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NASA NTRS1994

Standing shocks in a two-fluid solar wind

We present a numerical study of the formation of standing shocks in the solar wind using a two-fluid time-dependent model in the presence of Alfven waves. Included in this model is the adiabatic cooling and thermal conduction of both electrons and protons. In this study, standing shocks develop in the flow when additional critical points form as a result of either localized momentum addition or rapid expansion of the flow tube below the existing sonic point. While the flow speed and density exhibit the same characteristics as found in earlier studies of the formation of standing shocks, the inclusion of electron and proton heat conduction produces different signatures in the electron and proton temperature profiles across the shock layer. Owing to the strong heat conduction, the electron temperature is nearly continuous across the shock, but its gradient has a negative jump across it, thus producing a net heat flux out of the shock layer. The proton temperature exhibits the same characteristics for shocks produced by momentum addition but behaves differently when the shock is formed by the rapid divergence of the flow tube. The adiabatic cooling in a rapidly diverging flow tube reduces the proton temperature so substantially that the proton heat conduction becomes negligible in the vicinity of the shock. As a result, protons experience a positive jump in temperature across the shock. While Alfven waves do not affect the formation of standing shocks, they contribute to the change of the mmomentum and energy balance across them. We also find that for this solar wind model the inclusion of thermal conduction and adiabatic cooling for the elctrons and protons increases significantly the range of parameters characterizing the formation of standing shocks over those previously found for isothermal and polytropic models.

Habbal, Shadia R.↗

NASA NTRS1994

Shock propagation and the generation of magnetohydrodynamic wave fields in inhomogeneous molecular clouds

We develop a simple one-dimensional model for the interaction of a steady, thin, planar shock wave with a nonrigid cloud which may be in motion relative to the surrounding medium, and we apply the model to shocks impinging on, and propagating through, molecular clouds. Both 'adiabatic' (gamma = 5/3) and radiative (gamma = 1) shocks are considered and we allow for the presence of a uniform magnetic field directed either parallel or perpendicular to the shock normal. The former field orientation is equivalent to the hydrodynamic case, and the latter involves only fast MHD shocks. We focus on the manner in which such shocks can generate internal kinetic motions in the cloud on a range of size and density scales through the direct acceleration of cores and clumps by shocks transmitted into them and through the generation of an MHD wavefield via the reflection of the incident shock at clump boundaries. We find that stronger incident Mach numbers and smaller density contrasts lead to more efficient cloud acceleration, as do isothermal intercloud shocks and small intercloud magnetic field strengths. The acceleration efficiency is insensitive to the adiabatic index and the magnetic field strength in the cloud itself. For typical parameter choices, the direct acceleration of clouds and clumps by strong shocks is found to be substantial and could at least in part account for their observed velocity dispersions. If the shocks are moderately weak, the final velocity of the cloud is linearly related to its initial velocity, with higher acceleration giving shallower slopes (i.e., final velocity distributions which are less sensitive to the initial distribution). Compared to the kinetic energy of the postshock cloud, the energy given to the wavefield at each encounter is small, and the heating of the interclump medium by the dissipation of this wavefield is found to be insufficient to balance the cooling rate in the cloud as a whole (although it may be important in particular regions), even if this medium is warm, unless it is also extremely tenuous (n approximately less than 0.1/cu cm). Nevertheless, the correction for the velocity imparted to the cloud leads to a substantial increase in the critical incident Mach numner for wave emission over that reported by Spitzer for the rigid case. The implications of our model for shock-induced star formation are discussed briefly.

Miesch, Mark S.↗

NASA NTRS1995

Motion of the Heliospheric Termination Shock at High Heliographic Latitude

We expect the mean distance of the heliospheric termination shock to be greater (smaller) at polar latitudes than at equatorial latitudes, depending on whether the mean dynamic pressure of the solar wind is greater or smaller at high latitudes. The heliospheric termination shock is expected to move in response to variation in upstream solar wind conditions, so that at any particular instant the termination shock will resemble a distorted asymmetric balloon with some parts moving inward and others moving outward. If the shock is a gasdynamic or magnetohydrodynamic shock the results of the analysis depend only very weakly on the nature of the upstream disturbance; typical speeds of the disturbed shock are approximately 100 to 200 km/s. In the absence of a significant latitude gradient of the typical magnitude of solar wind disturbances typical motions of the disturbed shock at polar latitudes would be about twice as fast, due to the higher speed of the high-latitude wind. If the dynamics of the termination shock are dominated by acceleration of the anomalous component of the cosmic rays, the motion of the shock in response to a given disturbance is substantially slower than in the gasdynamic case. Conceivably, particle acceleration might be a less important effect at higher latitudes, and we envision the possibility of a termination shock that is dominated by particle acceleration at lower latitudes and is an MHD shock at high latitudes. In this event high latitude solar wind disturbances would produce substantially larger inward and outward motions of the shock in the polar regions.

