Downstream Distributions Research Articles

Electron heating in quasiperpendicular shocks

Electrons move in the shock ramp fields prescribed by ions. Observed ramp thicknesses and cross-shock potentials imply that in many cases adiabaticity in the lectron motion in the ramp is broken. A substantial fraction of the cross-shock potential is transferred into the electron gyration energy. As a result, electrons experience direct overadiabatic perpendicular heating. The heating magnitude is in agreement with observed values. Numerically obtained downstream distributions demonstrate a clear tendency to be flattopped both in parallel and perpendicular directions.

Ion and electron heating at the low‐Mach‐number, quasi‐parallel bow shock

The magnetic structure and energy dissipation at low‐Mach‐number, quasi‐parallel collisionless shocks are examined through observations obtained by the ISEE 1 and 2 spacecraft at seven crossings of the Earth's dayside bow shock. The Alfvén Mach number of the shocks in this set ranges from 2.0 to 3.7, and the angle θBn between the shock normal and the average upstream magnetic field direction ranges from 2° to 39°. The shocks all exhibit a fairly short‐scale‐length ramp where the principal jumps in the electron temperature, ion temperature, and magnetic field strength take place. Large‐amplitude, low‐frequency, transverse waves in the magnetic field are present in and downstream from the ramp, with more modest waves upstream. The amplitude of the downstream waves is typically larger than can be accounted for by shock compression of the upstream waves. The electron heating represents about 6% of the dissipated bulk flow energy, consistent with observations in other parameter regimes, and suggesting that the dominant electron heating process is the same. The electron share of the dissipated energy appears to increase somewhat with increasing θBn, and the ion share appears to decrease. Coherent reflection of incident ions does not appear to be very important for ion heating at these low Mach numbers, although a low level of reflection may contribute significantly to the generation of the large‐amplitude waves. Finally, the downstream ion distributions do not show the strong variability previously interpreted as evidence for a cyclic re‐formation process at higher‐Mach‐number, quasi‐parallel shocks. It is possible that the low‐Mach‐number shocks are re‐forming but do not exhibit the downstream variability because of the relatively low levels of reflected ions.

Plasma parameters near the comet Halley bow shock

We present the plasma data from the Johnstone Plasma Analyser (JPA) instrument on Giotto for the inbound and outbound crossings of the structures which up to now were assumed to be bow shocks at comet Halley. Proton bulk parameters from the Fast Ion Sensor (FIS) inbound have been analyzed taking into account the wider downstream distributions which require a different analysis method from the upstream solar wind. The water group densities from the Implanted Ion Sensor (IIS) are obtained using updated processing procedures. These densities are consistent with the density inferred from the slowdown of the solar wind. The cometary ion pressure dominates in the shock region. The outbound parameters are presented from IIS for the first time. The inbound and outbound data are used to infer the shock normal directions from Rankine‐Hugoniot analyses. We calculate the fast mode Mach numbers of the shock structures moving into the upstream solar wind following the method of Smith et al. (1986), giving values of 1.1–1.8 (inbound) and 1.6–1.7 (outbound). The positions of the shock features are consistent with the inferred critical point in the solar wind flow. In addition, both the solar wind protons and the water group ion populations are observed to thermalize across the shock region, and we therefore conclude that the comet Halley bow shock features were indeed shocks.

Electron Fermi acceleration in collapsing magnetic traps: Computational and analytical models

We consider the heating and acceleration of electrons trapped on magnetic field lines between approaching magnetic mirrors. Such a collapsing magnetic trap and consequent electron energization can occur whenever a curved (or straight) flux tube drifts into a relatively straight (or curved) perpendicular shock. Our relativistic, three‐dimensional, collisionless test particle simulations show that an initial thermal electron distribution is bulk heated while a few individual electrons are accelerated to many times their original energy before they escape the trap. Upstream field‐aligned beams and downstream pancake distributions perpendicular to the field are predicted. In the appropriate limit the simulation results agree well with a nonrelativistic analytic model of the distribution of escaping electrons which is based on the first adiabatic invariant and energy conservation between collisions with the mirrors. Space science and astrophysical applications are discussed.

