Quasi-parallel collisionless shocks

The magnetic field and plasma data from the ISEE 1, 2, and 3 spacecraft have greatly increased our knowledge of the quasi-parallel collisionless shock in space. Hybrid-code simulations have provided us with valuable insights into the physics of the quasi-parallel shock. Unfortunately, theoretical understanding of the nonlinear physics of the quasi-parallel shock is still in a qualitative stage of development. Generation of large-amplitude whistler waves and hydromagnetic waves observed in the quasi-parallel shock has been discussed either in terms of linear instabilities or qualitative nonlinear arguments. It appears that the ion reflection, ion heating, and leakage of the shock-heated downstream ions at the quasi-parallel shock can all be explained in terms of nonadiabatic scatterings of ions by the large-amplitude whistler-magnetosonic waves with frequencies near the ion gyrofrequency and wavelength near the ion inertial length. The nonadiabatic scattering is defined by the non-conservation of the magnetic moment. Future study of the quasi-parallel shock should focus on developing quantitative theoretical models for the nonlinear physical processes fundamental to the quasi-parallel shock.     

Radio emission from quasi-parallel shock waves in the corona

Shock waves in the solar corona manifest themselves in type II bursts in dynamic radio spectra. Recently, short large amplitude magnetic structures (SLAMS) have been observed in the vicinity of the quasi-parallel region of Earth's bow shock as an example of a collisionless shock wave in space plasmas. SLAMS are able to accelerate electrons to high energies by shock drift acceleration. Assuming that SLAMS also appear in the vicinity of super-critical, quasi-parallel shocks in the corona, electrons can also be accelerated at quasi-parallel shocks and, subsequently, generate radio waves manifesting in solar type II radio bursts.     

气相爆轰波马赫反射非自相似性特征的实验

为了研究在CJ(Chapman-Jouguet)状态下气相爆轰波马赫反射的非自相似性特征,搭建了由驱动段、传播段以及观测段组成的矩形管道;利用纹影和烟膜实验方法分别对3种预混气发生马赫反射现象进行了实验研究.实验结果表明:对稳态或非稳态气体,测量了马赫反射三波点位置高度,验证了马赫反射三波点轨迹线为波动的曲线,即自相似性对爆轰波马赫反射失效;非自相似性的重要特征是三波点轨迹线在楔角初始位置时基本遵循无反应冲击波理论计算结果,随后逐渐偏离并向有反应冲击波转变,之后接近平行于反应冲击波理论计算并稳定地处于两个理论值之间.最后给出在初始压力为10kPa和楔角为30°的条件下,对于所研究的3种气体,其马赫反射三波点发生转变的位置高度分别约为0.8,1.05cm以及0.5cm,可见相同初始条件下非稳态气体的马赫反射发生转变比稳态气体提前.      

Shock Acceleration of Ions in the Heliosphere

Energetic particles constitute an important component of the heliospheric plasma environment. They range from solar energetic particles in the inner heliosphere to the anomalous cosmic rays accelerated at the interface of the heliosphere with the local interstellar medium. Although stochastic acceleration by fluctuating electric fields and processes associated with magnetic reconnection may account for some of the particle populations, the majority are accelerated by the variety of shock waves present in the solar wind. This review focuses on “gradual” solar energetic particle (SEP) events including their energetic storm particle (ESP) phase, which is observed if and when an associated shock wave passes Earth. Gradual SEP events are the intense long-duration events responsible for most space weather disturbances of Earth’s magnetosphere and upper atmosphere. The major characteristics of gradual SEP events are first described including their association with shocks and coronal mass ejections (CMEs), their ion composition, and their energy spectra. In the context of acceleration mechanisms in general, the acceleration mechanism responsible for SEP events, diffusive shock acceleration, is then described in some detail including its predictions for a planar stationary shock, shock modification by the energetic particles, and wave excitation by the accelerating ions. Finally, some complexities of shock acceleration are addressed, which affect the predictive ability of the theory. These include the role of temporal and spatial variations, the distinction between the plasma and wave compression ratios at the shock, the injection of thermal plasma at the shock into the process of shock acceleration, and the nonlinear evolution of ion-excited waves in the vicinity of the shock.     

