Cosmological Shock Waves

Large-scale structure formation, accretion and merging processes, AGN activity produce cosmological gas shocks. The shocks convert a fraction of the energy of gravitationally accelerated flows to internal energy of the gas. Being the main gas-heating agent, cosmological shocks could amplify magnetic fields and accelerate energetic particles via the multi-fluid plasma relaxation processes. We first discuss the basic properties of standard single-fluid shocks. Cosmological plasma shocks are expected to be collisionless. We then review the plasma processes responsible for the microscopic structure of collisionless shocks. A tiny fraction of the particles crossing the shock is injected into the non-thermal energetic component that could get a substantial part of the ram pressure power dissipated at the shock. The energetic particles penetrate deep into the shock upstream producing an extended shock precursor. Scaling relations for postshock ion temperature and entropy as functions of shock velocity in strong collisionless multi-fluid shocks are discussed. We show that the multi-fluid nature of collisionless shocks results in excessive gas compression, energetic particle acceleration, precursor gas heating, magnetic field amplification and non-thermal emission. Multi-fluid shocks provide a reduced gas entropy production and could also modify the observable thermodynamic scaling relations for clusters of galaxies.     

Ion acceleration at shocks in interplanetary space: A brief review of recent observations

The mechanism by which ions are accelerated near the Earth's bow shock and near shocks propagating outward from the Sun in response to solar activity appears to be essentially the same. For both types of shock the solar wind thermal distribution acts as a seed population. Leaked magnetospheric ions and resident flare ions are additional seed populations for the bow shock and outward propagating shocks respectively. The acceleration of solar wind ions at these shocks begins with either the reflection of ions off the shock or leakage of shocked plasma back through the shock. Interaction with a disruption wave field self-generated by these backstreaming ions is responsible for the remainder of the acceleration at the bow shock. Both the disruption wave field and the ambient interplanetary wave field play important roles in accelerating ions at outward propagating shocks, but on different time scales. The geometry of the shock and the duration of field line connection to the shock play decisive roles in determining what is observed.     

Structure of reconnection layers in the magnetosphere

Magnetic reconnection can lead to the formation of observed boundary layers at the dayside magnetopause and in the nightside plasma sheet of the earth's magnetosphere. In this paper, the structure of these reconnection layers is studied by solving the one-dimensional Riemann problem for the evolution of a current sheet. Analytical method, resistive MHD simulations, and hybrid simulations are used. Based on the ideal MHD formulation, rotational discontinuities, slow shocks, slow expansion waves, and contact discontinuity are present in the dayside reconnection layer. Fast expansion waves are also present in the solution of the Riemann problem, but they quickly propagate out of the reconnection layer. Our study provides a coherent picture for the transition from the reconnection layer with two slow shocks in Petschek's model to the reconnection layer with a rotational discontinuity and a slow expansion wave in Levy et al's model. In the resistive MHD simulations, the rotational discontinuities are replaced by intermediate shocks or time-dependent intermediate shocks. In the hybrid simulations, the time-dependent intermediate shock quickly evolves to a steady rotational discontinuity, and the contact discontinuity does not exist. The magnetotail reconnection layer consists of two slow shocks. Hybrid simulations of slow shocks indicate that there exists a critical number,M _c, such that for slow shocks with an intermediate Mach numberM _IM _c, a large-amplitude rotational wavetrain is present in the downstream region. For slow shocks withM _I<M _c, the downstream wavetrain does not exist. Chaotic ion orbits in the downstream wave provide an efficient mechanism for ion heating and wave damping and explain the existence of the critical numberM _c in slow shocks.     

Collisionless Shocks in Partly Ionized Plasma with Cosmic Rays: Microphysics of Non-thermal Components

In this review we discuss some observational aspects and theoretical models of astrophysical collisionless shocks in partly ionized plasma with the presence of non-thermal components. A specific feature of fast strong collisionless shocks is their ability to accelerate energetic particles that can modify the shock upstream flow and form the shock precursors. We discuss the effects of energetic particle acceleration and associated magnetic field amplification and decay in the extended shock precursors on the line and continuum multi-wavelength emission spectra of the shocks. Both Balmer-type and radiative astrophysical shocks are discussed in connection to supernova remnants interacting with partially neutral clouds. Quantitative models described in the review predict a number of observable line-like emission features that can be used to reveal the physical state of the matter in the shock precursors and the character of nonthermal processes in the shocks. Implications of recent progress of gamma-ray observations of supernova remnants in molecular clouds are highlighted.     