Two‐state ion heating at quasi‐parallel shocks

In a previous study of ion heating at quasi‐parallel shocks, we showed a case in which the ion distributions downstream from the shock alternated between a cooler, denser, core/shoulder type and a hotter, less dense, more Maxwellian type. In this paper we further document the alternating occurrence of two different ion states downstream from several quasi‐parallel shocks. Three separate lines of evidence are presented to show that the two states are not related in an evolutionary sense (i.e., the hotter distributions do not evolve from the cooler ones), but rather both are produced alternately at the shock: (1) The asymptotic downstream plasma parameters (density, ion temperature, and flow speed) are intermediate between those characterizing the two different states closer to the shock, suggesting that the asymptotic state is produced by a mixing of the two initial states; (2) examples of apparently interpenetrating (i.e., mixing) distributions can be found during transitions from one state to the other; and (3) examples of both types of distributions can be found at actual crossings of the shock ramp. The alternation between the two different types of ion distribution provides direct observational support for the idea that the dissipative dynamics of at least some quasi‐parallel shocks is non‐stationary and cyclic in nature, as demonstrated by recent numerical simulations. Typical cycle times between intervals of similar ion heating states are ∼2 upstream ion gyroperiods. Both the simulations and the in situ observations indicate that a process of coherent ion reflection is commonly an important part of the dissipation at quasi‐parallel shocks; we suggest that cyclic variations in the fraction of reflected ions could account for the alternating regions of cooler and hotter downstream ion distributions documented in this paper.

Spanwise Mixing in Multistage Axial Flow Compressors: Part II—Throughflow Calculations Including Mixing

The important influence of spanwise mixing on the flow through multistage axial compressors has been investigated by incorporating the effect into an axisymmetric streamline curvature throughflow program. The mixing was modeled as a turbulent diffusion process based on the experimental observations reported in Part I of this paper, which showed that this was the dominant physical mechanism. The inclusion of the mixing was found to be crucial in accurately predicting spanwise variations of exit total temperature in multistage machines. The effect of mixing on loss distributions inferred from measurements was found to be significant so that upstream loss sources could only be determined from downstream distributions when the effect of mixing was included.

Electron velocity distributions near interplantary shocks

Solar wind electron velocity distributions measured across interplanetary shocks using the Los Alamos plasma analyzer on ISEE 3 have been studied to understand electron heating mechanisms for weak and intermediate strength collisionless shocks. This study thus complements earlier studies of electron heating at the earth's bow shock, an example of a highly supercritical collisionless shock. At the weakest interplanetary shocks (downstream to upstream density ratio N(d/u) ≲ 2 and velocity difference V(d‐u) ≲ 70 km/s), heating perpendicular to the magnetic field B predominates over parallel heating. Such heating may be a consequence of conservation of magnetic moment across the shock. At the stronger interplanetary shocks (N(d/u) ≳ 2 and V(d‐u) ≳ 70 km/s), heating parallel to B is dominant and the downstream velocity distributions are flat‐topped, similar to what is observed downstream of the earth's bow shock. This similarity suggests that electron heating in all collisionless shocks with N(d/u) ≳ 2 and V(d‐u) ≳ 70 km/s results in part from an acceleration parallel to B produced by the macroscopic shock electric field, followed by beam driven plasma instabilities.

Electron velocity distributions near the Earth's bow shock

A survey of two‐dimensional electron velocity distributions, ƒ(V), measured near the earth's bow shock using Los Alamos/Garching plasma instrumentation aboard ISEE 2 is presented. This survey provides clues to the mechanisms of electron thermalization within the shock and the relaxation of both the upstream and downstream velocity distributions. First, near the foreshock boundary, fluxes of electrons having a power law shape at high energies backstream from the shock. Although most often they appear as a monotonically decreasing extension of solar wind distributions in the backward hemisphere along the magnetic field direction, , they occasionally appear as a resolved peak in energy. Within the interior of the foreshock, in addition to the hot, isotropic electrons at higher energies, field‐aligned depressions in ƒ(V) are observed at the lowest energies (E ≲ 15 eV) and twin angular peaks centered on are observed at intermediate energies (15 eV ≲ E ≲ 45 eV). Such distributions are associated closely with 1‐Hz whistler waves. Second, within the shock, cuts through ƒ(V) along ƒ(V∥), often show single maxima offset toward the magnetosheath by speeds comparable to, but larger than, the upstream thermal speed. When sequences of such distributions are observed in a single shock transition, offset speeds increase and peak heights of ƒ(V∥) decrease with increasing penetration toward the downstream (magnetosheath) side. Third, magnetosheath distributions generally have flat tops out to an energy, E0, with maxima substantially lower than that in the solar wind. Occasionally, cuts through ƒ(V) along show one and sometimes two small peaks at the edge of the flat tops making them appear concave upward. The magnetosheath distributions often have strong angular anisotropies which depend on energy. For energies less than E0, ƒ(V∥) > ƒ(V⊥) at constant E, whereas for E > E0, ƒ(V∥) < ƒ(V⊥). The electron distributions characteristic of these three regions are interpreted as arising from the effects of macroscopic (scale size comparable to or larger than the shock width) electric and magnetic fields and the subsequent effects of microscopic (scale size small in comparison with the shock width) fields. In particular, our results suggest that field‐aligned instabilities are likely to be present in the earth's bow shock.

