Showing papers on "Shock wave published in 1975"

Nonthermal Processes in Large Solar Flares

Abstract: In many small solar flares the ~10–100 keV electrons accelerated during the flash phase contain the bulk of the total flare energy output. In large flares, such as those in the period 1972, August 2–7, the flash phase electrons are present in substantially greater numbers. These electrons can explosively heat the chromosphere-lower corona and eject flare material. The ejected matter can produce a shock wave which will then accelerate nucleons and electrons to relativistic energies. We analyze energetic particle, radio, X-ray, gamma ray and interplanetary shock observations of the 1972 August flares to obtain quantitative estimates of the energy contained in each facet of these large flares. In general these observations are consistent with the above hypothesis. In particular: (1) From the X-ray emission (van Beek et al., 1973) the energy contained in > 25 keV electrons is calculated to be≳ 2 × 1032 erg for the 1972, August 4 event. Since the lower energy cutoff to the electron spectrum is known to be below 25 keV and possibly below 10 keV, the electrons contain enough energy to produce the following interplanetary shock wave, which has by far the bulk of the energy dissipated in the flare. Similar numbers are obtained for the large August 7 flare event. (2) From the γ-ray emission (Chupp et al., 1973) the energy in protons dumped at the same level of the atmosphere, assuming a thick target situation, is at least a factor of three smaller than the electrons. Moreover the γ-ray emission indicates that the bulk of the protons are accelerated at least several minutes after the electrons. Thus it is more likely that the electrons are responsible for the flare optical (Hα and white light) emissions which occur in the chromosphere. (3) Approximately 5% of the electrons and≳ 99% of the protons escape into the interplanetary medium to be observed by spacecraft. This situation is consistent with the hypothesis of shock acceleration of the protons high in the solar corona. (4) The four most intense X-ray bursts observed during the period July 31—August 11 are the only bursts followed by an interplanetary shock wave and a new injection of energetic protons into the interplanetary medium.

On the formation of auroral arcs and acceleration of auroral electrons

Abstract: It is suggested that the highly structured auroral arc is caused by a current-driven laminar electrostatic shock oblique to the geomagnetic field. Electrons are accelerated by the potential jump associated with the shock. The shock is assumed to be confined to a plane. Self-consistent solutions to the Poisson-Vlasov systems are calculated for the electrostatic potential. Adiabatic theory is used to calculate the ion number density in terms of the electrostatic potential and its derivatives. The electrons are assumed to be highly magnetized so they can only move parallel to the magnetic field. Solutions are exhibited for two plasma models: (1) streaming electrons and a two-temperature distribution of ions and (2) streaming electrons and ions and thermal electrons and ions. In the latter model, solutions can be obtained for an arbitrary potential jump across the shock. The shock is identified with the linear electrostatic ion cyclotron wave, and stability of these waves is examined to determine conditions for the formation of oblique shocks. Finally, the theory is discussed in the context of the magnetosphere, and possible model shocks are exhibited and discussed in terms of auroral arc formation.

Shock waves and mach cones in fast nucleus-nucleus collisions

Abstract: Mach shock waves and head shock waves occur during the interpenetration of a light high energetic nucleus with a heavy one. Collisions of16O,12C and4He ions at energies between 0.25 and 2.1 GeV/N with Ag and Cl nuclei have been investigated. The theoretical concepts and the experiment are presented and interpreted. From that a velocity of first sound in nuclear matterc s ≈0.19c, a Mach shock velocityv s ≈0.58c and a nuclear compression constantK=300 MeV are deduced.

Shock wave oscillation driven by turbulent boundary layer fluctuations

Abstract: Pressure fluctuations due to the interaction of a shock wave with a turbulent boundary layer were investigated. A simple model is proposed in which the shock wave is convected from its mean position by velocity fluctuations in the turbulent boundary layer. Displacement of the shock is assumed limited by a linear restoring mechanism. Predictions of peak root mean square pressure fluctuation and spectral density are in excellent agreement with available experimental data.