The Dynamic Quasiperpendicular Shock: Cluster Discoveries

The physics of collisionless shocks is a very broad topic which has been studied for more than five decades. However, there are a number of important issues which remain unresolved. The energy repartition amongst particle populations in quasiperpendicular shocks is a multi-scale process related to the spatial and temporal structure of the electromagnetic fields within the shock layer. The most important processes take place in the close vicinity of the major magnetic transition or ramp region. The distribution of electromagnetic fields in this region determines the characteristics of ion reflection and thus defines the conditions for ion heating and energy dissipation for supercritical shocks and also the region where an important part of electron heating takes place. In other words, the ramp region determines the main characteristics of energy repartition. All these processes are crucially dependent upon the characteristic spatial scales of the ramp and foot region provided that the shock is stationary. The process of shock formation consists of the steepening of a large amplitude nonlinear wave. At some point in its evolution the steepening is arrested by processes occurring within the shock transition. From the earliest studies of collisionless shocks these processes were identified as nonlinearity, dissipation, and dispersion. Their relative role determines the scales of electric and magnetic fields, and so control the characteristics of processes such as ion reflection, electron heating and particle acceleration. The determination of the scales of the electric and magnetic field is one of the key issues in the physics of collisionless shocks. Moreover, it is well known that under certain conditions shocks manifest a nonstationary dynamic behaviour called reformation. It was suggested that the transition from stationary to nonstationary quasiperiodic dynamics is related to gradients, e.g. scales of the ramp region and its associated whistler waves that form a precursor wave train. This implies that the ramp region should be considered as the source of these waves. All these questions have been studied making use observations from the Cluster satellites. The Cluster project continues to provide a unique viewpoint from which to study the scales of shocks. During its lifetime the inter-satellite distance between the Cluster satellites has varied from 100 km to 10000 km allowing scientists to use the data best adapted for the given scientific objective. The purpose of this review is to address a subset of unresolved problems in collisionless shock physics from experimental point of view making use multi-point observations onboard Cluster satellites. The problems we address are determination of scales of fields and of a scale of electron heating, identification of energy source of precursor wave train, an estimate of the role of anomalous resistivity in energy dissipation process by means of measuring short scale wave fields, and direct observation of reformation process during one single shock front crossing.     

Computer modeling of test particle acceleration at oblique shocks

We review the basic techniques and results of numerical codes used to model the acceleration of charged particles at oblique, fast-mode, collisionless shocks. The emphasis is upon models in which accelerated particles (ions) are treated as test particles, and particle dynamics is calculated by numerically integrating along exact phase-space orbits. We first review the case where ions are sufficiently energetic so that the shock can be approximated by a planar discontinuity, and where the electromagnetic fields on both sides of the shock are defined at the outset of each computer run. When the fields are uniform and static, particles are accelerated by the scatter-free drift acceleration process at a single shock encounter. We review the characteristics of scatter-free drift acceleration by considering how an incident particle distribution is modified by interacting with a shock. Next we discuss drift acceleration when magnetic fluctuations are introduced on both sides of the shock, and compare these results with those obtained under scatter-free conditions. We describe the modeling of multiple shock encounters, discuss specific applications, and compare the model predictions with theory. Finally, we review some recent numerical simulations that illustrate the importance of shock structure to both the ion injection process and to the acceleration of ions to high energies at quasi-perpendicular shocks.     

