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Voyager 1 observations of plasma wave turbulence at Saturn's bow shock are discussed and compared with corresponding data from Jupiter, earth, and Venus. The results suggest that the plasma instabilities that develop at the lower Mach number bow shocks of the terrestrial planets differ from those found at the high Mach number bow shocks of the outer planets.
According to the Rankine-Hugoniot jump conditions, the magnetic field strength increases in passing from upstream to downstream of a magnetohydrodynamic shock. At the earth's bow shock the magnetic field often increases significantly more than is required by the Rankine-Hugoniot conditions before decaying in an oscillatory fashion to its downstream average value. Recent OGO-5 and ISEE studies, together with the realization that overshoots also occur in the bow shocks of Venus, Jupiter, and Saturn have focussed attention on these phenomena. It is found that none of the nonlinear dispersive wave theories in the shock literature can account for the overshoot. The present investigation documents the dependence of the overshoot amplitude and thickness on solar wind parameters. Magnetic field overshoots are found to be characteristic of supercritical quasi-perpendicular shocks. The overshoot thickness scales as the ion Larmor radius based upon the solar wind speed and magnetic field.
Four upstream energetic proton events (30 keV-75 keV), which were simultaneously observed by the ISEE-1 and ISEE-3 satellites, are investigated. A comparison was made between the absolute flux values about 200 earth radii from the bow shock and the flux values several earth radii in front of the bow shock at two different energies. Close to the bow shock the particle distribution is more or less isotropic and indicates relatively strong scattering of these particles in the upstream wave field. At ISEE-3 between 100 and 200 earth radii upstream from the earth's bow shock, the particles move essentially scatter-free from the general bow shock direction. The proton differential intensity at ISEE-3 is a factor of about 4-15 less than at ISEE-1 at 30 keV. The spectra at ISEE-1 are steeper than the spectra at ISEE-3. Flux ratios and spectra are discussed in terms of a first order Fermi acceleration model with a diffusion coefficient increasing approximately linearly with energy and a free escape boundary at some distance upstream.
Collisionless shocks can be nonstationary with periodic reformation shown in many simulation results, but direct observations are still tenuous and difficult to conclusively interpret. In this study, using Magnetospheric Multiscale (MMS) observations, we report direct observational evidence of Earth’s oblique bow shock reformation driven by the foreshock ultra-low frequency (ULF)waves. When the four MMS spacecraft were in a string-of-pearls formation roughly along the bow shock normal, they observed that when each period of foreshock ULF waves encountered the bow shock, a new shock ramp formed. Meanwhile, in the magnetosheath, the old bow shock’s remnants were observed periodically convecting downstream. We propose that the reformation mechanism of the oblique bow shock is the variation of the upstream conditions by the periodic ULF waves as they encounter the bow shock. We also examine the nature of reflected ions during the reformation process.
Voyager 1 plasma wave data show that the quasi-perpendicular, supercritical bow shock of Saturn exhibits the same plasma wave phenomenology observed near Jupiter. Using a quasi-linear model developed for the Jovian bow shock, it is shown that plasma waves at Saturn can generate a significant portion of the totalelectron temperature jump measured across the shock. In this respect, Saturn's bow shock more closely resembles Jupiter's than the earth's, where plasma waves contribute negligibly to the total electron temperature jump.
The thickness of magnetic structures associated with quasi-perpendicular bow shocks has been observed to vary over more than 2 orders of magnitude. In this paper, a criterion is employed which states that the magnetic structure of perpendicular shocks adjusts itself to keep electrostatic waves excited by the relative drift of electrons and ions at marginal stability. The marginal stability boundary and measured plasma parameters are used to calculate the expected thickness of bow-shock magnetic structures. The calculated and measured thicknesses are compared and found to be in good agreement over a range from less than 10 km to greater than 500 km. The conclusion is that the thickness of magnetic structures associated with quasi-perpendicular bow shocks is determined primarily by dissipation due to electron-ion streaming instabilities rather than by dispersive effects.
The location of the forward boundary of the upstream wave region ahead of the earth's bow shock is investigated statistically using plasma and magnetic-field data obtained by Heos 1. The analysis is conducted on the assumption that the waves are produced by protons reflected from the bow shock and traveling upstream with an effective velocity equal to the product of a parameter, p, and the solar-wind bulk velocity. The data-reduction methods are summarized, and uncertainties in the determination of the value of p are discussed. It is found that the overall average boundary corresponds to a velocity of approximately twice the solar-wind velocity for protons reflected from the daytime sector of the bow shock. More refined analysis of the data shows that the value of p is approximately 1.6 near the subsolar point and greater than 2 along the daytime flanks of the bow shock.