Interplanetary shock waves: Recent developments

Abstract: Direct and indirect observations of interplanetary shock waves have been extended to the study of (i) the shock structure itself; (ii) the disturbed solar wind in its wake; (iii) additional discontinuities such as reverse shocks and pistons; and (iv) the shock's kinematic behavior. The last item — the trajectory — has benefited by the procedure (suggested by Pinter) of matching type II radio drift-inferred velocities with indirectly-inferred initial velocities found from at least two successive measurements in space. The significance of making type II observations at hectometric and kilometric wavelengths (as made, for example, by Slysh and Malitson, Feinberg and Stone) cannot be over-emphasized due to this technique's ability to make unambiguous solar terrestrial relationships. More direct and physically-meaningful observations, however, are still dependent uponin situ plasma and magnetic field measurements. Additional emphasis is presently being placed on numerical modeling of shock-induced disturbances in the solar wind as generated by both flares and stream-stream interactions. The former mechanism is emphasized in this review with several recommendations for further research: (a) further numerical modeling for shocks, starting when they are ‘born’ within relatively low-Alfven speed coronal regions; (b) expanded synoptic studies by spacecraft at various heliocentric longitudes, radii, and (eventually) latitudes with coordinated diagnostics; and (c) extended patrol of natural probes, such as comets, augmented with theoretical studies of possible shock-induced mechanical and chemical effects.

Dislocation mechanisms for stress relaxation in shocked LiF

Abstract: A study of shock wave propagation along the 〈100〉 direction in LiF single crystals is presented. Plate impact experiments were conducted to produce elastic impact stresses of approximately 29 kbar. Stress time profiles at the impact surface and rear surface for thicknesses up to 3.2 mm were observed. Experiments were done for two impurity concentrations and three different heat treatments. Material characterization to supplement the shock data was provided by quasistatic yield stress measurements, dielectric relaxation data, initial dislocation density counts, and spectrographic analysis. Elastic wave attenuation is strongly influenced by both Mg++ impurities and heat treatments. Impurity clustering generally reduces the rate of precursor decay. The plastic strain rate at the elastic shock front was computed from the data by a near−exact method which incorporates material nonlinearities. Beyond the first 1 or 2 mm of propagation, significant contributions to stress decay arise from overtaking by relief waves. Application of dislocation theory reveals dislocation densities to be approximately 3 orders of magnitude larger than grown−in dislocations, at least in the region of rapid stress decay. Present analysis contradicts the idea of regenerative multiplication of dislocations causing this large increase in density. A model for heterogeneous nucleation of dislocation based on an energy criterion is proposed which appears to be well suited for explaining large increases in dislocation densities. The present data suggest an applied shear stress of 3−5 kbar as the lower bound at which dislocations can nucleate at heterogeneities present in our crystals. Better material characterization concerning impurity clusters is needed to consider the quantitative aspects of rate and magnitude of heterogeneous nucleation. The mechanism for stress decay in the very soft LiF crystals is still not well understood.

Electric energy generation by shock compression of ferroelectric ceramics: Normal−mode response of PZT 95/5

Abstract: Reproducible and predictable electrical pulses with peak powers of a few hundred kilowatts lasting for a few microseconds can be obtained from shock−wave compressed ferroelectrics. In this work, impact−loading techniques are used to investigate the electromechanical response of poled specimens of a ferroelectric ceramic, PZT 95/5, to long−duration shock pulses. The experiments are conducted in the normal mode in which the shock propagation vector is perpendicular to the remanent polarization. Current histories are obtained as a function of load resistance for a fixed shock amplitude of 1.4 GPa, and few additional experiments investigate the stress dependence of the electrical response. A simple, though specific, model is developed that gives good agreement with observed results. The extension of this model to other materials and shock−loading conditions is discussed.

Interaction of free electrons with electromagnetic radiation

Abstract: A study is made of the interaction of a random field of electromagnetic radiation with the free electrons of a plasma, with applications to astrophysical problems, in particular the theory of how thermodynamic equilibrium of the radiation in a hot universe is established. A kinetic equation describes the variation of the spectrum; special attention is devoted to induced scattering and the classical interpretation of induced energy and momentum transfer. In the spectra of radio sources with a high luminosity temperature, induced scattering can lead to a Bose condensation of photons, a shock wave and solitons. The scattering of strong low-frequency waves is considered in connection with their effect on pulsars and laboratory coherent generators.

