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NASA NTRS1993

Motion of the heliospheric termination shock - A gas dynamic model

A simple quantitative model is presented for the heliospheric termination shock's anticipated movement in response to upstream solar wind condition variations, under the assumption that the termination shock is initially a strong gasdynamic shock that is at rest relative to the sun, and that there is a discontinuous increase or decrease in the dynamical pressure upstream of the shock. The model suggests that the termination shock is constantly in motion, and that the mean position of the shock lies near the mean equilibrium position which corresponds to the balance between the mean solar wind dynamical pressure and the mean interstellar pressure.

Barnes, Aaron↗
NASA NTRS1993

Flow downstream of the heliospheric terminal shock - The magnetic field on the heliopause

Modeling the kinematic magnetic field in the solar wind beyond the terminal shock shows that a ridge of magnetic pressure is produced just inside the heliopause. This ridge is sufficiently large that it will cause the layer immediately inside the heliopause to thicken, pushing the heliopause outward and slightly affecting its position relative to the terminal shock. However, the ridge is far too thin to cause an important change in the distance of the terminal shock from the sun. We show that these conclusions are a simple consequence of geometrical arguments for incompressible, steady, laminar flows. Moreover, the heliopause magnetic field originates on the terminal shock near the substagnation point. Consequently, the heliospheric current sheet field reversals are painted onto the inside surface of the heliopause. Alternate magnetic polarity strips will be oppositely directed relative to the interstellar magnetic field, implying that reconnection inevitably occurs on a fine some near the nose of the heliosphere. This suggests that the heliopause is a leaky, diffuse surface.

Nerney, Steven↗
NASA NTRS1994

Motion of the heliospheric termination shock. 2: Energy loss due to energetic particle acceleration

We present a generalization of earlier analysis of the motion of the heliospheric termination shock in response to heliospheric disturbances (Barnes, 1993) (paper 1), to allow jump conditions that include an energy sink at the shock front. The motivation for this study is that acceleration of the anomalous cosmic ray component may in fact represent such a sink. We have idealized the situation by assuming an infinitely thin shock parameterized by a quantity lambda(0 less than or equals lambda less than or equals 1), defined as the fraction of solar wind energy that is lost due to acceleration of the energetic particle component. If the sink is strong (consuming, say, 50% or more of the incident solar wind energy), the model leads to the following principal conclusions: (1) the shocked plasma would be much denser and cooler than in the standard gasdynamic case, thereby leading to more favorable conditions for direct observation of the shocked plasma; (2) the equilibrium shock position would be slightly farther (less than 10%) from the Sun than in the standard model; (3) as in the gasdynamic case, the shock would normally be in motion, so that the instantaneous position of the termination shock is not determined by interstellar conditions but by the recent history of the wind that has passed through the termination shock; and (4) the response of the shock to upstream disturbances would be similar to the response in the gasdynamic case, but the speed of the new termination shock would be somewhat smaller (probably by a f actor of 4 or less). We estimate that this speed is typically, approximately a few tens of kilometers per second corresponding to an inward or outward excursion of order of less than 1 to several AU, rather less than conventional estimates of several tens of AU.

Barnes, Aaron↗
NASA NTRS2019

Measurement and Analysis of Terminal Shock Oscillation and Buffet Forcing Functions on a Launch Vehicle Payload Fairing

