Numerical Magnetohydrodynamic (MHD) Modeling of Coronal Mass Ejections (CMEs)

The Coronal Mass Ejection (CME) is arguably the most important discovery of solar eruptive phenomena in the 20th century. It is now also recognized that CMEs have great impact on the Earth's environment by inducing geomagnetic storms. Thus, development of simulation models to understand the physical mechanisms of CME initiation and propagation has become a challenge in the solar MHD community. In this paper we shall summarize chronologically the development of the theoretical analyses, and the successes and failures of the numerical magnetohydrodynamic (MHD) simulations of coronal mass ejections (CMEs) during the past two decades. The chronological development of numerical simulation models and the evolution of the numerical methods to treat this class of problems are presented. The most appropriate way to model CMEs is to have (i) a realistic pre-event coronal atmosphere, and (ii) realistic driving mechanisms. Details of the progress and assessment of the theoretical and modeling efforts for the understanding of the physics of the CME initiation and propagation will be presented, and the numerical methods to construct these simulation models will be discussed.     

Modeling and Simulating Flowing Plasmas and Related Phenomena

Simulation has become a valuable tool that compliments more traditional methods used to understand solar system plasmas and their interactions with planets, moons and comets. The three popular simulation approaches to studying these interactions are presented. Each approach provides valuable insight to these interactions. To date no one approach is capable of simulating the whole interaction region from the collisionless to the collisional regimes. All three approaches are therefore needed. Each approach has several implicit physical assumptions as well as several numerical assumptions depending on the scheme used. The magnetohydrodynamic (MHD), test-particle/Monte-Carlo and hybrid models used in simulating flowing plasmas are described. Special consideration is given to the implicit assumptions underlying each model. Some of the more common numerical methods used to implement each model, the implications of these numerical methods and the resulting limitations of each simulation approach are also discussed.     

电导率模拟对高超声速MHD控制影响

高温气体电导率是高超声速电磁流动控制数值模拟最重要的参数之一。针对电导率模拟准确性及其对高超声速磁流体控制影响的问题，考虑高超声速飞行器流场中高温气体热化学非平衡效应，采用三维低磁雷诺数磁流体动力学（MHD）数值模拟方法及程序，结合国内外常见电导率处理方法开展典型状态高超声速MHD控制数值模拟，分析电导率模拟对高超声速磁流体流场分布、气动力/热特性的影响。研究表明：磁控热流减缓效果与电导率呈非线性关系，电导率较大时将出现电导率的磁控热饱和现象，其产生的原因可能与化学反应趋向于平衡态存在一定关系；采用定电导率方法，会人为放大磁场洛仑兹力的磁阻力效果，使阻力系数的预测值偏大；不同电导率模型计算得到的电导率分布差异很大，甚至存在数量级的差别，显著影响了磁流体的控制效果，这与电导率模型的适用范围、参数选取原则存在很大关联；对于含多种离解、电离组分的高温气体流动来说，采用基于多电离组分迁移碰撞的电导率模型（本文模型M8），计算与试验一致性最好。     

Synthesis of CME-Associated Moreton and EIT Wave Features from MHD Simulations

Soft X-ray (SXR) waves, EIT waves, and Hα Moreton waves are all associated with coronal mass ejections (CMEs). The knowledge of the characteristics about these waves is crucial for the understanding of CMEs, and hence for the space weather researches. MHD numerical simulation is performed, with the consideration of the quiet Sun atmosphere, to investigate the CME/flare processes. On the basis of the numerical results, SXR, EUV, and Hα images of the eruption are synthesized, where SXR waves, EIT waves, and Hα Moreton waves are identified. It confirms that the EIT waves, which border the expanding dimmming region, are produced by the successive opening (or stretching) of the closed magnetic field lines. Hα Moreton waves are found to propagate outward synchronously with the SXR waves, lagging behind the latter spatially by ～27 Mm in the simulated scenario. However, the EIT wave velocity is only a third of the Moreton wave velocity. The synthesized results also suggest that Hα± 0.45Å would be the best off-band for the detection of Hα Moreton waves.     