Barnes, Aaron↗

NASA NTRS1997

A Study of Fundamental Shock Noise Mechanisms

This paper investigates two mechanisms fundamental to sound generation in shocked flows: shock motion and shock deformation. Shock motion is modeled numerically by examining the interaction of a sound wave with a shock. This numerical approach is validated by comparison with results obtained by linear theory for a small-disturbance case. Analysis of the perturbation energy with Myers' energy corollary demonstrates that acoustic energy is generated by the interaction of acoustic disturbances with shocks. This analysis suggests that shock motion generates acoustic and entropy disturbance energy. Shock deformation is modeled numerically by examining the interaction of a vortex ring with a shock. These numerical simulations demonstrate the generation of both an acoustic wave and contact surfaces. The acoustic wave spreads cylindrically. The sound intensity is highly directional and the sound pressure increases with increasing shock strength. The numerically determined relationship between the sound pressure and the Mach number is found to be consistent with experimental observations of shock noise. This consistency implies that a dominant physical process in the generation of shock noise is modeled in this study.

Meadows, Kristine R.↗

NASA NTRS1995

Hybrid Simulations of Interstellar Pickup Ion Acceleration at the Solar Wind Termination Shock

Hybrid (kinetic ion/fluid electron) simulations have been used to study self-consistently the injection and initial stages of acceleration of interstellar pickup ions at the solar wind termination shock. Results are presented from one-dimensional simulations of high Mach number oblique (40 deg-50 deg) shocks with a 10% population of interstellar pickup hydrogen. In these simulations, the pickup ions, the solar wind ions, the shock fields and the waves are all treated self-consistently. Pickup ions reflected by the shock excite large amplitude (DELTA.B / B approximately 0.3) upstream magnetosonic waves. These waves, in turn, scatter the pickup hydrogen, as expected in the diffusive shock acceleration process. The spectrum of excited waves broadens in time. We find that, for the parameters studied, the termination shock efficiently injects and accelerates the interstellar pickup hydrogen, and thus this work represents a microscopic verification of this anomalous cosmic ray injection mechanism. Comparison of injected fluxes from the simulations with Voyager fluxes extrapolated to the termination shock suggests that injection at the termination shock is probably greater than injection by interplanetary shocks. A study of accelerated pickup ion orbits shows that the energy gain comes predominantly from shock drift acceleration in the shock front, with the upstream waves aiding the acceleration by allowing multiple encounters with the shock.

Liewer, P. C.↗

NASA NTRS2003

Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

Shock jump conditions, i.e., the specification of the downstream parameters of the gas in terms of the upstream parameters, are obtained for steady-state, plane shocks with oblique magnetic fields and arbitrary flow speeds. This is done by combining the continuity of particle number flux and the electromagnetic boundary conditions at the shock with the magnetohydrodynamic conservation laws derived from the stress-energy tensor. For ultrarelativistic and nonrelativistic shocks, the jump conditions may be solved analytically. For mildly relativistic shocks, analytic solutions are obtained for isotropic pressure using an approximation for the adiabatic index that is valid in high sonic Mach number cases. Examples assuming isotropic pressure illustrate how the shock compression ratio depends on the shock speed and obliquity. In the more general case of gyrotropic pressure, the jump conditions cannot be solved analytically with- out additional assumptions, and the effects of gyrotropic pressure are investigated by parameterizing the distribution of pressure parallel and perpendicular to the magnetic field. Our numerical solutions reveal that relatively small departures from isotropy (e.g., approximately 20%) produce significant changes in the shock compression ratio, r , at all shock Lorentz factors, including ultrarelativistic ones, where an analytic solution with gyrotropic pressure is obtained. In particular, either dynamically important fields or significant pressure anisotropies can incur marked departures from the canonical gas dynamic value of r = 3 for a shocked ultrarelativistic flow and this may impact models of particle acceleration in gamma-ray bursts and other environments where relativistic shocks are inferred. The jump conditions presented apply directly to test-particle acceleration, and will facilitate future self-consistent numerical modeling of particle acceleration at oblique, relativistic shocks; such models include the modification of the fluid velocity profile due to the contribution of energetic particles to the momentum and energy fluxes.