Energization of auroral electrons by electrostatic shock waves

Abstract: Electrostatic shock waves are proposed as a possible mechanism for energizing electrons which are responsible for discrete auroras. It is shown that electrostatic shock solutions can exist in a Ti ≫ Te plasma carrying a field-aligned electron current if the plasma in the high-latitude plasma sheet has an earthward flow component. The model is formulated within the framework of the Vlasov-Poisson equations. The reflection of incident ions upstream, the trapping of electrons downstream, and the magnetic mirror of the earth's field are included in the present model. It is found that under the high-latitude plasma sheet conditions, a field-aligned potential jump of several kilovolts can be produced by the shock. Electrons passing through the shock are accelerated at the expense of the ion kinetic energy.

Structure of the quasi‐perpendicular laminar bow shock

Abstract: It was found that low solar wind parameters M (less than or around 2.5) and beta (much less than 1) and high angles to the local shock normal, theta (greater than or around 65 deg), produced oblique laminar shock profiles as expected from theory, with marginal or vanishing upstream standing whistlers probably damped by acoustic or other plasma wave instabilities. The whistler mode appeared to dominate the electromagnetic spectrum. The laminar shock ramp thickness was several hundred kilometers and equal to (2-4)c/omega-pi. Composition of the shock as an accumulation of near-standing waves and an evidently reproducible varying flux pattern was discernible. Electron thermalization occurred early in, or just before, the magnetic ramp, while proton thermalization appeared to occur later in the ramp. Instantaneous shock velocities derived from the standing whistler wavelength were consistent with average velocities derived from the elapsed time estimates and were as high as 200 km/sec.

A hybrid fluid-particle model of ion heating in high-Mach-number shock waves

Abstract: A hybrid model treating electrons as a dissipative fluid and ions as particles is used to investigate numerically the properties of high-Mach-number magnetoacoustic shock waves propagating perpendicular to a magnetic field. Upon increasing the Alfv?n Mach number MA, the electron pressure behind the shock becomes bounded for MA 15. Ion reflectivity a increases but stays rather small even for MA ? ?, B0 ? 0 (i.e. ? = 30 ? 40% for reasonable collision frequencies in the shock). Thermalization of the plasma by multiple bouncing in a cylindrical tube is studied for the case where the ion gyroradii are large compared to the tube radius. Strong damping is found to lead to equilibration after about two bounce oscillations. Ion reflection during the first implosion is found to be essential for non-adiabatic ion heating in the succeeding thermalization period.

Relativistic Hydrodynamic Theory of Heavy Ion Collisions

Abstract: By use of finite-difference methods the classical relativistic equations of motion for the head-on collision of two heavy nuclei are solved. For $sup 16$O projectiles incident onto various targets at laboratory bombarding energies per nucleon less than or equal to2.1 GeV, curved shock waves develop. The target and projectile are deformed and compressed into crescents of revolution. This is followed by rarefaction waves and an overall expansion of the matter into a moderately wide distribution of angles.

Direct observations of a flare related coronal and solar wind disturbance

Abstract: Numerous mass ejections from the Sun have been detected with orbiting coronagraphs Here for the first time we document and discuss the direct association of a coronagraph observed mass ejection, which followed a 2B flare, with a large interplanetary shock wave disturbance observed at 1 AU Estimates of the mass (24 × 1016 g) and energy content (11 × 1032 erg) of the coronal disturbance are in reasonably good agreement with estimates of the mass and energy content of the solar wind disturbance at 1 AU The energy estimates as well as the transit time of the disturbance are also in good agreement with numerical models of shock wave propagation in the solar wind

Shock wave stability

Abstract: The D’yakov work which deals with a shock that undergoes a slight disturbance is re−examined. Under a linear analysis the growth of perturbations is examined and this produces inequality restrictions for the shock to be stable. It is found that the shock is unstable for j2(dv/dp)H 〈−1 and j2(dv/dp)H〉 1 + 2M, where M is the Mach number of the shock with respect to the material behind, and −j2 is the slope of the Rayleigh line. These inequalities agree with those of D’yakov. It is also shown that these results are exactly the same as those derived by Erpenbeck by a different analysis. Some properties of general Hugoniot curves are also presented. It is demonstrated that the restriction to M<1, by itself, does not restrict the range of values for the slope of the Hugoniot curve.

