Convective instability in a rapidly rotating fluid layer in the presence of a non-uniform magnetic field

Magnetoconvective instabilities in a rapidly rotating, electrically conducting fluid layer heated from below in the presence of a non-uniform, horizontal magnetic field are investigated. It was first shown by Chandrasekhar that an overall minimum of the Rayleigh number may be reached at the onset of magnetoconvection when a uniform basic magnetic field is imposed. In this paper, we show that the properties of instability can be quite different when a non-uniform basic magnetic field is applied. It is shown that there is an optimum value of the Elsasser number provided that the basic magnetic field is a monotonically decreasing or increasing function of the vertical coordinate. However, there exist no optimum values of the Elsasser number that can give rise to an overall minimum of the Rayleigh number at the onset of magnetoconvection if the imposed basic magnetic field has an inflexion point. The project supported by the National Natural Science Foundation of China (40174026 and 40074041)     

一种适用于磁流体力学切向间断的HLLC黎曼算子

磁场的存在使得磁流体力学特征波模不同于流体力学, 因此直接由流体力学HLLC黎曼算子导出的HLLC双中间态在交界的间断面会出现不守恒的问题。通常降级采用HLL单磁场中间态代替HLLC双磁场中间态以实现守恒和计算稳定, 代价是切向间断的模拟精度不足。本文对此进行改进, 在模拟切向间断时仍然保留原有的HLLC双磁场中间态, 同时各守恒量仍然能够满足Toro相容条件; 改进型HLLC算子在间断两侧的磁场分量存在差异, 因此能够更精确还原切向间断面。基于数值测试, 包括一维激波管和切向间断的时变模拟, 以及地球磁层三维数值模拟, 将模拟结果进行对比, 结果表明: 相比于已发展的HLLC算子, 改进型HLLC算子对切向间断具有更好的捕捉精度, 能够达到或接近耗时更多的HLLD算子的模拟精度。     

Oscillation of Quasi-Steady Earth＇s Magnetosphere

A three-dimensional magnetohydrodynamics （MHD） code is designed specially for global simulations of the solar wind-magnetosphere-ionosphere system. The code possesses a high resolution in capturing MHD shocks and discontinuities and a low numerical dissipation in examining possible instabilities inherent in the system. The ionosphere is approximated by a spherical shell with uniform height-integrated conductance. The solar wind is steady, and the interplanetary magnetic field is either due northward or due southward. The code is then run to find solutions of the whole system. It is found that the system has never reached a steady state, but keeps oscillating with a period of about one hour in terms of density variation at the geosynchronous orbit. However, if a certain artificial resistivity is added either in the whole numerical box or in the reconnection sites only, the reconnections change from intermittent to steady regime and the oscillation disappears accordingly. We conclude that the Earth＇s magnetosphere tends to be in a ceaseless oscillation status because of the low dissipation property inherent in the magnetospheric plasma, and the oscillation may be driven by intermittent magnetic reconnections that occur somewhere in the magnetopause and/or the magnetotail.     

Response of the Earth＇s Magnetosphere and Ionosphere to Solar Wind Driver and Ionosphere Load： Results of Global MHD Simulations

Three-dimensional global magnetohydrodynamic simulations of the solar wind-magnetosphere-ionosphere system are carried out to explore the dependence of the magnetospheric reconnection voltage, the ionospheric transpolar potential, and the field aligned currents （FACs） on the solar wind driver and ionosphere load for the cases with pure southward interplanetary magnetic field （IMF）. It is shown that the reconnection voltage and the transpolar potential increase monotonically with decreasing Pedersen conductance （∑ p ）, increasing southward IMF strength （Bs） and solar wind speed （Vsw）. Moreover, both regions 1 and 2 FACs increase when Bs and vsw increase, whereas the two currents behave differently in response to ∑p. As ∑p increases, the region 1 FAC increases monotonically, but region 2 FAC shows a non-monotonic response to the increase of ∑p ： it first increases in the range of （0,5） Siemens and then decreases for ∑p 〉 5 Siemens.     

