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NASA NTRS2023

Multi-Spacecraft Observations of Shocklets at an Interplanetary Shock

Interplanetary (IP) shocks are fundamental building blocks of the heliosphere, and the possibility to observe them in situ is crucial to address important aspects of energy conversion for a variety of astrophysical systems. Steepened waves known as shocklets are known to be important structures of planetary bow shocks, but they are very rarely observed related to IP shocks. We present here the first multi-spacecraft observations of shocklets observed by upstream of an unusually strong IP shock observed on 3 No v ember 2021 by several spacecraft at L1 and near-Earth solar wind. The same shock was detected also by radially aligned Solar Orbiter at 0.8 AU from the Sun, but no shocklets were identified from its data, introducing the possibility to study the environment in which shocklets developed. The Wind spacecraft has been used to characterize the shocklets, associated with pre-conditioning of the shock upstream by decelerating incoming plasma in the shock normal direction. Finally, using the Wind observations together with ACE and DSCOVR spacecraft at L1, as well as THEMIS B and THEMIS C in the near-Earth solar wind, the portion of interplanetary space filled with shocklets is addressed, and a lower limit for its extent is estimated to be of about 110 R E in the shock normal direction and 25 R E in the directions transverse to the shock normal. Using multiple spacecraft also reveals that for this strong IP shock, shocklets are observed for a large range of local obliquity estimates (9° –64°).

plasmas↗

DOE OSTI2025

Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves

The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.

42 ENGINEERING↗

NASA NTRS1973

Turbulence in electrostatic ion acoustic shocks

Three types of collisionless electrostatic ion acoustic shocks are investigated using a double plasma (DP) device: (1) laminar shocks; (2) small amplitude turbulent shocks in which the turbulence is confined to be upstream of the shock potential jump; and (3) large amplitude turbulent shocks in which the wave turbulence occurs throughout the shock transition. The wave turbulence is generated by ions which are reflected from the shock potential; linear theory spatial growth increments agree with experimental values. The experimental relationship between the shock Mach number and the shock potential is shown to be inconsistent with theoretical shock models which assume that the electrons are isothermal. Theoretical calculations which assume a trapped electron equation of a state and a turbulently flattened velocity distrubution function for the reflected ions yields a Mach number vs potential relationship in agreement with experiment.

Means, R. W.↗

NASA NTRS1973

Turbulence in electrostatic ion-acoustic shocks

Three types of collisionless electrostatic ion-acoustic shocks are investigated using the University of California, Los Angeles, double plasma device: (1) laminar shocks; (2) small amplitude turbulent shocks in which the turbulence is confined to be upstream of the shock potential jump; and (3) large amplitude turbulent shocks in which the wave turbulence occurs throughout the shock transition. The wave turbulence is generated by ions which are reflected from the shock potential; linear theory spatial growth increments agree with experimental values. The experimental relationship between the shock Mach number and the shock potential is shown to be inconsistent with theoretical shock models which assume that the electrons are isothermal. Theoretical calculations which assume a trapped electron equation of a state and a turbulently flattened velocity distribution function for the reflected ions yields a Mach number vs potential relationship in agreement with experiment.

Means, R. W.↗

NASA NTRS1976

A summary of observations of the earth's bow shock

The earth's bow shock can be regarded as a fast steady-state collisionless magnetohydrodynamic shock exhibiting a wide range of plasma parameter values or as an example of superalfvenic flow of a MHD fluid past a blunt body. This paper summarizes our knowledge of the bow shock. Satellite crossings of the shock have given some empirical data on the position and shape of the bow shock. Theoretical calculations on position and shape show the critical nature of the Alfven number. The main physical process to be explained with regard to the bow shock is the mechanism of thermalization of the upstream solar wind. Some of the main classes of shocks observed are quasi-parallel shocks, low Mach number laminar shocks, and high beta shocks.

Fairfield, D. H.↗

NASA NTRS1979

Shock metamorphism of granulated lunar basalt

The paper deals with an extensive series of shock-recovery experiments performed on both nonporous crystalline basalt and its granulated and sieved counterpart to study the role of porosity and grain size in shock motomorphic effects under otherwise identical conditions. Shocked samples are compared with unshocked starting material in terms of textural and mineralogical modifications attributable to shock. A comparative petrographic and chemical characterization is presented of pulverized and sieved lunar basalt 75035 shocked between 6 and 75 GPa in comparison with holocrystalline disks of the same basalts shocked in 10 earlier experiments. Specifically, a petrographic classification of shock features is given, along with an estimation of relative amounts of shock glasses and a chemical characterization of shock glasses in each shocked granular basalt.