Shocks: Commonalities in Solar-Terrestrial Chains

Shocks are found throughout the heliosphere, wherever supersonic (or super-magnetosonic) flows encounter obstacles or other, slowly moving, media. Although some of the physical parameters are in different regimes, all shocks heat and decelerate the media incident upon them. Most shocks must propagate in a collisionless plasma, thereby adding importance to the particle interactions with the electromagnetic fields, and enabling some particles to be accelerated to high energies. This paper explores the commonalities, and differences, in shocks throughout the heliosphere, and concentrates on the role of shock microstructure in effecting the shock transition and in governing the resulting energy partition amongst the constituent species. Shocks play a significant role in the solar-terrestrial chain.     

Shock interactions in the outer heliosphere

Observations of plasma and magnetic fields by Pioneer 10 and 11 and Voyager 1 and 2 reveal that MHD shocks are an important component of the large-scale solar wind structures in the outer heliosphere. This review discusses recent progress in simulation studies of the nonlinear evolution of the solar wind structures, and in particular concentrates on the theoretical development and applications of the shock interactions model. Various stream propagation models, which do not use the Rankine-Hugoniot relations to calculate the jump conditions at shock crossings, have been used to simulate the essential evolution process of isolated streams and the formation and propagation of corotating and transient shocks. They produce fairly good results in the region up to a few AU. In 1984, the shock interactions model was introduced to study the evolution of large-scale solar wind structures in the region outside 1 AU up to several tens of AU. The model uses the exact Rankine-Hugoniot relations to calculate the shock speed and shock strength at all shock crossings. So that the model can more accurately calculate the shock speeds and the accumulated irreversible shock heating of plasma at several tens of AU. The applications of the shock interactions model are presented in three groups. (a) The first group covers the basic interaction of a shock with the ambient solar wind, the formation and propagation of shock pairs, and the collision and merging of shocks. (b) The second group covers the use of the shock interactions model to simulate the nonlinear evolution of large-scale solar wind structures in the outer heliosphere. These simulation results can provide the detailed evolution process for large-scale solar wind structures in the vast region not directly observed. Two selected studies are reported. (c) Finally, the shock interactions model is applied to studying the heating of the solar wind in the outer heliosphere. The model calculations support shocks being chiefly responsible for the heating of the solar wind plasma in the outer heliosphere at least up to 30 AU.     

Perpendicular Shock Reformation and Ion Acceleration

Kinetic simulations of supercritical, quasi-perpendicular shocks yield time-varying solutions that cyclically reform on proton spatio-temporal scales. Whether a shock solution is stationary or reforming depends upon the plasma parameters which, for SNR shocks and the heliospheric termination shock, are ill defined but believed to be within this time-dependent regime. We first review the time-dependent solutions and the acceleration processes of the ions for a proton–electron plasma. We then present recent results for a three-component plasma: background protons, electrons and a second ion population appropriate for SNR (heavy ions) or the termination shock (pickup protons). This ion acceleration generates a suprathermal “injection” population – a seed population for subsequent acceleration at the shock, which may in turn generate ions at cosmic ray energies.     

The plasma physics of shock acceleration

The notion that plasma shocks in astrophysical settings can and do accelerate charged particles to high energies is not a new one. However, in recent years considerable progress has been achieved in understanding the role particle acceleration plays both in astrophysics and in the shock process itself. In this paper we briefly review the history and theory of shock acceleration, paying particular attention to theories of parallel shocks which include the backreaction of accelerated particles on the shock structure. We discuss in detail the work that computer simulations, both plasma and Monte Carlo, are playing in revealing how thermal ions interact with shocks and how particle acceleration appears to be an inevitable and necessary part of the basic plasma physics that governs collisionless shocks. We briefly describe some of the outstanding problems that still confront theorists and observers in this field.     

