Multipole Models of the Earth's Magnetic Field

To develop a mathematical model of rotational motion of an artificial satellite about its center of mass under the action of various forces (magnetic, Lorentz, etc.) caused by the geomagnetic field, it is necessary to know the induction of the Earth's magnetic field (EMF) as a function of the radius vector of a given point in the near-Earth space. Because the EMF possesses a complex structure and the above-mentioned functional dependence is unavailable in explicit analytic form, a set of approximate models of the EMF should be used. The simplest such model—a right dipole (aligned with the axis of rotation)—does not enable one to reveal in detail the influence of diurnal EMF rotation on the rotational motion of a satellite. The next EMF approximation—an inclined magnetic dipole—does not suffer from the above-mentioned drawback. However, it is shown that not all corrections to the magnetic induction of the EMF of the same order of magnitude are taken into account in the course of transformation from the model of aligned dipole to the model of inclined dipole. So, to develop the EMF model accurately accounting for the absence of axial symmetry of the EMF with respect to the axis of diurnal rotation of the Earth, in general, the effect of the quadrupole component of the geomagnetic potential on the EMF induction (and, probably, even the components of higher orders) must be taken into consideration. By using the International Geomagnetic Reference Field IGRF-2000, the multipole models of the EMF, corresponding to quadrupole, octupole, and higher-order approximations, were constructed and studied in this work. The EMF potential is expressed in terms of its multipole tensors. As a result, projections of the induction and induction gradient of EMF in the center of mass of the satellite onto the axes of the orbital coordinate system can be written in convenient and concise form. The expressions for the first four multipole tensors through the known geomagnetic constants are found. A method for estimating the reliability of these models is put forward, and the regions of applicability of the quadrupole and octupole models are drawn on the plane of orbital parameters.     

三轴稳定微小卫星主动磁阻尼姿态控制

针对三轴稳定微小卫星,用四元数法建立了速率阻尼阶段的动力学和运动学模型.根据地磁场强度矢量投影到轨道坐标系的简便旋转关系,设计了采用主动磁控的拟比例微分控制器,同时分析了磁力矩器的磁偶极矩.速率阻尼仿真结果表明:该控制法有效可行,具有一定的应用价值.     

On dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gyroscopic waves. Problems of stability and quantization

Based on a mathematical model described in [1], some new aspects of the dynamics of a thin planar plasma ring rotating in the magnetic field of a central body are considered. The dipole field is considered assuming that the dipole has a small eccentricity, and the dipole axis is inclined at a small angle to the central body’s axis of rotation. Emphasis is placed on the problem of stability of the ring’s stationary rotation. Unlike [1], the disturbed motion is considered which has a character of eddy magneto-gyroscopic waves. The original mathematical model is reduced to a system of finite-difference equations whose asymptotic analytical solution is obtained. It is demonstrated that some “elite” rings characterized by integral quantum numbers are long-living, while “lethal” or unstable rings (antirings) are associated with half-integer quantum numbers. As a result, an evolutionally rife rotating ring of magnetized plasma turns out to be stratified into a large number of narrow elite rings separated by gaps whose positions correspond to antirings. The regions of possible existence of elite rings in near-central body space are considered. Quantum numbers determining elite eigenvalues of the mean sector velocity (normalized in a certain manner) of a ring coincide with the quantum numbers appearing in the solution to the Schrödinger equation for a hydrogen atom. Perturbations of elite orbits corresponding to these quantum numbers satisfy the de Brogli quantum-mechanical condition. This is one more illustration of the isomorphism of quantization in microcosm and macrocosm.     

Dust Plasma Dynamics in the Geomagnetic Tail

The results of numerical modeling of dust plasma dynamics in the geomagnetic tail are presented for the southward and northward orientations of the interplanetary magnetic field in the model with reconnection of magnetic field lines of geomagnetic and interplanetary magnetic fields. It is shown that in reconnection regions the compression shock waves arise, at the fronts of which the dust plasma fluxes with higher-than-background density are generated.     

Dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gravitational waves

The model problem of the dynamics of a planar plasma ring rotating in the dipole magnetic field of a central body is considered. A finite-dimensional mathematical model of the system is synthesized by the Boubnov-Galerkin method. The class of solutions corresponding to magneto-gravitational waves associated with deformations of the ring boundaries is investigated.     