The future of space plasma simulation

Space plasma simulation is a subject which is in its infancy, but which is already having an important impact on space science. Its growth is being spurred onward by the continuing increase in capacity (speed and memory) of computers and by advances in the sophistication of numerical models. These advances are making it possible to simulate more realistic situations using more complex models. Already significant three-dimensional MHD calculations of the magnetosphere and its interaction with the solar wind have been carried out. In addition multi-dimensional particle simulations are illuminating many of the microscopic physics processes which go on (instabilities, saturation levels and wave nonlinearity, shock structure, etc.). Notwithstanding these advances, the surface has only been scratched; many challenges and opportunities are provided by simulation both for the space physicist and the model builders (also for computer designers). In MHD models more physics need to be included (Hall effect, gyroviscosity, accurate models of boundaries, how do we put microscopic physics effects into macroscopic codes, etc.). For model builders correct treatments of systems containing a large range of important space and time scales, magnetic field strengths, Alfven wave velocity, etc. present real challenges. What are the best ways to diagnose these complex models and obtain meaningful information? What quantities should be looked at? How should they be displayed? A discussion of the promises, the prospects, and the challenges of the above topics will be given with examples taken from recent work.     

Resonant MHD Waves in the Solar Atmosphere

The linear theory of MHD resonant waves in inhomogeneous plasmas is reviewed. The review starts from discussing the properties of driven resonant MHD waves. The dissipative solutions in Alfvén and slow dissipative layers are presented. The important concept of connection formulae is introduced. Next, we proceed on to non-stationary resonant MHD waves. The relation between quasi-modes of ideal MHD and eigenmodes of dissipative MHD are discussed. The solution describing the wave motion in non-stationary dissipative layers is given. It is shown that the connection formulae remain valid for non-stationary resonant MHD waves. The initial-value problem for resonant MHD waves is considered. The application of theory of resonant MHD waves to solar physics is discussed.     

三维磁流体强化超燃冲压发动机数值模拟

建立了三维磁流体强化超燃冲压发动机内部黏性流场的求解模型.针对马赫数为6设计了联合应用磁控进气道和磁流体能量旁路的磁流体强化超燃冲压发动机模型.针对该模型进行了数值模拟研究,分析其中的三维流场结构、电参数分布规律以及能量转换特性.结果表明:当飞行马赫数为8时,磁控进气道的应用能够使头部压缩激波回到唇口,使分离区消失,内进气道中的流动恢复到设计状态.磁流体能量旁路可有效降低燃烧室入口处的马赫数,从而改善发动机性能.其中发生器中的流动参数和电参数的分布比较理想,效果显著;而加速器要取得显著的加速效果则需要大量的能量输入.在加速器中,电极附近焦耳耗散严重,导致局部高温以及流动的复杂性,性能不够理想.      

A Class of TVD Type Combined Numerical Scheme for MHD Equations With a Survey About Numerical Methods in Solar Wind Simulations

It has been believed that three-dimensional, numerical, magnetohydrodynamic (MHD) modelling must play a crucial role in a seamless forecasting system. This system refers to space weather originating on the sun; propagation of disturbances through the solar wind and interplanetary magnetic field (IMF), and thence, transmission into the magnetosphere, ionosphere, and thermosphere. This role comes as no surprise to numerical modelers that participate in the numerical modelling of atmospheric environments as well as the meteorological conditions at Earth. Space scientists have paid great attention to operational numerical space weather prediction models. To this purpose practical progress has been made in the past years. Here first is reviewed the progress of the numerical methods in solar wind modelling. Then, based on our discussion, a new numerical scheme of total variation diminishing (TVD) type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account convergence, stability and resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method (PPM). Finally, some conclusions are made. This revised version was published online in August 2006 with corrections to the Cover Date.     

NND格式在多维理想磁流体方程组中的应用

采用修正的四步Runge-Kutta方法求解三维一般曲线坐标系下的理想磁流体方程组,为克服数值振荡,加特征型NND格式进行后处理.特征型NND格式推广到求解三维磁流体(MHD)问题需要知道雅可比通量的左右特征矩阵,在具体计算时需要克服矩阵的奇性.本文用三维程序采用推广的特征NND格式计算了一维MHD激波管和二维(MHD)喷管流动,计算结果表明,特征NND格式保持了TVD格式高精度的优点,又具有计算简单的特点,在包括强弱间断等复杂波系的定常和非定常MHD流场数值模拟中是成功的.     