The buffet loads on a launch vehicle payload shroud can be impacted by the unsteadiness associated with a terminal shock at high subsonic speeds. At these conditions, flow accelerates to supersonic speeds on the nose of the payload fairing and is terminated by a normal shock on the cylindrical section downstream of the nose cone/cylinder shoulder. The location of the terminal shock and associated separated boundary layer is affected by the freestream Mach number, Reynolds number, and the pitch/yaw of the launch vehicle. Furthermore, even when the freestream conditions and vehicle attitude are constant, this terminal shock oscillates on the surface of the vehicle. The time-varying surface pressure associated with the terminal shock results in unsteady aerodynamic loads that may interact with vehicle structural dynamic modes and the guidance and control of the vehicle. Buffet testing of a 3-percent scale rigid buffet model of a launch vehicle cargo configuration with a tangent-ogive payload shroud was conducted in 2012 and in 2016. Initial buffet forcing functions (BFFs) utilized a coarse pressure sensor distribution on the vehicle surface in which a single longitudinal station with eight sensors observed the terminal shock environment at Mach 0.90. An examination of these circumferential pressures reveal large impulse-like pressure fluctuations and an asymmetry in pressure when the vehicle is at a nonzeroangle of attack that result in high BFFs. Revisions to the shock integration region were made based on computational fluid dynamics and shadowgraph video of shock motion to better represent the BFFs and reduce the high loads resulting from this environment. To more clearly understand this terminal shock environment, a second wind tunnel test was conducted with a dense distribution of 256 sensors at the terminal shock location. These sensor arrays presents a unique opportunity to observe the unsteady terminal shock environment and to characterize the impact of various integration schemes on the BFFs. This paper presents a summary of the development of BFFs for this terminal shock and a detailed analyses of shock region pressure coefficients, coherence, BFFs, shock location time histories, and power spectral density to help guide development of BFFs for other launch vehicle test and analysis programs.

Piatak, David J.↗
NASA NTRS1998

Direct Acceleration of Pickup Ions at The Solar Wind Termination Shock: The Production of Anomalous Cosmic Rays

We have modeled the injection and acceleration of pickup ions at the solar wind termination shock and investigated the parameters needed to produce the observed Anomalous Cosmic Ray (ACR) fluxes. A non-linear Monte Carlo technique was employed, which in effect solves the Boltzmann equation and is not restricted to near-isotropic particle distribution functions. This technique models the injection of thermal and pickup ions, the acceleration of these ions, and the determination of the shock structure under the influence of the accelerated ions. The essential effects of injection are treated in a mostly self-consistent manner, including effects from shock obliquity, cross- field diffusion, and pitch-angle scattering. Using recent determinations of pickup ion densities, we are able to match the absolute flux of hydrogen in the ACRs by assuming that pickup ion scattering mean free paths, at the termination shock, are much less than an AU and that modestly strong cross-field diffusion occurs. Simultaneously, we match the flux ratios He(+)/H(+) or O(+)/H(+) to within a factor approx. 5. If the conditions of strong scattering apply, no pre-termination-shock injection phase is required and the injection and acceleration of pickup ions at the termination shock is totally analogous to the injection and acceleration of ions at highly oblique interplanetary shocks recently observed by the Ulysses spacecraft. The fact that ACR fluxes can be modeled with standard shock assumptions suggests that the much-discussed "injection problem" for highly oblique shocks stems from incomplete (either mathematical or computer) modeling of these shocks rather than from any actual difficulty shocks may have in injecting and accelerating thermal or quasi-thermal particles.

Ellison, Donald C.↗
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 NTRS1992

Sensing the solar-wind termination shock from Earth's orbit

The solar-wind termination shock is inaccessible for repeated in situ investigation. We examine, therefore, the possibility of remote sensing the entire heliopause from Earth's orbit using the energetic neutral atoms (ENA) produced by charge exchange between energetic ions and the neutral atoms of the interstellar medium at and beyond the termination shock. We estimate the ENA fluxes at Earth's orbit coming from the thermalized solar-wind ions and the shock-accelerated anomalous cosmic rays (ACR) at the heliospheric boundary.

Hsieh, K. C.↗
NASA NTRS1973

Terminal shock position and restart control of a Mach 2.7, two-dimensional, twin duct mixed compression inlet

Experimental results of terminal shock and restart control system tests of a two-dimensional, twin-duct mixed compression inlet are presented. High-response (110-Hz bandwidth) overboard bypass doors were used, both as the variable to control shock position and as the means of disturbing the inlet airflow. An inherent instability in inlet shock position resulted in noisy feedback signals and thus restricted the terminal shock position control performance that was achieved. Proportional-plus-integral type controllers using either throat exit static pressure or shock position sensor feedback gave adequate low-frequency control. The inlet restart control system kept the terminal shock control loop closed throughout the unstart-restart transient. The capability to restart the inlet was non limited by the inlet instability.