Effect of orientation of the solar wind magnetic clouds on the seasonal variation of geomagnetic activity

An analysis is made of the causes of seasonal dependence of geomagnetic activity, taking into account orientation of large-scale plasma structures (of the magnetic cloud type) of the solar wind. The contribution of magnetic clouds of different orientation in the periods of equinoxes and solstices is demonstrated. It is established that in equinox periods the geomagnetic activity increases due to ejections with small angles of inclination of their axis to the ecliptic plane, most frequently detected in near-Earth space. In solstice periods, such clouds are not geoeffective structures because of a decreased magnitude of projection of the magnetic field of cloud axis onto the Earth’s magnetic dipole during such intervals. This effect reveals itself in a reduced level of geomagnetic activity in summer and winter.     

On the Origin of High-Latitude Boundary Layer of the Earth's Magnetosphere

Localization of the reconnection region at the dayside magnetopause is among the unsolved problems of magnetospheric physics. There are two alternative models, one of which predicts the reconnection at the equatorial magnetopause, and the other predicts the reconnection in the region where the magnetic field of the solar wind flowing around the magnetosphere is antiparallel to the geomagnetic field. The statistical analysis carried out for 53 INTERBALL-1crossings of the high-latitude magnetopause in a special coordinate frame invariant with respect to the interplanetary conditions shows that the model of a reconnection in antiparallel fields agrees well with the experimental data.     

高精度地磁场模拟系统的设计与研究

根据地磁导航半实物仿真中磁场环境仿真需求,建立了高精度地磁场模拟系统,通过试验说明了系统中建立零磁空间的必要性并验证了磁屏蔽筒的屏蔽效果,同时对系统的准确性和实时性进行了试验研究。仿真结果表明,在考虑响应时间的前提下,系统能够准确实时地模拟飞行航迹上的地磁总场值,能够为地磁匹配导航半实物仿真提供真实可信的磁场仿真环境。     

A method of calculation of vertical cutoff rigidity in the geomagnetic field

On the basis of generalization of the results of extensive trajectory calculations for trial charged particles moving in the geomagnetic field the method of calculation of effective vertical cutoff rigidity, taking into account the values of K _p -index and local time, is developed. The IGRF and Tsyganenko-89 models are used for the geomagnetic field. A comparison of the results of model simulations with the experimental data on penetration of charged particles into near-Earth space is made, and penetration functions for typical spacecraft orbits are calculated.     

航天器薄壳柔性附件展开耦合行为特性研究

为研究大范围运动柔性附件几何非线性和耦合效应与中心刚体的精确动力学行为,以薄壳结构柔性附件为研究对象,引入非线性应变和位移关系,利用虚功原理推导了做大范围运动带柔性附件航天机构的完整非线性动力学模型,所构建的模型包含了非线性几何变形及附加非线性项。针对线性和非线性模型,相应开展了大范围运动航天机构刚柔耦合数值分析。结果表明,随着转速增大,线性与非线性模型动力学特性产生根本差异,指出线性模型忽略了非线性耦合项的不足,而非线性模型可精确地预测大范围运动带柔性附件航天机构动力学行为。结论对航天机构定向和跟踪操作的动力学与控制具有重要的理论价值及工程实际意义。     

Attitude stabilization of a satellite by magnetic coils

Stabilization problem for a satellite is considered. The only measurement is of the geomagnetic field in the satellite coordinates. The control is carried out by a magnetic moment of current coils (magnetorquers) mounted on the satellite body. The stabilizer constructed in this work solves the problems of magnetic and gravitational stabilization. Qualitative analysis and results of numerical simulation are presented. The results of simulation show that the proposed stabilization system is reliable, and has an appropriate accuracy and does not need powerful sources of energy, and therefore can be used for attitude control of small satellites.     

中低轨道地磁动态模拟器

文章介绍了1台能为中低轨道飞行器提供动态地磁场环境的模拟器,详细论述了模拟器的系统组成、线圈结构、电源和磁强计指标参数、控制方式和调试方法,介绍了根据WMM2000地磁场模型计算出轨道上各点的磁场值,利用数值分析的方法找出输出电流与产生磁场大小的对应表达式,从而根据计算出的磁场值和输出电流,用程控电源成功实现了中低轨道地磁场的动态模拟.     