Double, Glen P.↗

NASA NTRS2012

Coronal Mass Ejection-driven Shocks and the Associated Sudden Commencements-sudden Impulses

Interplanetary (IP) shocks are mainly responsible for the sudden compression of the magnetosphere, causing storm sudden commencement (SC) and sudden impulses (SIs) which are detected by ground-based magnetometers. On the basis of the list of 222 IP shocks compiled by Gopalswamy et al., we have investigated the dependence of SC/SIs amplitudes on the speed of the coronal mass ejections (CMEs) that drive the shocks near the Sun as well as in the interplanetary medium. We find that about 91% of the IP shocks were associated with SC/SIs. The average speed of the SC/SI-associated CMEs is 1015 km/s, which is almost a factor of 2 higher than the general CME speed. When the shocks were grouped according to their ability to produce type II radio burst in the interplanetary medium, we find that the radio-loud (RL) shocks produce a much larger SC/SI amplitude (average approx. 32 nT) compared to the radio-quiet (RQ) shocks (average approx. 19 nT). Clearly, RL shocks are more effective in producing SC/SIs than the RQ shocks. We also divided the IP shocks according to the type of IP counterpart of interplanetary CMEs (ICMEs): magnetic clouds (MCs) and nonmagnetic clouds. We find that the MC-associated shock speeds are better correlated with SC/SI amplitudes than those associated with non-MC ejecta. The SC/SI amplitudes are also higher for MCs than ejecta. Our results show that RL and RQ type of shocks are important parameters in producing the SC/SI amplitude.

Coronal mass ejections↗

NASA NTRS2018

Kinetic Properties of an Interplanetary Shock Propagating Inside a Coronal Mass Ejection

We investigate the kinetic properties of a typical fast-mode shock inside an interplanetary coronal mass ejection (ICME) observed on 1998 August 6 at 1 au, including particle distributions and wave analysis with the in situ measurements from Wind. Key results are obtained concerning the shock and the shock-ICME interaction at kinetic scales: (1) gyrating ions, which may provide energy dissipation at the shock in addition to wave-particle interactions, are observed around the shock ramp; (2) despite the enhanced proton temperature anisotropy of the shocked plasma, the low plasma beta inside the ICME constrains the shocked plasma under the thresholds of the ion cyclotron and mirror-mode instabilities; (3) whistler heat flux instabilities, which can pitch-angle scatter halo electrons through a cyclotron resonance, are observed around the shock, and can explain the disappearance of bi-directional electrons (BDEs) inside the ICME together with normal betatron acceleration; (4) whistler waves near the shock are likely associated with the whistler heat flux instabilities excited at the shock ramp, which is consistent with the result that the waves may originate from the shock ramp; (5) the whistlers share a similar characteristic with the shocklet whistlers observed by Wilson et al., providing possible evidence that the shock is decaying because of the strong magnetic field inside the ICME.

Liu, Mingzhe↗

NASA NTRS2018

Novel Shock Microstructures in Accessory Minerals from the Haughton Dome, Devon Island, Nunavut, Canada

The 23 km-diameter, ca. 24 Ma Haughton Dome impact structure in the Canadian Arctic on Devon Island, Nunavut (89deg41′W, 75deg22′N) occurred within a two layered target composed of a shallowly-dipping ~1700 m thick succession of Paleozoic limestones and evaporates overlying ca.1.9 Ga high grade gneisses [1, 2]. Within the structure a well preserved impact melt bearing breccia unit contains a variety of shocked clasts from the pre-impact sediments and basement gneisses [3]. Due to their high level of preservation a variety of studies have been undertaken on the clast population of the melt bearing breccia, including characterization of shock within the accessory minerals of the basement lithologies [4, 5]. This study presents high resolution electron backscatter diffraction (EBSD) microstructural data for zircon and monazite from historic samples of the basement gneiss, in which bulk shock pressures have been previously constrained based on major phases [4, 6]. Shocked zircon and monazite grains have been investigated from shock stage 1b (sample 72110), 2 (7273) and 3 (7192, Dig-9) [4, 6]. At lower shock levels zircon displays planar microstructures consistent with mechanical shock {112} twin formation [7] and deviatoric transformation to the high pressure polymorph reidite [8]. Zircon grains from shock stage three show a more chaotic microstructure with multiple orientations of tightly spaced sets of reidite that are variably recrystallized to zircon neoblasts. Monazite from lower shock stages contains a number of mechanical twin orientations that are indicative of shock deformation [9]. At higher shock pressures a lath like structure of interlocking twin orientations has been identified. This microstructure is suggestive of a reversion transformation from a high pressure polymorph [10] and is the first evidence for the transformation of monazite during shock.