Design method with controllable velocity direction at throat for inward-turning inlets

In the design of a hypersonic inward-turning inlet by applying the traditional basic flowfield, a reflected shock-wave is formed in the isolator due to the continuous reflection of the cowlreflected shock wave in the basic flow-field, which interacts with the boundary layer to produce a considerable influence on the performance of the inlet. Here, a basic flow-field design method that can control the velocity direction at the throat section is developed, and numerical simulations are conducted to demonstrate the effectiveness of this method. The method presented in this paper can achieve the absorption of the reflected waves at the shoulder of the basic flow-field by adjusting the variation law of the center radius in the basic flow-field, and a smooth transition between the compression surface and the isolator can also be produced. The Mach number and total pressure recovery coefficient of the inlet designed according to this method are 3.00 and 0.657, respectively, at design point(the incoming flow Mach number Ma1= 6.0). The results show that with this method, the inlet can efficiently weaken both the reflection of the shock wave and the interaction between the boundary layer and the reflected shock waves, which improves the aerodynamic performance of the inlet.     

The Two Sources of Solar Energetic Particles

Evidence for two different physical mechanisms for acceleration of solar energetic particles (SEPs) arose 50 years ago with radio observations of type III bursts, produced by outward streaming electrons, and type II bursts from coronal and interplanetary shock waves. Since that time we have found that the former are related to “impulsive” SEP events from impulsive flares or jets. Here, resonant stochastic acceleration, related to magnetic reconnection involving open field lines, produces not only electrons but 1000-fold enhancements of ³He/⁴He and of (Z>50)/O. Alternatively, in “gradual” SEP events, shock waves, driven out from the Sun by coronal mass ejections (CMEs), more democratically sample ion abundances that are even used to measure the coronal abundances of the elements. Gradual events produce by far the highest SEP intensities near Earth. Sometimes residual impulsive suprathermal ions contribute to the seed population for shock acceleration, complicating the abundance picture, but this process has now been modeled theoretically. Initially, impulsive events define a point source on the Sun, selectively filling few magnetic flux tubes, while gradual events show extensive acceleration that can fill half of the inner heliosphere, beginning when the shock reaches ～2 solar radii. Shock acceleration occurs as ions are scattered back and forth across the shock by resonant Alfvén waves amplified by the accelerated protons themselves as they stream away. These waves also can produce a streaming-limited maximum SEP intensity and plateau region upstream of the shock. Behind the shock lies the large expanse of the “reservoir”, a spatially extensive trapped volume of uniform SEP intensities with invariant energy-spectral shapes where overall intensities decrease with time as the enclosing “magnetic bottle” expands adiabatically. These reservoirs now explain the slow intensity decrease that defines gradual events and was once erroneously attributed solely to slow outward diffusion of the particles. At times the reservoir from one event can contribute its abundances and even its spectra as a seed population for acceleration by a second CME-driven shock wave. Confinement of particles to magnetic flux tubes that thread their source early in events is balanced at late times by slow velocity-dependent migration through a tangled network produced by field-line random walk that is probed by SEPs from both impulsive and gradual events and even by anomalous cosmic rays from the outer heliosphere. As a practical consequence, high-energy protons from gradual SEP events can be a significant radiation hazard to astronauts and equipment in space and to the passengers of high-altitude aircraft flying polar routes.     

Ion Acceleration at the Earth’s Bow Shock

The Earth’s bow shock is the most studied example of a collisionless shock in the solar system. It is also widely used to model or predict the behaviour at other astrophysical shock systems. Spacecraft observations, theoretical modelling and numerical simulations have led to a detailed understanding of the bow shock structure, the spatial organization of the components making up the shock interaction system, as well as fundamental shock processes such as particle heating and acceleration. In this paper we review the observations of accelerated ions at and upstream of the terrestrial bow shock and discuss the models and theories used to explain them. We describe the global morphology of the quasi-perpendicular and quasi-parallel shock regions and the foreshock. The acceleration processes for field-aligned beams and diffuse ion distribution types are discussed with connection to foreshock morphology and shock structure. The different possible mechanisms for extracting solar wind ions into the acceleration processes are also described. Despite several decades of study, there still remain some unsolved problems concerning ion acceleration at the bow shock, and we summarize these challenges.     

