Terrestrial Bow Shock Research Articles

Whistler damping at oblique propagation: Laminar shock precursors

This paper addresses the collisionless damping of whistlers observed as precursors standing upstream of oblique, low‐Mach number terrestrial bow shocks. The linear theory of electromagnetic waves in a homogeneous Vlasov plasma with Maxwellian distribution functions and a magnetic field is considered. Numerical solutions of the full dispersion equation are presented for whistlers propagating at an arbitrary angle with respect to the magnetic field. It is demonstrated that electron Landau damping attenuates oblique whistlers and that the parameter which determines this damping is βe. In a well‐defined range of parameters, this theory provides damping lengths which are the same order of magnitude as those observed. Thus electron Landau damping is a plausible process in the dissipation of upstream whistlers. Nonlinear plasma processes which may contribute to precursor damping are also discussed, and criteria for distinguishing among these are described.

The structure of oblique subcritical bow shocks: ISEE 1 and 2 observations

We have studied the structural elements, including shock ramps and precursor wave trains, of a series of oblique low‐Mach number terrestrial bow shocks. We used magnetic field data from the dual ISEE 1 and 2 spacecraft to determine the scale lengths of various elements of shock structure as well as wavelengths and wave polarizations. Bow shock structure under these conditions is essentially that of a large‐amplitude damped whistler mode wave which extends upstream in the form of a precursor wave train. Shock thicknesses, which are determined by the dispersive properties of the ambient plasma, are too broad to support current‐driven electrostatic waves, ruling out such turbulence as the source of dissipation in these shocks. Dissipative processes are reflected in the damping of the precursors, and dissipative scale lengths are ∼200–800 km (several times greater than shock thicknesses). Precursor damping is not related to shock normal angle or Mach number, but is correlated with Te/Ti. The source of the dissipation in the shocks does not appear to be wave‐wave decay of the whistlers, for which no evidence is found. We cannot rule out the possibility of contributions to the dissipation from ion acoustic and/or lower‐hybrid mode turbulence, but interaction of the whistler itself with upstream electrons offers a simpler and more self‐consistent explanation for the observed wave train damping.

Computer simulations of collisionless shock waves

A review of the contributions of particle computer simulations to the understanding of the physics of magnetic shock waves in collisionless plasmas is presented. The emphasis is on the relation between the computer simulation results, spacecraft observations of shocks in space, and related theories, rather than on technical aspects of the numerics. It is shown that much has been learned from the comparison of ISEE spacecraft observations of the terrestrial bow shock and particle computer simulations concerning the quasi-perpendicular, supercritical shock (ion scale structure, ion reflection mechanism and ultimate dissipation processes). Particle computer simulations have also had an appreciable prospective role in the investigation of the physics of quasi-parallel shocks, about which still little is known observationally. Moreover, these numerical techniques have helped to clarify the process of suprathermal ion rejection by the shock into the foreshock, and the subsequent evolution of the ions in the foreshock.

Plasma astrophysics at Santa Barbara

Plasma astrophysics at Santa Barbara

Interaction of small-amplitude fluctuations with a strong magnetohydrodynamic shock

The interaction of small fluctuations with a strong magnetohydrodynamic shock is considered theoretically in the most general situation using an ideal model. An analytical treatment of the cutoff conditions for penetration of the upstream fluctuation through the bow shock is presented. The situation in which there exist unique solutions of the interaction is investigated quantitatively. Numerical examples of the interaction of waves in the solar wind with the terrestrial bow shock are given to illustrate the refracted waves to be found in the earth’s magnetosheath.

Solar wind flow about the terrestrial planets 1. Modeling bow shock position and shape