Erickson, Timmons M.↗

NASA NTRS2018

Detrital Shocked Zircon Provides First Radiometric Age Constraint of <1472 Ma for the Santa Fe Impact Structure, New Mexico, USA

Impact structures are prone to erosion, burial and tectonic deformation. The Santa Fe impact structure in New Mexico contains shatter cones and shocked quartz, but is highly tectonized and eroded; estimates of the impact age (1200-300 Ma) and size (6-13 km) are poorly constrained. Here we report the first occurrence of shock-twinned zircon identified both in modern sediments and bedrock at the Santa Fe impact structure. Zircon {112} twin lamellae are considered diagnostic evidence of shock deformation and have been identified at several impact structures including Vredefort, Sudbury, Ries, Rock Elm, and in lunar impact breccia. A total of 6619 grains from fifteen sediment samples and two rock samples were surveyed; seven shocked grains were identified (7/6619 = 0.1%). One shocked zircon was identified in a biotite schist shatter cone. Five of seven shocked zircon grains were EBSD mapped; three were analyzed with multiple SIMS spots. EBSD mapping revealed {112} deformation twin lamellae in each of the five zircon grains. U-Pb geochronology for three of the shocked zircon grains yield crystallization ages from 1715+/-22 to 1472+/-35 Ma. LA-ICPMS U-Th-Pb analysis of detrital zircon grains from five samples yielded Paleoproterozoic (1800-1600 Ma) and Mesoproterozoic (1500-1300 Ma) ages. We reveal the first confirmed shocked zircon at the Santa Fe structure. Zircon is the third shocked mineral identified at this site, in addition to xenotime and quartz]; the {112} twin lamellae indicate that exposed bedrock may have experienced shock pressures up to ~20 GPa. The 1472+/-35 Ma age determined from a shock-twinned zircon is the first reliable maximum impact age constraint based on analysis of shocked material and extends the window for the Santa Fe impact event into the Mesoproterozoic.

Montalvo, Pedro E.↗

NASA NTRS2019

Understanding the Role of 𝛼 Particles in Oblique Heliospheric Shock Oscillations

Recent observations by DSCOVR provide high temporal resolution (50 samples per second) magnetic vector field data that allows investigating the details of oblique heliospheric shock oscillations. It was found that some of these shocks exhibit magnetic oscillations, both downstream and upstream of the shock front. The DSCOVR/MAG magnetic field data are supplemented by an extensive database of low Mach number (M < 3) low‐β (<1) shock data observed by Wind albeit with lower temporal resolution. Motivated by the observations, we use the 2.5D hybrid model of the oblique shocks with α particles in addition to kinetic protons and electron fluid. We model the properties of the oblique shocks for a number of typical parameters found in observations and study the effects of the shock parameters and the relative α particle abundances on the properties of the shock magnetic field, density, and velocity oscillations. We find the α particles “surf” on the shock front and produce a wake of density oscillations. We examine the details of the phase space of the ions as well as the ion velocity distribution functions in various parts of the shock and study their nonthermal properties. We determine the effects of the α particle kinetic properties and abundances on the structure and dynamics of the shock downstream oscillations for a range of parameters relevant to low Mach number low‐β heliospheric shocks.