A theoretical examination of the jump conditions of the bow shock is used to investigate the influence of the solar wind magnetic fields on the structure of the parameters behind the bow shock. Through the assumption that the average values of the parameters along the radial direction in the magnetosheath are equal to their values just behind the bow shock, the influence of the direction of the solar wind magnetic fields on the average structure of the magnetosheath is determined. From this assumption, a zero-order formula for the thickness of the magnetosheath is deduced which satisfies the boundary conditions and conservation laws of mass and momentum flux. The theoretical estimate of the thickness is compared with satellite observations to check the assumption and select the optimum value of the polytropic exponent of the plasma gas.
Lockheed spectrometer data from orbits 1 through 20 of Ogo 5 are used to study proton scattering near the bow shock. Correlative UCLA fluxgate magnetometer data from the satellite are used to complete motion studies of the bow shock when spectrometer data are missing. Thirty-eight analyzable sets of multiple shock crossings show 358 shock encounters ranging from 10 to 22 earth radii and spanning sun-earth-satellite angles from 30 to 90 deg. Gross features of the study show that the location and shape of the bow shock are in good agreement with the hydrodynamic model of the bow shock.
The paper reports on two sets of bow shock crossings observed by the ISEE 1 and ISEE 2 spacecraft, in which very large electron temperature increases were found. When the two sets of shocks with the large electron heating were compared with the rest of the 52 bow shock crossings of the compiled series, these sets were found to correlate with an unusually high upstream solar wind flow speed. The highest correlation was found between the amount of electron heating, expressed by the difference in temperature between the downstream and upstream electrons (rather than their ratio), and the total change in the bulk flow energy per particle across the shock. The results suggest that the appropriate quantity to consider in studies of electron heating at shocks is the temperature difference rather than the temperature ratio. The latter can be artificially elevated by low upstream temperatures.
Observations of the bow shock location and the structure of the magnetotail of Mars by the Phobos spacecraft and of Venus by the Pioneer Venus Orbiter reveal the solar wind interactions with these two planets to be quite similar. The subsolar bow shocks of both Venus and Mars lie at 1.47 planetary radii while at the terminator they are at 2.40 and 2.65 planetary radii, respectively. Both bow shocks have oval cross sections when viewed from the sun whose major axes are controlled by the orientation of the interplanetary magnetic field. The tail lobes of both planets are similarly controlled by the IMF orientation. The strength of the solar/antisolar component of the magnetic field is 17 nT at Venus and 14 nT at Mars. The component perpendicular to the tail axis is about 1/2 the corresponding IMF component at Venus and 2 times this component at Mars. However, when these measurements are compared in terms of the distance down the tail at which each were taken, the data from the two planets are quite consistent. Hence both Venus and Mars have principally induced magnetospheres and magnetotails which stand off the solar wind flow.
The Martian magnetosphere is a product of the interaction of Mars with the interplanetary magnetic field and the supersonic solar wind. The location of the bow shock has been previously modeled as conic sections using data from spacecraft such as Phobos 2, Mars Global Surveyor, and Mars Express. The Mars Atmosphere and Volatile EvolutioN (MAVEN) mission spacecraft arrived in orbit about Mars in November 2014 resulting in thousands of crossings to date. We identify over 1,000 bow shock crossings. We model the bow shock as a three-dimensional surface accommodating asymmetry caused by crustal magnetic fields. By separating MAVEN's bow shock encounters based on solar condition, we also investigate the variability of the surface. We find that the shock surface varies in shape and location in response to changes in the solar radiation, the solar wind Mach number, dynamic pressure of the solar wind, and the relative local time location of the strong crustal magnetic fields (i.e., whether they are on the dayside or on the nightside).
Some open questions in the physics of bow shock formation, the evolution of the particle distributions from solar wind into the magnetosheath, and the acceleration of ions at the moment of the shock are summarized. A layout of the current situation is presented in view of recent theoretical developments and the new diagnostic tools provided by the Cluster mission. The transition of ions across the quasi-perpendicular bow shock and their downstream thermalization are discussed. The processes and spatial scales are found to be species dependent and are discussed for H(+), He(2+), and He(+). The theory of particle acceleration at quasi-parallel shocks are reviewed. It is shown how Cluster can study the time variable structures of the shock as predicted by hybrid simulation. It is emphasized that high time resolution measurement with simultaneous species separation is necessary for the study of the ion acceleration. Suggestions for the spacecraft separations at the bow shock are suggested.