Cole, G. L.↗
NASA NTRS1983

Numerical solutions of Navier-Stokes equations for compressible turbulent two/three dimensional flows in terminal shock region of an inlet/diffuser

The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.

Liu, N. S.↗
NASA NTRS1983

Numerical solution of the Navier-Stokes equations for compressible turbulent two/three dimensional flows in the terminal shock region of an inlet/diffuser

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations in conjunction with mixing length turbulence model and shock capturing technique have been used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations have been carried out: (1) 2-D, steady, subsonic; (2) 2-D, steady, transonic with normal shock, (3) 2-D, steady, supersonic with terminal shock, (4) 2-D, transient process of shock development and (5) 3-D, steady, transonic with normal shock. The numerical results obtained for the 2-D and 3-D transonic shocked flows have been compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data. The predicted transient responses of the flow to externally applied impulsive disturbance are consistent with results obtained via asymptotic analysis.

Liu, N.-S.↗
NASA NTRS1991

Flow downstream of the heliospheric terminal shock - Magnetic field kinematics

A kinematic model of the interplanetary magnetic field in the heliosheath beyond the solar wind terminal shock is presented in order to evaluate the possible importance of MHD effects in that region of space. The need for this evaluation arises because the interplanetary magnetic field is compressed across the terminal shock and further amplified by the decreasing flow speed beyond the shock. Streamlines which approach the stagnation point before turning in the downstream direction lead to the strongest effects due to the extreme slowing of the solar wind and consequent compression of the embedded magnetic field. The magnetic volume force therefore cannot be neglected on streamlines that approach the heliopause in the upstream direction, where the volume containing them is a large fraction of the overall of the heliosheath in the upstream direction. The increase in the magnetic pressure may act to bring the upstream terminal shock significantly closer to the sun, potentially reconciling a conflict between models and observations.

Nerney, S.↗
DOE OSTI2021

Fermi-type particle acceleration from magnetic reconnection at the termination shock of a relativistic striped wind

An oblique-rotating pulsar generates a relativistic striped wind in a pulsar wind nebula (PWN). The termination shock of the PWN compresses the Poynting-flux-dominated flow and drives magnetic reconnection. By carrying out particle-in-cell simulations of the termination shock of the PWN, we study the shock structure as well as the energy conversion processes and particle acceleration mechanisms. With the recent advances in the numerical methods, we extend the simulations to the ultrarelativistic regime with a bulk Lorentz factor of up to γ 0 = 10 6 . Magnetic reconnection at the termination shock is highly efficient at converting magnetic energy to particle kinetic energy and accelerating particles to high energies. Similar to earlier studies, we find that the resulting energy spectra crucially depend on λ/d e (λ is the wavelength of the striped wind and de is the relativistic plasma skin depth). When λ/d e is large (λ ≳ 40d e ), the downstream particle spectra form a power-law distribution in the magnetically dominated relativistic wind regime. By analyzing particle trajectories and statistical quantities relevant to particle energization, we find that Fermi-type mechanism dominates the particle acceleration and power-law formation. We find that the results for particle acceleration are scalable as γ 0 and σ 0 increase to large values. The maximum energy for electrons and positrons can reach hundreds of TeV if the wind has a bulk Lorentz factor of γ0 ≈ 106 and a magnetization parameter of σ 0 = 10, which can explain the recent observations of high-energy gamma rays from PWNe

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1993

How to bet on the location of the termination shock - A summary overview of the Symposium

This paper loosely summarizes the Symposium in the context of estimating the distance to the solar wind termination shock. Thus the major constituents of the heliosphere are first reviewed including the solar wind and its shocks, magnetic structure and stream structure, the interstellar neutral gas and its daughters, the interstellar pickup ions and the cosmic ray anomalous component, and the galactic cosmic rays. Then a direct calculation of the distance to the termination shock is presented, which yields 80 AU but with large error bars. Finally information carried by messengers from the termination shock and heliosheath (the kHz radio bursts observed by Voyager, galactic cosmic rays, the cosmic ray anomalous component, and the interstellar neutral gas and backscattered photons) is assessed and interpreted. The paper concludes that 80 AU is the best bet.