磁流体管流准一维模型的数值验证与性能分析

为了快速分析磁流体管流,采用涡轮喷气发动机模型对磁流体管流进行类比分析,引入变截面管流理论和修改过的多变效率表达式,推导了磁流体发电器和加速器的准一维模型,采用二维数值方法验证了准一维模型的可行性,利用该准一维模型对磁流体管流进行了性能分析,结果表明,多变效率的引入使准一维模型更加完整,当负载系数不变时,磁流体装置中的平均马赫数越低,其等熵效率越高。     

Alfvén wave heating

This review discusses Alfvén wave heating in non-uniform plasmas as a possible means for explaining the heating of the solar corona. It focusses on recent analytical results that enable us to understand the basic physics of Alfvén wave heating and help us with the interpretation of results of numerical simulations. First we consider the singular wave solutions that are found in linear ideal MHD at the resonant magnetic surface where the frequency of the wave equals the local Alfvén frequency. Next, we use linear resistive MHD for describing the waves in the dissipative region and explain how dissipation modifies the singular solutions found in linear ideal MHD.     

Laboratory and Numerical Simulations of the Impulsive Penetration Mechanism

Plasma interaction at the interface between the magnetosheath and magnetosphere has been extensively studied during recent years. As a consequence various theoretical models have emerged. The impulsive penetration mechanism initially proposed by Lemaire and Roth as an alternative approach to the steady state reconnection, is a non-stationary model describing the processes which take place when a 3-D solar wind plasma irregularity interacts with the outer regions of the Earth's magnetosphere. In this paper we are reviewing the main features of the impulsive penetration mechanism and the role of the electric field in driving impulsive events. An alternative point of view and the controversy it has raised are discussed. We also review the numerical codes developed to simulate the impulsive transport of plasma across the magnetopause. They have illustrated the relationship between the magnetic field distribution and the convection of solar-wind plasma inside the magnetosphere and brought into perspective non-stationary phenomena (like instabilities and waves) which were not explicitly integrated in the early models of impulsive penetration. Numerical simulations devoted to these processes cover a broad range of approximations, from ideal MHD to hybrid and kinetic codes. The results show the limitation of these theories in describing the full range of phenomena observed at the magnetopause and magnetospheric boundary layers.     

Transonic Flows in Two-Fluid Plasmas

Transonically rotating toroidal plasmas occur at all scales in the plasma universe and, recently, also in laboratory tokamak plasmas. This offers great opportunities for new insights of the effects of transonic transitions on the background equilibrium flows, and on the waves and instabilities excited. Transfer of knowledge and computational methods on MHD and two-fluid waves and instabilities in magnetically confined laboratory fusion plasmas to space and astrophysical plasmas is seriously hampered though by two related difficulties:

1. in contrast to laboratory plasmas, astrophysical plasmas always have sizeable plasma flows so that they can never be described as a static equilibrium;
2. these flows are usually ‘transonic’, i.e., surpass one of the critical speeds related to the different flow regimes with quite different physical characteristics.

Based on previously obtained MHD results on the stationary states and instabilities of transonically rotating accretion disks about compact objects, the extension to two-fluid plasmas is initiated: A variational principle for the computation of two-fluid stationary states is constructed which involves seven fields determining the different physical variables, and six arbitrary stream functions that should be determined by spatially resolved astrophysical observations. It exhibits all the intricacies due to the electron and ion flow excursions from the magnetic flux surfaces. New hyperbolic flow regimes are found with quite different properties than the MHD ones.     

Towards a new paradigm: from a quasi-steady description to a dynamical description of the magnetosphere

A great deal of the research done on the dynamical process of the solar wind- magnetosphere interaction is based on large-scale, quasi-steady theoretical models, such as the classical reconnection model. However, it can be argued that the theoretical and observational foundations of these commonly believed paradigms are not always strong, and support for these models is sometimes weak, controversial or inconsistent. This paper discusses the need for a transition from an oversimplified quasi-steady paradigm towards a more realistic one including the dynamics of MHD waves and wave packets. The effects of localized wave packets may be most important in active plasma regions, where ideal MHD breaks down and localized, time-dependent processes become dominant. New insights into the theories of field-aligned current generation, auroral particle acceleration and the concept of reconnection may be found by including MHD wave propagation and wave packet dynamics.     