A numerical simulation is used to predict the interaction between the earth's bow shock and lithium to be released in the solar wind during the Active Magnetospheric Particle Tracer Explorers program in 1984. Based on the simulation results for a release near the subsolar point, it is recommended that a favorable release condition is when the garden-hose angle of the interplanetary magnetic field exceeds about 60 to 70 deg so that the transmission of Li(+) ions through the bow shock is optimized. The model also predicts that the Li(+) is 'shock-drift' accelerated at the bow shock. The energy gain of Li(+) ions is on the average less for the transmitted particles (below a factor of about 4) than for the reflected particles (below a factor of about 16).
A previous MHD theory for the density jump at the Earth's bow shock, which assumed the Alfven M(A) and sonic M(s) Mach numbers are both much greater than 1, is reanalyzed and generalized. It is shown that the MHD jump equation can be analytically solved much more directly using perturbation theory, with the ordering determined by M(A) and M(s), and that the first-order perturbation solution is identical to the solution found in the earlier theory. The second-order perturbation solution is calculated, whereas the earlier approach cannot be used to obtain it. The second-order terms generally are important over most of the range of M(A) and M(s) in the solar wind when the angle theta between the normal to the bow shock and magnetic field is not close to 0 deg or 180 deg (the solutions are symmetric about 90 deg). This new perturbation solution is generally accurate under most solar wind conditions at 1 AU, with the exception of low Mach numbers when theta is close to 90 deg. In this exceptional case the new solution does not improve on the first-order solutions obtained earlier, and the predicted density ratio can vary by 10-20% from the exact numerical MHD solutions. For theta approx. = 90 deg another perturbation solution is derived that predicts the density ratio much more accurately. This second solution is typically accurate for quasi-perpendicular conditions. Taken together, these two analytical solutions are generally accurate for the Earth's bow shock, except in the rare circumstance that M(A) is less than or = 2. MHD and gasdynamic simulations have produced empirical models in which the shock's standoff distance a(s) is linearly related to the density jump ratio X at the subsolar point. Using an empirical relationship between a(s) and X obtained from MHD simulations, a(s) values predicted using the MHD solutions for X are compared with the predictions of phenomenological models commonly used for modeling observational data, and with the predictions of a modified phenomenological model proposed recently. The similarities and differences between these results are illustrated using plots of X and a(s) predicted for the Earth's bow shock. The plots show that the new analytic solutions agree very well with the exact numerical MHD solutions and that these MHD solutions should replace the corresponding phenomenological relations in comparisons with data. Furthermore, significant differences exist between the standoff distances predicted at low M(A) using the MHD models versus those predicted by the new modified phenomenological model. These differences should be amenable to observational testing.
New information is presented on the general characteristics of electron distribution functions upstream, within, and downstream of the earth's bow shock, thereby providing new insights into the instabilities in collisionless shocks. The results presented are from a survey of electron velocity distributions measured near the earth's bow shock between October 1977 and December 1978 using the Los Alamos/Garching plasma instrumentation aboard ISEE 2. A wide variety of distribution shapes is found within the different plasma regions in close proximity to the bow shock. It is found that these shapes can be classified into general types that are characteristic of three different plasma regions, namely the upstream region or electron foreshock, the shock proper where most of the heating occurs, and the downstream region or the magnetosheath. Evidence is provided that field-aligned, rather than cross-field, instabilities are the major source of electron dissipation in the earth's bow shock.
Data obtained with the Magma magnetometer on the subsolar passes of the Phobos spacecraft during its 3 elliptic orbits reveals a turbulent bow shock with a strong foot consistent with the reflection of solar wind protons. The bow shock lies at a subsolar distance of 1.47 + or - .03 R(M). The circular orbit phase of the mission reveals a bow shock with a highly varying location. The median terminator crossing lies at 2.72 Mars radii. The location of the bow shock in the terminator plane is sensitive to neither the EUV flux nor to planetary longitude.
Observations of particle spectra, intensity, and enhancement of alpha particles over protons at diffuse ion events at the quasi-parallel earth bow shock are compared to a Monte Carlo simulation of diffusive shock acceleration. The simulation includes the back reaction of accelerated particles on the shock structure, particle escape at an upstream free escape boundary, and a low energy per nucleon threshold for thermal leakage of downstream, shock-heated particles into the upstream region. The simulation assumes that the same scattering operator that gives rise to shock acceleration can also describe a viscous shock governed by hydrodynamic turbulence. This implies that accelerated ions can be drawn directly from the thermal solar wind with no separate superthermal seed population. Good agreement between the simulation and observations made during nearly radial magnetic field configurations lends support to thermal leakage of downstream, shock-heated ions as the mode of injection for diffusion ion events.