Viscosity effects on weak irregular reflection of shock waves in steady flow

The viscosity effects on weak shock wave reflection are investigated with the Navier–Stokes and DSMC flow solvers. It is shown that the viscosity plays a crucial role in the vicinity of three-shock intersection. Instead of a singular triple point, in viscous flow there is a smooth three shock transition zone, where one-dimensional shock jump relations cannot be applied. At the flow parameters corresponding to the von Neumann reflection, when no inviscid three-shock solution exists, the computations predict an irregular shock-wave configuration similar to that observed previously in experiments. The existence of a viscous zone in the region of shock-wave interaction allows a continuous transition from the parameters behind the Mach stem to the parameters behind the reflected shock, which is impossible in the inviscid three-shock theory. Results of numerical simulations agree qualitatively with the conclusions of the approximate viscous theory, which describes the flow in the vicinity of the three-shock intersection.     

Microinstabilities associated with a high Mach number,perpendicular bow shock

The instabilities associated with a high Mach number perpendicular shock are reexamined in light of recent enhanced understanding of the Earth's bow shock. The insights provided by both the ISEE observations and hybrid simulations are reviewed and subsequently incorporated into the instability analyses. The discussion of the instabilities is divided according to their location in the shock layer. In the regions in front of and at the shock transition the cross-field instabilities are subdivided into low frequency modes (e.g. ion-ion streaming, kinetic cross-field streaming, drift lower hybrid instabilities) and high frequency modes (electron cyclotron drift, ion sound and electron whistler instabilities). Further downstream various ion ring-like and anisotropy driven instabilities are considered. In each case the instability analysis is reviewed and recent developments are emphasized. Implications of these results concerning the wave signatures and plasma heating and acceleration are also discussed.     

Upstream Ion Cyclotron Waves at Venus and Mars

The occurrence of waves generated by pick-up of planetary neutrals by the solar wind around unmagnetized planets is an important indicator for the composition and evolution of planetary atmospheres. For Venus and Mars, long-term observations of the upstream magnetic field are now available and proton cyclotron waves have been reported by several spacecraft. Observations of these left-hand polarized waves at the local proton cyclotron frequency in the spacecraft frame are reviewed for their specific properties, generation mechanisms and consequences for the planetary exosphere. Comparison of the reported observations leads to a similar general wave occurrence at both planets, at comparable locations with respect to the planet. However, the waves at Mars are observed more frequently and for long durations of several hours; the cyclotron wave properties are more pronounced, with larger amplitudes, stronger left-hand polarization and higher coherence than at Venus. The geometrical configuration of the interplanetary magnetic field with respect to the solar wind velocity and the relative density of upstream pick-up protons to the background plasma are important parameters for wave generation. At Venus, where the relative exospheric pick-up ion density is low, wave generation was found to mainly take place under stable and quasi-parallel conditions of the magnetic field and the solar wind velocity. This is in agreement with theory, which predicts fast wave growth from the ion/ion beam instability under quasi-parallel conditions already for low relative pick-up ion density. At Mars, where the relative exospheric pick-up ion density is higher, upstream wave generation may also take place under stable conditions when the solar wind velocity and magnetic field are quasi-perpendicular. At both planets, the altitudes where upstream proton cyclotron waves were observed (8 Venus and 11 Mars radii) are comparable in terms of the bow shock nose distance of the planet, i.e. in terms of the size of the solar wind-planetary atmosphere interaction region. In summary, the upstream proton cyclotron wave observations demonstrate the strong similarity in the interaction of the outer exosphere of these unmagnetized planets with the solar wind upstream of the planetary bow shock.     

