双带耀斑过程中非稳态磁重联的数值模拟
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摘要
磁重联在太阳耀斑过程中扮演着重要角色。积累在磁场中的能量通过磁重联过程快速释放出来,转化为等离子体动能、热能,并加速了高能粒子。在双带耀斑过程中,有很长的电流片形成,这些电流片的大尺度的结构一般为从太阳耀斑向上一直延伸至日冕高层。随着电流片变得薄而长,当它的长度与厚度比值超过2π时,电流片内的电阻不稳定模,如撕裂模发展起来,该不稳定模的发展倾向于将电流片撕裂成分离的电流细丝及相应的磁岛结构。在该过程中,磁场的拓扑结构被改变,磁能释放。这是非稳态的磁重联过程,并可能出现爆发式重联。撕裂模不稳定性的研究对理解耀斑等爆发活动中的重联有重要意义。对于这样的非稳态的重联问题,因为求解非线性磁流体方程组的困难,数值实验成为研究磁重联的重要方法。
我们使用有限差分法求MHD方程组,它是数值模拟中常见的方法,差分的精度随网格间距的减小而提高。然而由于受限于数值计算的条件,主要是计算机计算能力的限制,在磁重联扩散区的高分辨率的演化图象还需进一步的研究。因此,我们尝试在已有的磁流体计算程序中使用自适应网格技术,对程序进行改造,另外在高磁雷诺数环境下进行了磁重联模拟,本部分工作主要包括以下两方面的内容:
一、对现有的成熟的磁流体力学问题计算程序SHASTA进行改造。SHASTA是求解二维磁流体动力学问题的单一网格程序。在我们将其用于磁重联问题的数值模拟时,我们对它进行了修改,使之成为采用自适应网格方法的程序,可以针对扩散区进行细化计算,模拟二维非稳态的磁重联过程。在SHASTA程序的自适应计算实现过程中,我们采用了插入式的自适应修改策略,原二维磁流体力学偏微分方程的求解算法被作为独立单元使用。我们使用分层的数据结构,将每个细化层次的物理量用二维可变数组描述,并标记磁场和压强分布的陡变区为细化区域,再通过插值的方法得到细化层网格点上的物理量分布和边界条件,最后细化区域的计算结果被赋予给其上一层网格,并对其内容进行更新。采用细化计算进行的磁重联的模拟实验表明,相比单一网格计算,细节分辨率得到提高,相应的计算时间的增加则与模拟中的参数选择有关;而自适应程序部分带来的计算精度和稳定性的影响则依赖于边界设置、单步长的推进策略和插值算法。
二、模拟了高磁雷诺数环境的双带耀斑中的磁重联过程。在磁重联过程中,电流片内的电导率是至关重要的因素,磁重联发生的快慢受到它的制约和影响。在太阳日冕大气中,电导率很高,日冕环境中典型的磁雷诺数高达10~6～10~(12),因此在高磁雷诺数环境的磁重联模拟对理解双带耀斑过程中的能量释放等过程具有重要意义。相对于已有的研究,本工作中进行了磁雷诺数10~4以上的磁重联数值模拟。
Magnetic reconnection process play an important role in solar flares. Through the process of fast magnetic reconnection, magnetic energy be released into plasma kinetic energy, geothermal energy, and accelerate the high-energy particles. In two-ribbon flare, there is a long current sheet. The large-scale current sheet general upward from solar flares has been extended to the higher coronal. With the current sheet becomes thin and long, when the ratio of length and thickness more than (2π), the resistive instabilitise, such as the tearing mode show up, then the development of the tearing mode in the current sheet tends to tear current sheet into the current filaments and associated magnetic islands. In the process, the magnetic field topology has been changed and magnetic energy has been released. This is a unsteady reconnection process and the appearance of explosive reconnection will be possible. Tearing mode instability research have great significance for understanding the activities of magnetic reconnection in solar flares. For unsteady reconnection problem, as for solving nonlinear equations of MHD problems, numerical experiments as a research study magnetic reconnection in an important way.