Schaal, R. B.↗

NASA NTRS1980

Location and propagation of shock associated noise from supersonic jets

Shock associated noise from unheated supersonic jets is investigated through acoustic measurements in both the near and far fields. The peak Helmholtz number of broadband shock noise is found to be independent of nozzle pressure ratio when based on the length of the shock cells and the ambient speed of sound. This indicates that the acoustic wavelengths generated in the shock noise process are limited in size by the shock cell spacing. Excellent agreement between power spectral densities measured at various far-field angles is obtained at and above the peak shock noise frequency when source convection effects are included. Results show a directivity of broadband shock noise pointed in the upstream direction, with omnidirectionality being approached only at high pressure ratios. The relative importance of shock noise with respect to jet mixing noise is found to be maximum near the pressure ratio at which a Mach disc begins to form in the jet. Near-field measurements point to the downstream shock cells as the region where the dominant shock noise eminates from the jet.

Norum, T. D.↗

NASA NTRS1980

Aerodynamic aspects of shock containing jet plumes

Aerodynamic and acoustic measurements of shock-free and shock-containing plumes were acquired for several supersonic free-jet model nozzles. The purpose was to investigate important features of the broadband shock noise generation process. The aerodynamic measurements include the variation of shock cell spacing and strength as a function of nozzle pressure ratio, and longitudinal turbulent-mass-flux axial development as determined by a hot-film probe. In addition, correlations of the hot-film probe with a near-field microphone were obtained. These measurements provide useful information concerning the relation of peak shock noise frequency and level with variations in shock cell spacing and strength. In general, it is shown that a distinction must be made between plumes containing weak and strong imbedded shocks. Strong shocks diminish the level of emitted shock noise and influence the behavior of the jet mixing noise process. The probable location and spectral content for the shock-shear layer interaction mechanism is indicated by the correlations. Numerical inviscid plume comparisons with experimental data are also included.

Seiner, J. M.↗

NASA NTRS1982

CAS22 - FORTRAN program for fast design and analysis of shock-free airfoil cascades using fictitious-gas concept

A user-oriented computer program, CAS22, was developed that is applicable to aerodynamic analysis and transonic shock-free redesign of existing two-dimensional cascades of airfoils. This FORTRAN program can be used: (1) as an analysis code for full-potential, transonic, shocked or shock-free cascade flows; (2) as a design code for shock-free cascades that uses Sobieczky's fictitious-gas concept; and (3) as a shock-free design code followed automatically by the analysis in order to confirm that the newly obtained cascade shape provides for an entirely shock-free transonic flow field. A four-level boundary-conforming grid of an O type is generated. The shock-free design is performed by implementing Sobieczky's fictitious-gas concept of elliptic continuation from subsonic into supersonic flow domains. Recomputation inside each supersonic zone is performed by the method of characteristics in the rheograph plane by using isentropic gas relations. Besides converting existing cascade shapes with multiple shocked supersonic regions into shock-free cascades, CAS22 can also unchoke previously choked cascades and make them shock free.

Dulikravich, D. S.↗

NASA NTRS1983

The association of energetic particles and shocks in the heliosphere

The observational and theoretical work on heliospheric shocks and cosmic rays in the recent past is surveyed. The data have come mainly from spacecraft in the regions from 0.3-25 AU, and include detection of particles and plasma waves upstream of the earth's bow shock. The theory of shock acceleration is reviewed, together with analytical models of energetic particle enhancement in association with shocks or shocks within the heliosphere. It has been determined that shocks in the heliosphere are associated with energetic suprathermal particles, which are conversely all associated with shocks. Solar cosmic rays and other anomalous components are therefore accelerated by shocks, a factor that is significant for studies of the acceleration mechanisms for galactic cosmic rays. The Solar Polar Mission will provide data on all solar latitudes, and the ISEE-3 spacecraft will continue to gather information on shock accelerated ions in travelling interplanetary shock waves.

Lee, M. A.↗

NASA NTRS1984

Infrared spectroscopy of interstellar shocks

Infrared emission lines from interstellar shocks provide valuable diagnostics for violent events in the interstellar medium, such as supernova remnants and mass outflow from young stellar objects. There are two types of interstellar shocks: in J shocks, gas properties 'jump' from their preshock to their postshock values in a shock front with a thickness equal to or less than one mean free path; radiation is emitted behind the shock front, primarily in the visible and ultraviolet, but with a few strong infrared lines, such as OI(63 microns). Such shocks occur in ionized or neutral atomic gas, or at high velocities (equal to or greater than 50 km/s) in molecular gas. In C shocks, gas is accelerated and heated by collisions between charged particles, which have a low concentration and are coupled to the magnetic field, and neutral particles; radiation is generated throughout the shock and is emitted almost entirely in infrared emission lines. Such shocks occur in weakly ionized molecular gas for shock velocities below about 50 km/s.

Mckee, C. F.↗

NASA NTRS1985

Selfsimilar time dependent shock structures

Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The ame argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions.