Ofman, L.↗

NASA NTRS2021

Direct Multipoint Observations Capturing the Reformation of a Supercritical Fast Magnetosonic Shock

Using multipoint Magnetospheric Multiscale (MMS) observations in an unusual string-of-pearls configuration, we examine in detail observations of the reformation of a fast magnetosonic shock observed on the upstream edge of a foreshock transient structure upstream of Earth’s bow shock. The four MMS spacecraft were separated by several hundred km, comparable to suprathermal ion gyro-radius scales or several ion inertial lengths. At least half of the shock reformation cycle was observed, with a new shock ramp rising up out of the “foot” region of the original shock ramp. Using the multipoint observations, we convert the observed time-series data into distance along the shock normal in the shock’s rest frame. That conversion allows for a unique study of the relative spatial scales of the shock’s various features, including the shock’s growth rate, and how they evolve during the reformation cycle. Analysis indicates that: the growth rate increases during reformation, electron-scale physics play an important role in the shock reformation, and energy conversion processes also undergo the same cyclical periodicity as reformation. Strong, thin electron-kinetic-scale current sheets and large-amplitude electrostatic and electromagnetic waves are reported. Evidence is also presented of nonlinear wave decay from electromagnetic whistler-mode “lion roars” to electrostatic solitary waves in the downstream plasma regime. Results highlight the critical cross-scale coupling between electron-kinetic-and ion-kinetic-scale processes and details of the nature of nonstationarity, shock-front reformation at collisionless, fast magnetosonic shocks.

D L Turner↗

DOE OSTI2021

Temporally and spatially resolved X-ray densitometry in a shock tube

Gas densities were measured by x-ray absorption spectroscopy to examine spatial inhomogeneity in density behind incident and reflected shock waves in a miniature (12.7 mm bore) high repetition rate shock tube. Shock waves were generated in argon. The pressure and temperature behind the incident shock were P 2 ~ 1.72 bar and T 2 ~ 800 K, while those behind the reflected shock were P 5 ~ 6.5 bar and T 5 ~ 1480 K. Time-resolved line-of-sight transmission measurements using x-rays at 9 keV photon energy were made along various axial and transverse locations covering the entire shock tube cross section. The x-ray transmission at each location was converted to pathlength-integrated densities, which in some conditions could be further converted to pathlength-averaged densities. The measured gas densities were compared with those calculated by the normal shock wave relations, and good agreement was found in the preshock and immediately behind the incident shock regions. Similar agreement was found for reflected shock conditions very near the endwall. However, increasingly large differences between the measured and calculated gas densities were found as distance from the endwall increased. Furthermore, reconstruction by Abel inversion allowed time and radially resolved densities to be obtained from the transverse measurements. While the profiles measured in this experiment are of insufficient signal-to noise level and resolution to definitively assign boundary layer thicknesses, future improvements may be able to do this. The radially resolved densities reveal growing sidewall thermal boundary layers in gases behind the reflected shock. These reconstructions were compared with a model of the thermal boundary layer and are consistent with values of the thermal boundary layer thickness being between 0.25 mm and 1 mm at 0.7 ms after shock reflection.

42 ENGINEERING↗

DOE OSTI2023

Mesoscale shock structure in particulate composites

Multiscale experiments in heterogeneous materials and the knowledge of their physics under shock compression are limited. Here, this study examines the multiscale shock response of particulate composites comprised of soda-lime glass particles in a PMMA matrix using full-field high speed digital image correlation (DIC) for the first time. Normal plate impact experiments, and complementary numerical simulations, are conducted at stresses ranging from 1.1 - 3.1 GPa to elucidate the mesoscale mechanisms responsible for the distinct shock structure observed in particulate composites. The particle velocity from the macroscopic measurement at continuum scale shows a relatively smooth velocity profile, with shock thickness decreasing with an increase in shock stress, and the composite exhibits strain rate scaling as the second power of the shock stress. In contrast, the mesoscopic response was highly heterogeneous, which led to a rough shock front and the formation of a train of weak shocks traveling at different velocities. Additionally, the normal shock was seen to diffuse the momentum in the transverse direction, affecting the shock rise and the rounding-off observed at the continuum scale measurements. The numerical simulations indicate that the reflections at the interfaces, wave scattering, and interference of these reflected waves are the primary mechanisms for the observed rough shock fronts.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Electron acceleration in laboratory-produced turbulent collisionless shocks