进口斜激波、膨胀波干扰下等直隔离段内的激波串特性

 超燃冲压发动机的隔离段在实际工作中会受到进气道唇罩激波及肩部膨胀扇的显著干扰,本文针对这一特定问题进行了专门研究。提出了唇罩入射激波及肩部膨胀扇的模拟方法,并利用德国Achen的风洞试验对其进行了检验,而后以此研究了入射激波及肩部膨胀扇干扰下隔离段内激波串的基本形态,并分析了出口反压和激波入射位置的影响。仿真结果表明：当激波串在隔离段内不断前移时,受唇罩入射激波及其反射激波的干扰,其高速核心区交替地偏向上下壁面;与无激波入射的情况相比,此时激波串的耐反压能力显著降低,且入射点位置越高,降低幅度越大,管道内的沿程静压分布规律与Waltrup经验公式偏离程度也越来越大。该文结果可为进气道/隔离段的一体化设计提供依据。     

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.     

变比热斜冲波解析解

首次推导了变比热斜冲波的基本公式及其衍生形式，分别就求解转角、波角、最大尖劈角、最小马赫数等典型问题，拟就解法及双精度计算机程序，一一作出例题，进入了变比热斜冲波园地。可以预见到的深入研究问题不少，尚待进一步探索。     

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.     

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.     

Propagating Shocks

A survey of propagating interplanetary shocks reveals the following properties: (1) More shocks are observed around solar-activity maximum than minimum. (2) The maximum frequency of shock occurrence is between 2 and 5 AU. (3) Shocks slow down in the inner solar system, but in the outer solar system some may get a boost in speed when overtaken by a following shock. (4) The average shock strength (as measured by either the Mach number or the density ratio) also reaches peak values at distances of 2–5 AU. (5) Shocks are stronger at their noses than at their flanks. (6) At 1 AU, there are many more quasiperpendicular than quasiparallel shocks with the frequency of occurrence roughly constant with the cosine of the angle between the upstream field and the shock normal.     

Magnetohydrodynamic discontinuities in space plasmas: Interrelation between stability and structure

It is believed that shock waves and other discontinuous flows form the basis of a wide range of phenomena in space medium. We review the results concerning the particular property of MHD discontinuities, the interrelation between their stability and structure. Such an interrelation is associated primarily with the requirement of their evolutionarity. For a non-evolutionary discontinuity the amplitudes of reflected and refracted waves caused by a small amplitude incident wave are not determined unambiguously from the conservation laws at the discontinuity surface. Since the problem of the further time evolution of the initial small perturbation does not have a unique solution, such a discontinuity cannot exist in a real medium as a single steady-state configuration. Therefore it is unstable with respect to a disintegration into several discontinuities or to a transition to some more general unsteady flow. This is confirmed by the fact that, in the studied cases, the non-evolutionary shock transitions can, while the evolutionary ones cannot, be represented as a set of several discontinuities and waves of rarefaction. One more fundamental property of the non-evolutionary shocks that argues for their non-existence is that they do not have a unique structure for all values of the dissipative transport coefficients. At the same time, the possibility of their existence cannot be excluded when the shock has a unique structure or when the disintegration is forbidden for some reasons. Besides the non-evolutionarity, which is a direct reason for a disintegration, there is an indirect one. It can be shown that the hydrodynamic shocks without magnetic field that are corrugationally unstable also allow the shock transitions through more than one discontinuity. This suggests that the shocks unstable in the ordinary sense, for which the small perturbation grows with time, do not exist at all, but they disintegrate into stable ones. However, the physical mechanism that distinguishes between these two scenarios remains unclear. The interrelation between the stability and structure of MHD discontinuities thus governs their nonlinear evolution. This fact is essential when describing shock waves and other discontinuous flows in the space medium.     