Beck, R.↗

NASA NTRS1986

Observations of shock acceleration processes in the solar wind

Substantial evidence was accumulated over more than two decades that ion acceleration occurs at all collisionless shocks sampled directly in the solar system. The various shock waves in the heliosphere and the associated energetic particle phenomena are shown schematically. Three shocks have attracted considerable attention in recent years: corotating shocks due to the interaction of fast and slow solar wind streams during solar minimum, travelling interplanetary shocks due to coronal mass ejections, and planetary bow shocks. The signatures of these shocks and of their energetic particles are briefly reviewed. The most prominent theoretical models for shock acceleration are also reviewed. Recent observations at the earth's bow shock and at quasi-parallel interplanetary shocks are discussed in detail.

Scholer, M.↗

NASA NTRS1986

The chemical shock tube as a tool for studying high-temperature chemical kinetics

Although the combustion of hydrocarbons is our primary source of energy today, the chemical reactions, or pathway, by which even the simplest hydro-carbon reacts with atmospheric oxygen to form CO2 and water may not always be known. Furthermore, even when the reaction pathway is known, the reaction rates are always under discussion. The shock tube has been an important and unique tool for building a data base of reaction rates important in the combustion of hydrocarbon fuels. The ability of a shock wave to bring the gas sample to reaction conditions rapidly and homogeneously makes shock-tube studies of reaction kinetics extremely attractive. In addition to the control and uniformity of reaction conditions achieved with shock-wave methods, shock compression can produce gas temperatures far in excess of those in conventional reactors. Argon can be heated to well over 10 000 K, and temperatures around 5000 K are easily obtained with conventional shock-tube techniques. Experiments have proven the validity of shock-wave theory; thus, reaction temperatures and pressures can be calculated from a measurement of the incident shock velocity. A description is given of the chemical shock tube and auxiliary equipment and of two examples of kinetic experiments conducted in a shock tube.

Brabbs, Theodore A.↗

NASA NTRS1985

Collisionless shocks in the heliosphere: Reviews of current research

The present conference on heliospheric collisionless shocks considers such macrostructure-, microstructure-, and particle acceleration-related topics as interplanetary shock phenomena near and within 1 AU, as well as beyond, planetary bow shocks, shock formation and evolution in the solar atmosphere, MHD and gasdynamic theories for planetary bow waves, and subcritical collisionless shock waves. Also discussed are ion reflection, gyration, and dissipation at supercritical shocks, the numerical simulation of quasi-perpendicular collisionless shocks, electron distributions near collisionless shocks, the microtheory of collisionless shock current layers, plasma waves and instabilities, the electron foreshock, upstream suprathermal ions, and both diffusive and shock drift acceleration.

Tsurutani, Bruce T.↗

NASA NTRS1990

The merging of quasiperpendicular collisionless shocks

The overtaking of one collisionless shock by another is studied by means of hybrid numerical simulations. The two shocks merge into a stronger shock and trailing nonshock discontinuities. The strong shock continues to propagate in the same direction as the two weaker shocks. The merging is shown to occur by a self-consistent process involving the interaction of ions reflected at the overtaking shock with the plasma upstream of the leading shock. The characteristic time scale for the merging is typically 1/Omega(i), where Omega(i) is the ion gyrofrequency. For exactly perpendicular shocks, the trailing discontinuity is a tangential discontinuity. It has a width of 2-3 ion Larmor radii. For oblique shocks, a contact discontinuity is present in the downstream plasma state. These results are of relevance to shock interactions in the very distant solar wind as well as in other energetic astrophysical situations such as solar flares.

Cargill, P. J.↗

NASA NTRS1991

Electrostatic potential jump across fast-mode collisionless shocks

The electrostatic potential jump across fast-mode collisionless shocks is examined by comparing published observations, hybrid simulations, and a simple model, in order to better characterize its dependence on the various shock parameters. In all three, it is assumed that the electrons can be described by an isotropic power-law equation of state. The observations show that the cross-shock potential jump correlates well with the shock strength but shows very little correlation with other shock parameters. Assuming that the electrons obey an isotropic power law equation of state, the correlation of the potential jump with the shock strength follows naturally from the increased shock compression and an apparent dependence of the power law exponent on the Mach number which the observations indicate. It is found that including a Mach number dependence for the power law exponent in the electron equation of state in the simple model produces a potential jump which better fits the observations. On the basis of the simulation results and theoretical estimates of the cross-shock potential, it is discussed how the cross-shock potential might be expected to depend on the other shock parameters.

Mandt, M. E.↗

NASA NTRS1993

Double shock pairs in the solar wind

A numerical study of the evolution of a velocity enhancement disturbance in the solar wind is presented in terms of a 1D isentropic MHD flow model. It is shown that the disturbance steepens and evolves into a double shock pair while propagating outward away from the sun. The double shock pair consists of a reverse fast shock, a reverse slow shock, a forward slow shock, and a forward fast shock in order of distance away from the sun. The formation time of the double shock pair is nearly inversely proportional to the average velocity gradient of the disturbance. When the double shock pair is fully developed, the strength of the fast shocks is essentially determined by the disturbance amplitude, while the slow shocks behave differently. Their strength increases first with the disturbance amplitude but starts to decrease once the disturbance amplitude exceeds a certain value.

Hu, Y. Q.↗