Two-Dimensional Shock Wave-Boundary Layer Interactions in High Speed Flows,

Abstract: : A review is made of two-dimensional supersonic interactions including separation for laminar and turbulent flows. Part 1 discusses recent theoretical developments in interacting flows and presents numerical techniques for calculating these flows, including finite difference and integral methods. Theoretical discussions are presented for both laminar and turbulent interactions. Part 2 reviews recent experimental studies which have been directed towards understanding the fluid mechanics of attached and separated regions of shock wave-boundary layer interaction in the supersonic annd hypersonic flow.

Control of shock-wave boundary-layer interactions by bleed in supersonic mixed compression inlets

Abstract: An experimental investigation has been conducted to determine the effect of bleed region geometry and bleed rate on shock wave-boundary layer interactions in an axisymmetric, mixed-compression inlet at a Mach number of 2.5. The full realizable reduction in transformed form factor is obtained by bleeding off about half the incident boundary layer mass flow. Bleeding upstream or downstream of the shock-induced pressure rise is preferable to bleeding across the shock-induced pressure rise. Slanted holes are more effective than normal holes. Two different bleed hole sizes were tested without detectable difference in performance.

Standing waves at low Mach number laminar bow shocks

Abstract: Explorer 43 data were used to study 34 bow shock crossings observed from 5 to 16 earth radii upstream of the average bow shock location. Waves with periods of 6 to 130 s having amplitudes up to delta-B/B = 1 were detected. Wave polarization for the low-frequency waves is right-handed in relation to the average field direction when the observer moves from the upstream to downstream direction but is left-handed when the observer moves in the opposite sense. This fact identified the waves as standing whistler waves in the coordinate system of the shock. The waves are in agreement with collisionless low Mach number laminar shock theory. When the measured parameters were used to calculate theoretical wavelengths, the observed wave frequencies could be used to calculate velocities for the shock-wave coordinate system past the spacecraft; such velocities are mostly between 10 and 30 km/s. It is suggested that the higher-frequency propagating whistler waves may evolve from the standing whistler waves through a decay instability.

Structure and variations of solar wind-Mars interaction region

Abstract: Measurements of ion fluxes in close vicinity to Mars have been made by the space probes Mars 2 and Mars 3 during 1971–1972. Analysis of measurements confirms the earlier preliminary conclusion by these authors about the existence of bow shock wave near Mars. Seventeen crossings of the bow shock are used to obtain the mean location of the bow shock and to estimate the dimension of the obstacle. The mean distance to the bow shock subsolar point is estimated as ∼1200 km, and the corresponding height of the stagnation point, as ∼400 km. Anomalously far positions of bow shock, ∼2800 km, have been observed by the two satellites. New features of the interaction region have been observed. This region is characterized by high-intensity fluxes of ions with temperatures of some tens of electron volts and convective velocities well below the convective velocity in the magnetosheath. This ‘cushion’ of hot ions is situated inside the magnetosheath but above the Martian ionosphere. Intercomparison of these measurements with magnetic field data shows that observations of decelerated hot ions usually coincide with an increase of the magnetic field up to 15–30 γ. A gradual change of the ion transport velocity at the transition from the magnetosheath to the cushion of hot ions favors the piling up model of magnetic field rather than the model of the internal dipole field of Mars.

Shock‐compression and release behavior near melt states in aluminum

Abstract: The response of porous aluminum (ρ0=1.6 g/cm3) when shock‐compressed to states of partial melting and then released has been investigated. There are no detectable changes in any of the Hugoniot properties in the region where melting should occur. However, release wave speeds in the completely compacted state of the porous aluminum specimens were found to depend critically upon the magnitude of the initial shock loading. For impact stresses below about 7 GPa, the measured release‐wave velocity is well described by the assumption that the initial release is elastic. For initial impact stresses above 7 GPa, the speed of the release wave is observed to be about 20% lower than the elastic wave velocity and approaches the bulk sound speed predicted by equilibrium thermodynamics. All calculations of wave speeds were made with a complete equation of state which was obtained by constructing semiempirical free‐energy functions for both solid and liquid pure phases. These were developed by first assuming self‐consistent forms for the second derivatives of the Helmholtz free energy and then adjusting coefficients in the second derivatives using known quasistatic thermodynamic properties for each phase until agreement with all available data was achieved. Calculation of the intersection of the Hugoniot with the melt boundary (7.5 GPa, 1340 K) using this equation of state when compared with the observed change in sound speed gives strong support to the assumption that melting occurred in these experiments. The release‐wave technique shows promise for measuring phase boundaries in regions of pressure and temperature not accessible by ordinary quasistatic techniques.