Initial ISEE magnetometer results: Shock observation

ISEE-1 and -2 magnetic field profiles across 6 terrestrial bow shock and one interplanetary shock are examined. The interplanetary shock illustrates the behavior of a low Mach number shock. It had an upstream whistler wave precursor with an apparent wavelength of 180 km. The shock thickness was about 90 km for the thickness of the final field jump or 270 km for the exponential growth of the precursor wave packet. The ion inertial length was 50 km, upstream of the shock.Three examples of low or moderate , high Mach number, quasiperpendicular shocks are examined. These did not have upstream waves, but rather had waves growing in the field gradient. The growth length for these waves and the shock profile was of the order of the ion inertial length.Two examples of high shocks showed little coherence in field variation even though the two vehicles were only a few hundred kilometers apart. Thus, we cannot gauge their velocity and turn the time profiles into distances. The final crossing examined shows clearly the effect of changing the orientation of the interplanetary magnetic field. Initially the upstream magnetic field made an angle of about 80° to the shock normal and the shock position remained fairly steady. Then the field rotated to 45° to the normal and the field profiles became very irregular and the shock position very unstable. Discrete wave packets appeared.Finally, we present the joint behavior of wave, particle and field data across some of these shocks to show some of the myriad of shock features whose behavior we are now beginning to investigate.     

振动激发对激波反射的影响

定常激波反射分为规则反射和马赫反射,在不同条件下2种反射结构之间会相互转变。高超声速流动中的激波反射问题常面临高温气体效应,随着温度逐渐升高,最先出现的是空气分子振动激发。通过理论分析和定量计算,研究了振动激发对激波反射及其转变规律的影响。首先给出考虑振动激发的空气热力学模型,并分析其与量热完全气体的差异以及对激波关系的影响;接着分析在规则反射和马赫反射中,振动激发对激波反射流场的影响规律;最后讨论振动激发对激波反射转变2个准则点的影响。研究结果表明,振动激发使激波极线的整体轮廓变大,且这种差异在经过一次激波反射之后被明显放大,会对激波反射的流场产生重大影响;对于激波反射的转变,振动激发使转变的2个准则点都变大,且对规则反射向马赫反射转变的脱体准则影响更大。     

准定常强激波马赫反射波形的数值研究

应用DCD频散控制激波捕捉格式,求解二维、多组分、带有化学反应的Euler方程组,数值模拟了准定常强激波的马赫反射问题.研究结果表明:与经典马赫反射理论相比,在强激波条件下,激波诱导的气体分子振动激发和化学反应使马赫反射的三波点轨迹角变小、马赫杆高度变低、楔顶附体激波倾角变小;马赫杆的相对突出量随入射激波马赫数和楔角的增大而增大,而气体分子的振动、离解等真实气体效应能进一步加剧马赫杆的向前突出.     

Electron-Ion Temperature Equilibration in Collisionless Shocks: The Supernova Remnant-Solar Wind Connection

Collisionless shocks are loosely defined as shocks where the transition between pre-and post-shock states happens on a length scale much shorter than the collisional mean free path. In the absence of collision to enforce thermal equilibrium post-shock, electrons and ions need not have the same temperatures. While the acceleration of electrons for injection into shock acceleration processes to produce cosmic rays has received considerable attention, the related problem of the shock heating of quasi-thermal electrons has been relatively neglected. In this paper we review the state of our knowledge of electron heating in astrophysical shocks, mainly associated with supernova remnants (SNRs), shocks in the solar wind associated with the terrestrial and Saturnian bowshocks, and galaxy cluster shocks. The solar wind and SNR samples indicate that the ratio of electron temperature, (T _e ) to ion temperature (T _p ) declining with increasing shock speed or Alfvén Mach number. We discuss the extent to which such behavior can be understood on the basis of waves generated by cosmic rays in a shock precursor, which then subsequently damp by heating electrons, and speculate that a similar explanation may work for both solar wind and SNR shocks.     