General technique for modeling the position and shape of planetary bow waves are reviewed. A three‐parameter method was selected to model the near portion (i.e.,x′ > −1 Rob) of the Venus, earth, and Mars bow shocks and the results compared with existing models using 1 to 6 free variables. By limiting consideration to the forward part of the bow wave, only the region of the shock surface that is most sensitive to obstacle shape and size was examined. In contrast, most other studies include portions of the more distant downstream shock, thus tending to reduce the planetary magnetosphere in question to a point source and constrain the resultant model surfaces to be paraboloid or hyperboloid in shape to avoid downstream closure. It was found by this investigation that the relative effective shapes of the near Martian, Cytherean, and terrestrial bow shocks are ellipsoidal, paraboloidal, and hyperboloidal, respectively, in response to the increasing bluntness of the obstacles that Mars, Venus, and earth present to the solar wind. The position of the terrestrial shock over the years 1965 to 1972 showed only a weak dependence on the phase of the solar cycle after the effects of solar wind dynamic pressure on magnetopause location were taken into account. However, the bow wave of Venus was considerably more distant around solar maximum in 1979 than at minimum in 1975–6 suggesting a solar cycle variation in its interaction with the solar wind. Finally, no significant deviations from axial symmetry were found when the near bow waves of the earth and Venus were mapped into the aberrated terminator plane. This finding is in agreement with the predictions of gas dynamic theory which neglects the effects of the IMF on the grounds of their smallness. Farther downstream where the bow wave position is being limited by the MHD fast mode Mach cone, an elliptical cross section is expected and noted in the results of other investigations.

Energy spectrum of ions accelerated through Fermi process at the terrestrial bow shock

The observed energy spectra of the upstream energetic ions (up to ∼ 150 keV per charge) are compared with the expectations from a first‐order Fermi acceleration process, i.e., a multiple reflection process between the bow shock and the upstream wave field. The escape of particles into the far upstream region (≳ several tens to 100 RE) is found important for the formation of the energy spectrum. The predicted energy spectrum has exponential dependence on energy like N(E)dE ∼ exp (− E/Ec)dE, which is consistent with the observation. One of the remarkable features of the observation, the invariance of the abundance ratios among various ion species when evaluated at the same energy per charge, can also be explained by the Fermi acceleration process: At the same energy per charge, the elementary acceleration process at the shock front is more efficient for particles of higher mass to charge ratio (M/Q), while the scattering process in the upstream waves is less efficient for these particles. It is shown that the above two effects compensate each other and make the energy spectra of accelerated particles independent of particle species when evaluated by energy per charge unit.

Three‐dimensional interaction of interplanetary shock waves with the bow shock and magnetopause: A comparison of theory with ISEE observations

The propagation of shock waves in the solar wind and their three‐dimensional interaction with the terrestrial bow shock, magnetosheath, and magnetopause is examined theoretically and compared with observations made by the ISEE spacecraft. First the formulae underlying the new position and orientation of the bow shock front after the interaction are given. Then magnetic field and plasma data from the ISEE 1, 2, and 3 spacecraft are compared with the theoretical estimates of the propagation time of the shock waves between ISEE 1 and 3. Examination of data obtained on August 18, 1978, when both ISEE 1 and 3 were in the solar wind, show good agreement with theory. Using a simple model of the magnetosheath, we can extend our predictions to include the propagation time through the magnetosheath. Two examples of the interplanetary shock interaction with the magnetosphere while ISEE 1 and 2 were in the outer magnetosphere on August 27 and October 4, 1978, show quite satisfactory agreement with the predictions of this simple model. On August 27, 1978, the magnetopause is blown well past ISEE 1 and 2, and the two spacecraft pass completely through the magnetosheath in 2.5 min. Rapid as this may appear, we show that this behavior is as predicted by the theoretical treatment.

Pioneer magnetometer observations of the Venus bow shock

Venus has a bow shock in many respects similar to that of the Earth. The Venus bow shock was probed twice by Mariner 5, once by Mariner 10, Venera 4, and Venera 6 (refs 1–4 respectively) and repeatedly by Venera 9 and 10 (ref. 5). The Pioneer Venus orbiter is now circling Venus in a 24-h elliptical orbit which crosses the bow shock twice a day6. Here we report the somewhat surprising result that the Venus bow shock is not as strong as the terrestrial bow shock.

Initial ISEE observations of the bow shock

ISEE 1 and 2 magnetic-field profiles across three terrestrial bow shock crossings are shown to illustrate the control of the bow shock structure and upstream waves by solar-wind conditions, especially by the direction of the interplanetary field. The quasi-perpendicular shocks examined have thicknesses of the order of a ion inertial length. Upstream waves observed for field directions of about 45° to the shock normal are observed to be carried back towards the bow shock by the solar wind, while propagating upstream at what appears to be the magnetosonic velocity. These studies are continuing.