Astrophysical collisionless shocks are among the most powerful particle accelerators in the Universe. Generated by violent interactions of supersonic plasma flows with the interstellar medium, supernova remnant shocks are observed to amplify magnetic fields and accelerate electrons and protons to highly relativistic speeds. In the well-established model of diffusive shock acceleration, relativistic particles are accelerated by repeated shock crossings. However, this requires a separate mechanism that pre-accelerates particles to enable shock crossing. This is known as the ‘injection problem’, which is particularly relevant for electrons, and remains one of the most important puzzles in shock acceleration. In most astrophysical shocks, the details of the shock structure cannot be directly resolved, making it challenging to identify the injection mechanism. In this letter we report results from laser-driven plasma flow experiments, and related simulations, that probe the formation of turbulent collisionless shocks in conditions relevant to young supernova remnants. We show that electrons can be effectively accelerated in a first-order Fermi process by small-scale turbulence produced within the shock transition to relativistic non-thermal energies, helping overcome the injection problem. Our observations provide new insight into electron injection at shocks and open the way for controlled laboratory studies of the physics underlying cosmic accelerators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Evidence of non-isentropic release from high residual temperatures in shocked metals measured with ultrafast x-ray diffraction

Shock experiments are widely used to understand the mechanical and electronic properties of matter under extreme conditions. However, after shock loading to a Hugoniot state, a clear description of the post-shock thermal state and its impacts on materials is still lacking. We used diffraction patterns from 100-fs x-ray pulses to investigate the temperature evolution of laser-shocked Al–Zr metal film composites at time delays ranging from 5 to 75 ns driven by a 120-ps short-pulse laser. We found significant heating of both Al and Zr after shock release, which can be attributed to heat generated by inelastic deformation. A conventional hydrodynamic model that employs (i) typical descriptions of Al and Zr mechanical strength and (ii) elevated strength responses (which might be attributed to an unknown strain rate dependence) did not fully account for the measured temperature increase, which suggests that other strength-related mechanisms (such as fine-scale void growth) could play an important role in thermal responses under shock wave loading/unloading cycles. Our results suggest that a significant portion of the total shock energy delivered by lasers becomes heat due to defect-facilitated plastic work, leaving less converted to kinetic energy. This heating effect may be common in laser-shocked experiments but has not been well acknowledged. High post-shock temperatures may induce phase transformation of materials during shock release. Another implication for the study is the preservability of magnetic records from planetary surfaces that have a shock history from frequent impact events.

42 ENGINEERING↗

DOE OSTI2024

Weak shock compaction on granular salt

This study conducted integrated experiments and computational modeling to investigate the speeds of a developing shock within granular salt and analyzed the effect of various impact velocities up to 245 m/s. Experiments were conducted on table salt utilizing a novel setup with a considerable bore length for the sample, enabling visualization of a moving shock wave. Experimental analysis using particle image velocimetry enabled the characterization of shock velocity and particle velocity histories. Mesoscale simulations further enabled advanced analysis of the shock wave’s substructure. In simulations, the shock front’s precursor was shown to have a heterogeneous nature, which is usually modeled as uniform in continuum analyses. The presence of force chains results in a spread out of the shock precursor over a greater ramp distance. With increasing impact velocity, the shock front thickness reduces, and the precursor of the shock front becomes less heterogeneous. Furthermore, mesoscale modeling suggests the formation of force chains behind the shock front, even under the conditions of weak shock. This study presents novel mesoscale simulation results on salt corroborated with data from experiments, thereby characterizing the compaction front speeds in the weak shock regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Magnetic ramp scale at supercritical perpendicular collisionless shocks: Full particle electromagnetic simulations

Supercritical perpendicular collisionless shocks are known to exhibit foot, ramp, and overshoot structures. The shock ramp structure is in a smaller scale in contrast to other microstructures (foot and overshoot) within the shock front. One-dimensional full particle simulations of strictly perpendicular shocks over wide ranges of ion beta β{sub i}, Alfvén Mach number M{sub A}, and ion-to-electron mass ratio m{sub i}/m{sub e} are presented to investigate the impact of plasma parameters on the shock ramp scale. Main results are (1) the ramp scale can be as small as several electron inertial length. (2) The simulations suggest that in a regime below the critical ion beta value, the shock front undergoes a periodic self-reformation and the shock ramp scale is time-varying. At higher ion beta values, the shock front self-reformation is smeared. At still higher ion beta value, the motion of reflected ions is quite diffuse so that they can lead to a quasi-steady shock ramp. Throughout the above three conditions, the shock ramp thickness increases with β{sub i}. (3) The increase (decrease) in Mach number and the decrease (increase) in the beta value have almost equivalent impact on the state (i.e., stationary or nonstationary) of the shock ramp. Both of front and ramp thicknesses are increased with M{sub A}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