Simulation of solar flare particle interaction with interplanetary shock waves

Abstract: In order to study the propagation of solar cosmic rays in interplanetary space a computer program has been developed using a Monte-Carlo technique, which traces the histories of particles released impulsively at the Sun. The particle propagation model considers the adiabatic deceleration during the convective and diffusive transport of the particles, and the model of the interplanetary medium incorporates a radially expanding blast wave which exerts a sweeping action on the particles and accelerates them through the first-order Fermi process. It is shown that energetic storm particle events cannot be simulated by assuming a pure sweeping action of the interplanetary blast wave, but that energization of the particles while reflected at the shock can explain many observed features of such events.

A model for generation of bow‐shock‐associated upstream waves

Abstract: A model is proposed for the generation of upstream hydromagnetic waves by proton beams reflected at the earth's bow shock. It is assumed that the reflection process can produce some gyrophase bunching of the protons, thus creating a gyrophase disturbance that propagates with the beam as it streams back along interplanetary field lines. This leads to the production of driven hydromagnetic waves in the left-hand mode. The resulting theory predicts a wave amplitude, frequency, and polarization in the solar wind rest frame. The amplitude depends on the fraction of protons assumed to be phase coherent in their gyromotion and on the plasma beta, beam velocity, temperatures, and the Alfven Mach number. The theory also predicts the Doppler-shifted frequencies and the apparent sense of polarization that would be observed in satellite measurement frames.

Interplanetary shock waves and comet brightness fluctuations during June–August 1972

Abstract: A series of anomalous events associated with solar activity occurred in interplanetary space in June and August 1972. These events include non-Io-associated decametric emission from Jupiter; brightness variations of the periodic comets Schwassmann-Wachmann 1 and Giacobini-Zinner; interplanetary shock waves detected by Pioneer 9 and 10, Heos 2, and Prognoz and Prognoz 2; interplanetary scintillations; and sudden commencements of geomagnetic storms. Trajectories and deceleration characteristics for the shock waves are estimated primarily from observations using solar radio, in situ, and geomagnetic data. Generally, the trajectories indicate a piston-driven character to about 0.3–0.4 AU, after which the shocks decay to a blastlike motion with a shock velocity variation approximately inversely proportional to the heliocentric radius. Most of the shock waves apparently decayed into magnetoacoustic waves between 2 and 4 AU. In our opinion this decay explains the fact that no anomalous events occurred at either Jupiter or P/Schwassmann-Wachmann I at 5.2 and 5.6 AU, respectively, during August 1972.

Correlation of stress‐wave profiles and the dynamics of the plasma produced by laser irradiation of plane solid targets

Abstract: The interaction of 20‐nsec 300‐MW pulses of 1.06‐μm laser radiation with thick aluminum targets in vacuum has been studied. The time history of the target impulse has been measured with a Sandia quartz gauge. A time sequence of plasma density maps constructed from floating double‐probe data has been used with measured expansion velocities to estimate the plasma momentum. The results show that the stress wave is predominantly produced by about 10% of the evaporated target material which is ionized and expands from the surface in the form of a hot plasma during and shortly after the laser pulse. The estimated momentum of the plasma and neutral emitted particles is 5.6 g cm/sec for a typical case compared with the measured target impulse of 6.1 g cm/sec.

Isothermal blast wave model of supernova remnants

Abstract: The validity of the 'adiabatic' assumption in supernova-remnant calculations is examined, and the alternative extreme of an isothermal blast wave is explored. It is concluded that, because of thermal conductivity, the large temperature gradients predicted by the adiabatic model probably are not maintained in nature. Self-similar solutions to the hydrodynamic equations for an isothermal blast wave have been found and studied. These solutions are then used to determine the relationship between X-ray observations and inferred parameters of supernova remnants. A comparison of the present results with those for the adiabatic model indicates differences which are less than present observational uncertainties. It is concluded that most parameters of supernova remnants inferred from X-ray measurements are relatively insensitive to the specifics of the blast-wave model.