Mass transfer for turbulent flow in an annulus with non-axisymmetric boundary conditions

The principal objective of this investigation was to determine the magnitude of circumferential diffusion arising from non-axisymmetric boundary conditions in symmetrical passages free from secondary flows. A concentric annulus was chosen because, with its relatively long circumferential diffusion path, it provides a more sensitive test of diffusion models than does a circular tube; a mass-transfer method was preferred because it avoids problems of heat loss and heat conduction in the tube walls. Nitrous oxide was introduced into the air stream through porous regions in the outer wall and the measured downstream concentration distributions were compared with theoretical solutions. Preliminary measurements were made to verify the representation of the velocity profile and, using an axisymmetric nitrous oxide source, the formulation for the radial eddy diffusivity of mass. Finally, measured concentration distributions arising from non-axisymmetric injection were compared with predictions based upon several alternative formulations for the diffusivity ratio, ε M,φ ε M,r . The isotropic assumption underestimates the magnitude of circumferential diffusion. An excellent fit to all the experimental data was obtained with a model due to Ramm and Johannsen in which the ratio ε M,φ ε M,r varies with radial position and increases markedly as the walls are approached.

周囲気体と密度の異なる乱流噴流

Predicting the flow field where gases of different kinds are mixing is important in providing design guidance in a number of engineering systems, e.g. diffusion type chemical lasers, rocket injectors and scramjets.By using mixtures of air and helium, density and velocity distributions in axially symmetric jet exhausting into the free atmosphere are measured with a high accuracy. It is shown that the far downstream radial distributions of velocity and density are similar and they may all be approximated by the Gaussian distribution. The velocity and density at the centerline are inversely proportional to the streamwise coordinate. The linear increase of the half radius with the axial coordinate is observed, however, the rate of linear spread is found to be strongly dependent upon the difference in density between the jet and the receiving medium. On the basis of the measurements the eddy viscosity and the turbulent Schmit number in fully developed region are calculated by numerical analysis.

Fluid flow around and through a screen

A mathematical model is proposed for steady two-dimensional flow around a submerged screen. The general problem analysed is the flow in a parallel-sided channel partially spanned by a screen, and the fluid is considered to be inviscid except at the screen, where the flow has the required pressure drop. The model is constructed by first replacing the screen with a distribution of sources and then manipulating the stream function for this flow so that the mass and momentum balances across the screen are satisfied. Consequently the model predicts a flow field which is realistic except for the expected discontinuity in velocity between the wake and external flow. In general, the governing equations must be solved numerically, but for the important case of a plane screen oriented normal or roughly normal to the approaching flow, an approximate analytical solution is possible. The accuracy of the model was ascertained by conducting wind-tunnel tests on screens of various solidities and orientations, and comparing the measured downstream velocity distributions with those predicted by the numerical and analytical solutions of the model. Overall, the theoretical results agree well with the experimental data, showing that the model is valid for screens of low and high solidity, in fact, for pressure drop coefficients up to 10. Comparisons with the work of others show that the proposed model is also accurate for the special cases of a screen submerged in an infinite flow field and of a screen spanning the full width of the channel.

Downstream pressure distributions for two- dimensional jet interactions

Downstream pressure distributions for two- dimensional jet interactions