。并从空间探测与实验室托克马克(Tokamak)装置两个方面简要阐述了磁重联研究的应用前景,面临的挑战以及亟待解决的问题。
第二章,主要介绍了本文在磁重联研究中使用的数值处理方法,着重介绍了MHD的模拟过程以及对模拟结果的解释与诊断。
在磁层和行星际等离子体中经常可以观测到垂直于反平行磁场重联平面的剪切流。第三章,我们采用电阻MHD模型模拟了受迫磁重联电流片的非线性演化,讨论了这种垂直磁重联平面的剪切流对磁重联的影响。模拟结果发现在不考虑Hall效应时这种剪切流可以产生双极或者四极结构的垂直平面磁场分布。这种四极结构与典型的Hall-MHD重联中平面内电子回流过程产生的四极结构极其相似。这个结果将对以往的对于空间等离子体的快速磁重联现象的卫星观测判据提出新的挑战和思路。
基于第三章的结论,为了更好的弄清楚重联过程中的这种剪切流效应,在第四章中,我们采用Hall-MHD模型研究了Hall效应与剪切流效应共同存在时的重联过程。通过模拟发现垂直平面的四极磁场分量可以由两种效应共同产生,并且能够互相叠加产生出新的磁场分布。
在第五章中讨论了一些与第三章和第四章相关的问题。
(1)研究了导向场的空间分布效应。在这一部分定义了两个作为比较的无量纲参数:导向场强度参数α和导向场剪切长度参数χ。通过模拟发现重联过程随着导向场的增强以及χ的增加而减慢。
(2)首先采用和可压缩Hall-MHD模型讨论了无力场近似下撕裂模不稳定性的非线性演化,并与Bian和Vekstein近期的线性理论结果进行了比较。
(3)研究了不同导向场分布下所能产生的四极结构分量。并讨论了卫星观测中,对于(2)和(3)情况下实际四极场的可观测性研究。
第六章,讨论了极向剪切流驱动Alfvén共振的问题及其应用。日冕加热问题近几十年一直是太阳物理和空间物理难以解决的问题。人们设想了欧姆加热和波加热等多种加热机制,试图来解释日冕加热现象。但无论哪种加热模型中,磁场的小尺度变化效应都是很重要的。如果此时剪切流足够强,就可能激发Alfvén共振并形成薄电流片。这样欧姆加热和电流片中的波加热都可以为日冕加热提供足够的加热来源。
最后以工作成果总结全文并对所研究领域提出前景展望。
Magnetic reconnection is a fundamental phenomenon in plasma physics. It provides a theoretical basis for many phenomena in space astrophysical and magnetic confinement fusion plasmas. Through reconnection, the magnetic field topology can be changed and high-speed plasma jets can be ejected. The theories of magnetic reconnection have been developed for many years. However, debates on many specific issues still outstand due to the complexity of the problem and the insufficient data. For example, most researches on magnetic reconnection are based on the static state equilibrium due to the difficulty in energy principle description for steady state equilibria with shear flows. Nevertheless, the effect of the shear flows on magnetic reconnection and related processes is important and sometimes crucial, such as for suppressing island growth and stabilizing the tearing mode in fusion devices.
Numerical simulation is a powerful method to describe complicated, particularly nonlinear, physical processes and a bridge between theory and observation. Therefore, in this thesis, we apply MHD models numerically for magnetic reconnection studies. Thus, both toroidal and poloidal shear flows, as well as Hall effects and guide fields can be taken into consideration and certain important results, particularly the observability of the Hall quadrupolar field in different cases, are obtained.
The thesis then is organized as follows.
In Sec.1, a brief review of magnetic reconnection studies is introduced, including the origin, the basis and current achievements and progresses. We then discuss the applications and prospects, as well as challenges and outstanding issues that need to be resolved in both space physics exploration and magnetic confinement fusion.
In Sec.2, the applied numerical method is presented, especially the MHD simulation code. Then the diagnostic methods of the results are also introduced.
Sheared flows perpendicular to the anti-parallel reconnecting magnetic field are often observed in magnetosphere and interplanetary plasmas. In Sec. 3, we apply the reduced resistive MHD model for compressible plasmas to investigate the nonlinear evolution of the reconnection current sheet with such flows. Our study finds that the shear flows can generate bipolar or quadrupolar out-of-plane magnetic field perturbations in a two-dimensional resistive MHD reconnection without Hall effects. The quadrupolar structure has otherwise been thought a typical Hall MHD reconnection feature caused by the in-plane electron convention. The results will challenge the conventional understanding and satellite observations of the signature of reconnection evidence in space plasmas.
To further understand the effect investigated in Sec.3 on reconnection processes, we develop a Hall-MHD Model with the shear flows. In Sec.4 we have studied the effects of toroidal shear flows on magnetic reconnection with Hall effects exist and found that the quadrupolar out-of-plane magnetic field components generated both by the Hall effects and the shear flows can be added up and new reconnection patterns are formed.
In Sec.5, several problems relevant to our discussions in Sections 3 and 4 are discussed:
(1) First, the effect of spatial variation of the guide field is investigated. We defineαas the intensity and x as the typical length for the spatial variation of the guide field and find that the spatial variation of the guide field slows the reconnection process as x increases.
(2) We use the compressible Hall-MHD model to discuss the nonlinear evolution of the tearing modes in force-free field approximation, in compare with Bian & Vekstein's recent work in questioning if the quadrupolar structure during such reconnection processes is solely due to the effect.
(3) We also study the effect of the guide field of different profiles on magnetic reconnection generated quadrupole field components. And then the observability of the quadrupole field by satellite observations in the cases of (2) and (3) is discussed.
In Sec. 6, Alfven resonance generated by the poloidal sheared flows are studied for coronal heating application. Coronal heating has been an outstanding problem difficulty to solve for years. There are two categories of heating models: current sheet heating and wave heating. To both kinds of models however, small scale effect of the magnetic field is important. If the sheared flows are big enough, Alfvén resonance can be excited and a thin current sheet can be formed. The both the Ohmic dissipation and wave resonance on the current can provide the heating sources for the corona.
Finally, a brief summary and conclusion are given to complete the thesis.
引文
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