Storm deviations of the geomagnetic trap core from dipole configuration deduced from data on relativistic electrons

Satellite data on the position of maximum L _m of the belt of relativistic electrons during strong storms, obtained at low altitudes (∼500 km) and at high altitudes (near the geomagnetic equator plane), are compared (L is the McIlwain parameter). Both at low and high altitudes the maximum of the storm belt of relativistic electrons is formed on the outer edge of the ring current. It is shown that the geomagnetic field can substantially deviate from dipole configuration not only at the geomagnetic trap periphery, but at its core as well (at L ∼ 2.5–3.5), and these deviations are nonlinear. Simultaneous measurements of the fluxes of relativistic electrons at low and high altitudes can serve for estimation of the real shape of magnetic field lines at L < 4 during geomagnetic disturbances.     

Orbital corrections by a single-input impulsive control applied along the geomagnetic field

This paper examines the possibility of regular orbital corrections for a satellite controlled by an impulsive force applied along the induction vector of the local geomagnetic field. The main purpose of the correcting considered in the paper is to eliminate the drift in secular variation of the relative orbital parameters over the orbital period. The obtained results are applied to the formation flying problem. The developed method is tested using numerical simulation.     

Orbital corrections by a single-input impulsive control applied along the geomagnetic field

This paper examines the possibility of regular orbital corrections for a satellite controlled by an impulsive force applied along the induction vector of the local geomagnetic field. The main purpose of the correcting considered in the paper is to eliminate the drift in secular variation of the relative orbital parameters over the orbital period. The obtained results are applied to the formation flying problem. The developed method is tested using numerical simulation.     

近地空间磁场梯度分布特性及磁力效应研究

以国际地磁参考场模型IGRF11为基础,推导出地球磁场梯度分布公式,并对近地空间磁场分布特点进行了分析。由基本磁力学可知,带强磁体的航天器在地磁环境中不仅受到磁力矩作用,还将受到与地磁梯度相关的磁力的影响。根据地磁环境下的磁体受力机理,文章讨论了以弱磁力改变轨道倾角的方法,并通过数值仿真验证了其有效性。     

关于磁强计与磁力矩器分时工作方案的研究

鉴于磁力矩器与磁强计同时工作会对磁强计地磁测量精度产生很大影响,本文提出一个磁强计与磁力矩器分时工作的方案,然后比较了卫星姿控系统采用不分时/分时两种方案的差异,最后研究了不同分时比例对卫星姿态控制的影响。通过仿真发现:当姿控系统采用分时方案时,电能消耗较少,早期阶段的控制精度较高,而后期稳态阶段的控制精度则相对较低;随着磁力矩器占用时间比例的下降,卫星姿态控制精度呈抛物线下降,卫星进入稳态控制阶段的时间也大大延长;分时比例存在一个相当大的范围,当在此范围内变化时,卫星姿态控制精度较高且变化幅值不大。此外,研究结果也反映出PD控制律良好的控制能力和鲁棒性。     

Reconstruction of space weather physical parameters on 400-year scale

The main goal of this paper is to get physically informative comprehensive data about dynamics of the solar magnetic field, geomagnetic field, and interplanetary magnetic field over large time scales. The total sunspot magnetic flux, aa and IDV indices of geomagnetic activity, the IMF strength, the dipole-octopole index of the large-scale magnetic field of the Sun, and the open magnetic flux are reconstructed for 400 years. The reconstruction of the π index of the large-scale polar magnetic field of the Sun is performed for 150 years.     

基于矩谐分析的高精度局部地磁场建模研究

高精度地磁基准图的绘制是实现地磁导航的关键。本文论述了应用矩谐分析方法进行地磁场     

Specific features of solar cosmic ray fluxes and geomagnetic conditions on December 5–18, 2006

Results of the analysis of specific features of solar activity, dynamics of solar cosmic ray fluxes, and state of the interplanetary medium are presented for the period December 5–18, 2006. The data analysis is based on new model concepts on coronal and interplanetary propagation of solar cosmic rays: partial capture into the magnetic field traps and oscillations at reflections from magnetic mirrors. Some new hypotheses about possible relations of the features of the interplanetary medium with processes in the Earth’s magnetosphere are put forward: the influence of the discrete interplanetary medium on processes in the Earth’s magnetosphere does exist always and, in this sense, it is a fundamental phenomenon; the discreteness of the inter-planetary medium can be one of the causes of geomagnetic substorms.