We use the finite difference method for MHD equations, it is commonly found in numerical simulation methods. The accuracy of difference increase with the grid spacing reduce. However, due to numerical calculation conditions, mainly on computing power of compute, a large number of magnetic reconnection numerical experiments just can choose parameters in a very small range. For unsteady magnetic reconnection problem, evolution of high-resolution images in the diffusion zone need more detail research. Therefore, we try to modify existing MHD code using the adaptive mesh refinement method. Then we carried out magnetic reconnection simulation in high-magnetic Reynolds number environment. The work mainly includes the following two aspects:
First, modification of existing MHD code. SHASTA is an explicit code with single grid to solve the resistive magnetohydrodynamic equations. To deal with magnetic reconnection question, it is modified by using adaptive mesh refinement method. Then, the new adaptive mesh refinement code perform refined calculation in magnetic diffusion regions, and simulate two- dimensional unsteady magnetic reconnection process. In the process of the single grid SHASTA code be modified by adaptive algorithm, "plug-and-play" strategy is used, and the original algorithm for solving magnetohydrodynamic equations is treated as independent cells. Instead of the single data structure, a hierarchical data structure is used. The physics variables are treated as different 2D adjustable arrays in different refinement levels. During monitoring the magnetic field and the pressure of the whole calculation box, the regions where the variables change the most are flagged as next refines regions. On the new level, the solution at mesh grids and boundary conditions is obtained through copying or injecting from old grid. The refined calculation results are update to the old grid on each time-step. The result of the magnetic reconnection problems performed on the new code shows, compared with single grid code, new program using adaptive method can distinguish more phthisic details. But the increased computational time is effected by the parameter of calculation. The accuracy of the solution and numerical stability is related with boundary condition setting, one time-step advance stage and interrogations] algorithm.
Second, the magnetic reconnection simulation in two ribbon flare of high magnetic Reynolds number environment. In the process of magnetic reconnection, the electrical conductivity of current sheet is a decisive factor and it have a great impact on the speed of magnetic reconnection. In the coronal atmosphere, the conductance is very high, such as a typical coronal magnetic Reynolds number as high as (10~6～10~(12)), so the simulation of magnetic reconnection in high-magnetic Reynolds number environment have great significance for understanding energy release process of flares. Compared to existing studies, we carried out the numerical simulation of magnetic reconnection with Reynolds number (10~4) above.
我们使用有限差分法求MHD方程组,它是数值模拟中常见的方法,差分的精度随网格间距的减小而提高。然而由于受限于数值计算的条件,主要是计算机计算能力的限制,在磁重联扩散区的高分辨率的演化图象还需进一步的研究。因此,我们尝试在已有的磁流体计算程序中使用自适应网格技术,对程序进行改造,另外在高磁雷诺数环境下进行了磁重联模拟,本部分工作主要包括以下两方面的内容:
一、对现有的成熟的磁流体力学问题计算程序SHASTA进行改造。SHASTA是求解二维磁流体动力学问题的单一网格程序。在我们将其用于磁重联问题的数值模拟时,我们对它进行了修改,使之成为采用自适应网格方法的程序,可以针对扩散区进行细化计算,模拟二维非稳态的磁重联过程。在SHASTA程序的自适应计算实现过程中,我们采用了插入式的自适应修改策略,原二维磁流体力学偏微分方程的求解算法被作为独立单元使用。我们使用分层的数据结构,将每个细化层次的物理量用二维可变数组描述,并标记磁场和压强分布的陡变区为细化区域,再通过插值的方法得到细化层网格点上的物理量分布和边界条件,最后细化区域的计算结果被赋予给其上一层网格,并对其内容进行更新。采用细化计算进行的磁重联的模拟实验表明,相比单一网格计算,细节分辨率得到提高,相应的计算时间的增加则与模拟中的参数选择有关;而自适应程序部分带来的计算精度和稳定性的影响则依赖于边界设置、单步长的推进策略和插值算法。
二、模拟了高磁雷诺数环境的双带耀斑中的磁重联过程。在磁重联过程中,电流片内的电导率是至关重要的因素,磁重联发生的快慢受到它的制约和影响。在太阳日冕大气中,电导率很高,日冕环境中典型的磁雷诺数高达10~6～10~(12),因此在高磁雷诺数环境的磁重联模拟对理解双带耀斑过程中的能量释放等过程具有重要意义。相对于已有的研究,本工作中进行了磁雷诺数10~4以上的磁重联数值模拟。