Contribution from the Earth＇s Bow Shock to Region 1 Current under Low Alfven Mach Numbers

Using global MHD simulations of the solar wind-magnetosphere-ionosphere system, we investigate the dependence of the contribution from the Earth＇s bow shock （I1bs） to ionospheric region 1 field aligned current （FAC） （I1）. R is found that Ilbs increases with increasing southward interplanetary magnetic field （IMF） strength Bs, if the AIfven Mach number MA of the solar wind exceeds 2, a similar result as obtained by previous authors. However, if MA becomes close to or falls below 2, I1ba will decrease with Bs in both magnitude and percentage （i.e., I1bs/I1） because of the resultant reduction of the bow shock strength. Both the surface current density Jbs at the nose of the bow shock and the total bow shock current Ibs share nearly the same relationship with MA, and vary non-monotonically with MA or Bs. The maximum point is found to be located at MA = 2.7. Three conclusions are then made as follows： （1） The surface current density at the nose, which is much easier to be evaluated, may be used to largely describe the behaviour of the bow shock instead of the total bow shock current. （2） The peak of the total bow shock current is reached at about MA = 2.7 when only Bs is adjusted. （3） The non-monotonic variation of the bow shock current with MA causes a similar variation of its contribution to region 1 FAC. The turning point [or such contribution is found to be nearly MA = 2. The implication of these conclusions to the saturation of the ionospheric transpolar potential is briefly discussed.     

Earth＇s Magnetosphere Impinged by Interplanetary Shocks of Different Orientations

Using a recently developed PPMLR-MHD code, we carry out a global numerical simulation of the interaction between interplanetary shocks and Earth＇s magnetosphere. The initial magnetosphere is in a quasi-steady state, embedded in a uniform solar wind and a spiral interplanetary magnetic field （IMF）. An interplanetary （IP） shock interacts in turn with the bow shock, the magnetosheath, the magnetopause, and the magnetosphere, and changes the magnetosphere in shape and structure, and the distribution of the electric current and potential in the ionosphere as well. A preliminary comparison is made between two IP shocks of the same solar wind dynamic pressure and a vanishing IMF Bz on the downstream side, but with different propagation directions, one parallel and the other oblique to the Sun-Earth line. The numerical results show that both shocks cause a compression of the magnetosphere, an enhancement of magnetic field strength and field-aligned current in the magnetosphere, and an increase of the dawn-dusk electric potential drops across the polar ionosphere. Moreover, the magnetosphereionosphere system approaches a similar quasi-steady state after the interaction, for the downstream states are very close for the two shocks. However, the evolution processes of the system are remarkably different during the interaction with the two shocks of different orientations. The shock with the normal oblique to the Sun-Earth line results in a much longer evolution time for the system. This demonstrates that the shock orientation plays an important role in determining the associated geophysical effects and interpreting multisatellite observations of IP shock-magnetosphere interaction events.     

Catastrophe of coronal magnetic flux ropes in fully open magnetic field

The catastrophe of coronal magnetic flux ropes is closely related to solar explosive phenomena, such as prominence eruptions, coronal mass ejections, and two-ribbon solar flares. Using a 2-dimensional, 3-component ideal MHD model in Cartesian coordinates, numerical simulations are carried out to investigate the equilibrium property of a coronal magnetic flux rope which is embedded in a fully open background magnetic field. The flux rope emerges from the photosphere and enters the corona with its axial and annular magnetic fluxes controlled by a single "emergence parameter". For a flux rope that has entered the corona, we may change its axial and annular fluxes artificially and let the whole system reach a new equilibrium through numerical simulations. The results obtained show that when the emergence parameter, the axial flux, or the annular flux is smaller than a certain critical value, the flux rope is in equilibrium and adheres to the photosphere. On the other hand, if the critical value is exceeded, the flux rope loses equilibrium and erupts freely upward, namely, a catastrophe takes place. In contrast with the partly-opened background field, the catastrophic amplitude is infinite for the case of fully-opened background field.     

二维磁静平衡态的能量原理

磁静平衡态被广泛用来解释各种恒星大气结构。为了分析这些平衡态的稳定性,本文从Bernstein能量原理出发,导出了重力场中二维磁静平衡态的能量原理。对于二维二分量问题,能量积分进一步简化,并得到如下结论:系统稳定的充分必要条件是它沿每根磁力线对可忽视坐标方向的大波数模稳定。本文还给出了二维二分量磁静平衡态稳定的充分条件和必要条件,这些条件可方便地用来进行稳定性判断。     

太阳表面新磁通量的喷发和环形日冕瞬变

观测表明,日冕瞬变大多和日面物质向外喷发有关。由于冻结效应,物质喷发将伴随着磁场喷发,并且一般会在背景磁场和新喷发磁场之间形成中性电流片。在磁场喷发过程中,电流片不断向外扩张变形。另一方面,电流片根部附近的电流密度最大,磁场重联将首先在该处发生。当新喷发磁通量超过背景磁通量时,磁场重联将使电流片向外扩张;否则电流片将随着重联往里收缩。本文在线磁荷简化模型下论证了上述电流片的演化性质,指出扩张的电流片和环形日冕瞬变的高密度区有类似的几何形状,它可能是产生这类瞬变的主要机制。