Numerical investigation on flow nonuniformity-induced hysteresis in scramjet isolator

Numerical simulation and theoretical analysis were conducted to study the hysteresis inside scramjet isolator during the reciprocating process of back pressure variation. It is revealed that only a regular reflection is theoretically possible for two leading shocks when the inflow Mach number is greater than 2.0, and no hysteresis can occur in the transition between shock reflection types. Nevertheless, wall suction, gas injection, and background waves cause non-uniformity of the incoming flow and would make hysteresis possible. Besides the classical hysteresis in the transition between shock reflection, new kinds of hysteresis were found in both the deflection angle of separated boundary layer and the location of the shock train. Moreover, the occurrence of hysteresis in the deflection angle of the separated boundary layer is accompanied with the shock reflection hysteresis. In the case with background waves or gas injection, hysteresis in the starting position of leading shock was observed too. As back pressure decreases, the leading shock does not follow the same path as that as the back pressure increases, and it is anchored at the location where the background shock or the injection interacts with the leading shock. It is inferred that, if two strong adverse pressure gradient regions move towards and interact with each other, hysteresis will take place when they start to separate.     

动态间断装配法模拟斜激波壁面反射

基于非结构动网格技术和边界装配思想提出了动态间断装配法,该方法能够应用于求解含有间断的流动问题。无论入射激波还是反射激波都是作为边界进行处理,激波运动速度由兰金-许贡纽(Rankine-Hugoniot)关系确定。激波作为动网格的一部分,其运动由动网格技术实现。采用该方法模拟了超声速二维流场中激波与壁面相交问题,并且与捕捉法进行比较,二者的流场结构符合良好,但是在细节上还是存在明显差异。通过对流动结构的分析,得出采用装配方法得到的流场要优于捕捉方法的结论。激波壁面反射的问题模拟,也说明了边界激波装配方法对于复杂的激波相交问题是具有处理能力的。     

Pickup Ion Acceleration at the Termination Shock and in the Heliosheath

We discuss pickup ion acceleration and transport near the solar wind termination shock from the perspective of their spectral, spatial, and pitch-angle distributions. Our study is performed in the framework of a recently developed anisotropic transport model based on a Legendre polynomial expansion technique. Voyager 1 LECP angular distributions of 1 MeV protons, represented in the form of an expansion in spherical harmonics in the frame aligned with the measured interplanetary magnetic field, are used as benchmarks for our theory. We find the observed distributions consistent with our model predictions for particle acceleration and reflection at a highly oblique shock wave. It is shown that first-order (field aligned) anisotropy is a measure of shock obliquity while the second-order (transverse) anisotropy reflects the energy dependence of the particle scattering mean free path. We also discuss the role of enhanced scattering and momentum diffusion on the spectral properties of energetic charged particles.     

Shock wave configurations and reflection hysteresis outside a planar Laval nozzle

When the pressure ratio increases from the perfectly expanded condition to the third limited condition in which a normal shock is located on the exit plane, shock wave configurations outside the nozzle can be further assorted as no shock wave on the perfectly expanded condition, weak oblique shock reflection in the regular reflection(RR) pressure ratio condition, shock reflection hysteresis in the dual-solution domain of pressure ratio condition, Mach disk configurations in the Mach reflection(MR) pressure ratio condition, the strong oblique shock wave configurations in the corresponding condition, and a normal shock forms on the exit plane in the third limited condition. Every critical pressure ratio, especially under regular reflection and Mach reflection pressure ratio conditions, is deduced in the paper according to shock wave reflection theory. A hysteresis phenomenon is also theoretically possible in the dual-solution domain. For a planar Laval nozzle with the cross-section area ratio being 5, different critical pressure ratios are counted in these conditions, and numerical simulations are made to demonstrate these various shock wave configurations outside the nozzle. Theoretical analysis and numerical simulations are made to get a more detailed understanding about the shock wave structures outside a Laval nozzle and the RRMMR transition in the dual-solution domain.