Magnetic reconnection process play an important role in solar flares. Through the process of fast magnetic reconnection, magnetic energy be released into plasma kinetic energy, geothermal energy, and accelerate the high-energy particles. In two-ribbon flare, there is a long current sheet. The large-scale current sheet general upward from solar flares has been extended to the higher coronal. With the current sheet becomes thin and long, when the ratio of length and thickness more than (2π), the resistive instabilitise, such as the tearing mode show up, then the development of the tearing mode in the current sheet tends to tear current sheet into the current filaments and associated magnetic islands. In the process, the magnetic field topology has been changed and magnetic energy has been released. This is a unsteady reconnection process and the appearance of explosive reconnection will be possible. Tearing mode instability research have great significance for understanding the activities of magnetic reconnection in solar flares. For unsteady reconnection problem, as for solving nonlinear equations of MHD problems, numerical experiments as a research study magnetic reconnection in an important way.
We use the finite difference method for MHD equations, it is commonly found in numerical simulation methods. The accuracy of difference increase with the grid spacing reduce. However, due to numerical calculation conditions, mainly on computing power of compute, a large number of magnetic reconnection numerical experiments just can choose parameters in a very small range. For unsteady magnetic reconnection problem, evolution of high-resolution images in the diffusion zone need more detail research. Therefore, we try to modify existing MHD code using the adaptive mesh refinement method. Then we carried out magnetic reconnection simulation in high-magnetic Reynolds number environment. The work mainly includes the following two aspects:
First, modification of existing MHD code. SHASTA is an explicit code with single grid to solve the resistive magnetohydrodynamic equations. To deal with magnetic reconnection question, it is modified by using adaptive mesh refinement method. Then, the new adaptive mesh refinement code perform refined calculation in magnetic diffusion regions, and simulate two- dimensional unsteady magnetic reconnection process. In the process of the single grid SHASTA code be modified by adaptive algorithm, "plug-and-play" strategy is used, and the original algorithm for solving magnetohydrodynamic equations is treated as independent cells. Instead of the single data structure, a hierarchical data structure is used. The physics variables are treated as different 2D adjustable arrays in different refinement levels. During monitoring the magnetic field and the pressure of the whole calculation box, the regions where the variables change the most are flagged as next refines regions. On the new level, the solution at mesh grids and boundary conditions is obtained through copying or injecting from old grid. The refined calculation results are update to the old grid on each time-step. The result of the magnetic reconnection problems performed on the new code shows, compared with single grid code, new program using adaptive method can distinguish more phthisic details. But the increased computational time is effected by the parameter of calculation. The accuracy of the solution and numerical stability is related with boundary condition setting, one time-step advance stage and interrogations] algorithm.
Second, the magnetic reconnection simulation in two ribbon flare of high magnetic Reynolds number environment. In the process of magnetic reconnection, the electrical conductivity of current sheet is a decisive factor and it have a great impact on the speed of magnetic reconnection. In the coronal atmosphere, the conductance is very high, such as a typical coronal magnetic Reynolds number as high as (10~6～10~(12)), so the simulation of magnetic reconnection in high-magnetic Reynolds number environment have great significance for understanding energy release process of flares. Compared to existing studies, we carried out the numerical simulation of magnetic reconnection with Reynolds number (10~4) above.
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