The Solar Dynamo

Observations relevant to current models of the solar dynamo are presented, with emphasis on the history of solar magnetic activity and on the location and nature of the solar tachocline. The problems encountered when direct numerical simulation is used to analyse the solar cycle are discussed, and recent progress is reviewed. Mean field dynamo theory is still the basis of most theories of the solar dynamo, so a discussion of its fundamental principles and its underlying assumptions is given. The role of magnetic helicity is discussed. Some of the most popular models based on mean field theory are reviewed briefly. Dynamo models based on severe truncations of the full MHD equations are discussed.     

超声速非平衡电离磁流体流动控制试验和数值模拟

为了开展磁流体(MHD)流动控制原理研究,建立了磁流体技术试验系统,采用电容耦合射频-直流组合放电对Ma=3.5气流进行电离,在磁场作用下产生顺/逆气流方向的洛伦兹力控制流场,采用试验段静压变化来监测磁流体流动控制效果,通过一维模型计算磁流体流动控制过程中流场变化情况,分析磁流体流动控制效果;通过添加电磁源项的Navier-Stokes方程耦合电势泊松方程建立了二维磁流体动力模型,对磁流体流动控制进行数值模拟研究。主要结论如下:在磁场约束下,电容耦合射频-直流组合放电能够在Ma=3.5流场中产生大体积均匀电流,电导率约0.015S/m;在焦耳热和洛伦兹力作用下,磁流体加速时静压升高了130Pa,减速时静压升高了200Pa;磁流体流动控制过程中,仅有不足10%的能量在磁流体通道内发生了作用;数值模拟结果显示,在试验条件下,加速时静压升高了128Pa,减速时静压升高了208Pa,与试验结果基本吻合。     

Interplanetary shock waves generated by solar flares

Recent observational and theoretical studies of interplanetary shock waves associated with solar flares are reviewed. An attempt is made to outline the framework for the genesis, life and demise of these shocks. Thus, suggestions are made regarding their birth within the flare generation process, MHD wave propagation through the chromosphere and inner corona, and maturity to fully-developed coronal shock waves. Their subsequent propagation into the ambient interplanetary medium and disturbing effects within the solar wind are discussed within the context of theoretical and phenomenological models. The latter — based essentially on observations — are useful for a limited interpretation of shock geometric and kinematic characteristics. The former — upon which ultimate physical understanding depends — are used for clarification and classification of the shocks and their consequences within the solar wind. Classification of limiting cases of blast-produced shocks (as in an explosion) or longer lasting ejecta (or piston-driven shocks) will hopefully be combined with the study of the flare process itself.The theoretical approach, in spite of its contribution to clarification of various concepts, contains some fundamental limitations and requires further study. Numerical simulations, for example, depend upon a non-unique set of multi-parameter initial conditions at or near the Sun. Additionally, the subtle but important influence of magnetic fields upon energy transport processes within the solar wind has not been considered in the numerical simulation approach. Similarity solutions are limited to geometrical symmetries and have not exploited their potential beyond the special cases of the blast and the constant-velocity, piston-driven shock waves. These continuum fluid studies will probably require augmentation or even replacement by plasma kinetic theory in special situations when observations indicate the presence of anomalous transport processes. Presently, for example, efforts are directed toward identification of detailed shock structures (as in the case of Earth's bow shock) and of the disturbed solar wind (such as the piston).Further progress is expected with extensive in situ and remote monitoring of the solar wind over a wide range of heliographic radii, longitudes and latitudes.This paper is a revised and updated version of an invited review originally presented at the IUGG XV General Assembly, Moscow, U.S.S.R., 2–14 August 1971.     

MHD Waves and Heating in Coronal Holes

Coronal holes have been identified as source regions of the fast solar wind, and MHD wave activity has been detected in coronal holes by remote sensing, and in situ in fast solar wind streams. I review some of the most suggestive wave observations, and discuss the theoretical aspects of MHD wave heating and solar wind acceleration in coronal holes. I review the results of single fluid 2.5D MHD, as well as multi-fluid 2.5D MHD models of waves in coronal holes, the heating, and the acceleration of the solar wind be these waves.