Electron Acceleration in the Heliosphere

We review the evidence for electron acceleration in the heliosphere putting emphasis on the acceleration processes. There are essentially four classes of such processes: shock acceleration, reconnection, wave particle interaction, and direct acceleration by electric fields. We believe that only shock and electric field acceleration can in principle accelerate electrons to very high energies. The shocks known in the heliosphere are coronal shocks, traveling interplanetary shocks, CME shocks related to solar type II radio bursts, planetary bow shocks, and the termination shock of the heliosphere. Even in shocks the acceleration of electrons requires the action of wave particle resonances of which beam driven whistlers are the most probable. Other mechanisms of acceleration make use of current driven instabilities which lead to electron and ion hole formation. In reconnection acceleration is in the current sheet itself where the particles perform Speiser orbits. Otherwise, acceleration takes place in the slow shocks which are generated in the reconnection process and emanate from the diffusion region in the Petschek reconnection model and its variants. Electric field acceleration is found in the auroral zones of the planetary magnetospheres and may also exist on the sun and other stars including neutron stars. The electric potentials are caused by field aligned currents and are concentrated in narrow double layers which physically are phase space holes in the ion and electron distributions. Many of them add up to a large scale electric field in which the electrons may be impulsively accelerated to high energies and heated to large temperatures.     

Selected Problems in Collisionless-Shock Physics

The physics of collisionless shocks is a very broad topic, which has been well studied for many decades. However, there are a number of important issues which remain unresolved. Moreover, there have been new findings, which cast doubt on well-established ideas. The purpose of this review is to address a subset of unresolved problems in collisionless shock physics from a theoretical and/or numerical modeling point of view. The topics which are addressed are: the nonstationarity of the shock front, the heating and dynamics of electrons through the shock layer, particle diffusion in turbulent electric and magnetic fields, particle acceleration, and the interaction of pickup ions with collisionless shocks.     

Simulation of underexpanded supersonic jet flows with chemical reactions

To achieve a detailed understanding of underexpanded supersonic jet structures influenced by afterburning and other flow conditions, the underexpanded turbulent supersonic jet with and without combustions are investigated by computational fluid dynamics(CFD) method.A program based on a total variation diminishing(TVD) methodology capable of predicting complex shocks is created to solve the axisymmetric expanded Navier–Stokes equations containing transport equations of species. The finite-rate ratio model is employed to handle species sources in chemical reactions. CFD solutions indicate that the structure of underexpanded jet is typically influenced by the pressure ratio and afterburning. The shock reflection distance and maximum value of Mach number in the first shock cell increase with pressure ratio. Chemical reactions for the rocket exhaust mostly exist in the mixing layer of supersonic jet flows. This tends to reduce the intensity of shocks existing in the jet, responding to the variation of thermal parameters.     

Shock train and pseudo-shock phenomena in internal gas flows

The interaction between a normal shock wave and a boundary layer along a wall surface in internal compressible flows causes a very complicated flow. When the shock is strong enough to separate the boundary layer, the shock is bifurcated and one or more shocks appear downstream of the bifurcated shock. A series of shocks thus formed, called “shock train”, is followed by an adverse pressure gradient region, if the duct is long enough. Thus the effect of the interaction extends over a great distance. The flow is decelerated from supersonic to subsonic through the whole interaction region. In this sense, the interaction region including the shock train in it is referred to as “pseudo-shock” in the present paper, as Crocco called it. The shock train and pseudo-shock strongly affect the performance and efficiency of various flow devices. In the present review some fundamental characteristics of the shock train and pseudo-shock are first described. Some simple predictions are made to simulate these very complicated phenomena. Pseudo-shocks appearing in various flow devices are explained. Control methods of the pseudo-shocks are also described. Finally, the current understanding of self-excited oscillation of pseudo-shock is reviewed.     

高超声速二维前体进气道一体化优化设计研究

在飞行器前体进气道的一体化优化设计中,最大总压恢复系数是一个必须考虑的参数.本文从二维高超声速进气道的最大总压恢复系数入手,通过理论分析给出了高超声速飞行器从2波系到6波系的二维高超声速飞行器前体进气道的一体化优化设计计算模型.采用拉格朗日乘子法和序列二次规划法(SQP)分别计算了进气道内一道内激波和两道内激波时的情况,给出了进气道的最大总压恢复系数、进气道内马赫数、激波偏转角和激波强度随来流马赫数的变化关系.比较两种方法的计算结果可知采用的计算方法是合理的.