Lee, Martin A.↗
NASA NTRS1995

Heliospheric Termination Shock Motion Due to Fluctuations in the Solar Wind Upstream Conditions: Spherically Symmetric Model

Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.

Ratkiewicz, R.↗
NASA NTRS1995

Motion of the termination shock in response to an 11 year variation in the solar wind

A two-dimensional hydrodynamic numerical model was used to study the motion of the termination shock in response to an 11 year variation in the solar wind ram pression. For a total variation in the ram pressue by a factor of 2, a termination shock at 89 AU was found to move inward and outward about +/- 8% of its distance with a typical velocity of 12 km/sec. This movement may be understood in terms of the various time scales associated with the response of the termination shock and heliopause to variations in the solar wind ram pressure.

Karmesin, S. Roy↗
NASA NTRS1994

Structure, Shape and Movement of the Termination Shock

In this paper we review current ideas concerning the morphology and dynamics of the heliospheric termination shock. The mean distance of the shock is expected to lie somewhere in the range 50-200 AU, and should vary with latitude, depending on mean latitude variation of the dynamical pressure of the solar wind. The 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. The simplest model of the shock is that of an infinitely thin gasdynamic or magnetohydrodynamic shock wave, which moves inward or outward at speeds of approximately 100 kilometers per second. The structure and motion of the shock will be strongly modified if an appreciable fraction of the incident solar wind energy goes into acceleration of energetic particles, specifically the anomalous cosmic rays.

Barnes, Aaron↗
NASA NTRS1995

Distances to the termination shock and heliopause from a simulation analysis of the 1992-93 heliospheric radio emission event

A new heliospheric radio emission event observed by Voyagers 1 and 2 in mid-1992 is believed to have been produced by the interaction of an interplanetary shock with the heliopause. The shock is thought to have oriented near the Sun during a period of intense solar activity in late-May and early-June, 1991. The observed travel time of the shock to the heliopause is 408 days; the initial speed is estimated to be between 600 and 800 km/s. We use a numerical gasdynamic simulation of an interplanetary shock, propagating through an equilibrium solution of the solar wind/interstellar medium interaction, to compute the distances to the termination shock and the heliopause that are consistent with these observations. For a shock speed of 600 km/s, the termination shock is located at 92 AU, and the heliopause is located at 128 AU. These distances increase to 112 AU and 156 AU when the shock speed is increased to 800 km/s.

Steinolfson, R. S.↗
NASA NTRS1994

Termination shock response to large-scale solar wind fluctuations

The analysis of data recorded by the Voyager 2 spacecraft indicates the presence of large-scale fluctuations in the solar wind ram pressure on the time scale of tens of days. The amplitude of the fluctuations is highly variable but often lies within a factor of 5 to 10 change from an average or mean value of the ram pressure. Since the spacecraft has presumably not encountered the termination shock yet, these fluctuations should eventually interact with the shock and thereby play a role in determining the shock location. Numerical solutions of the time-dependent gasdynamic equations are used to simulate the response of the termination shock to fluctuations in the solar wind ram pressure comparable to those observed. The primary result of this study is that the maximum shock excursion due to the fluctuations is of the order of 1 AU, which is much smaller than that predicted by other studies. Additional simulations show that the limited movement is due to the fact that the time scale for the termination shock response is substantially larger than the time scale of the fluctuations. It is also shown that the heliopause acts as a barrier for the fluctuations and confines them to the heliosphere.

Steinolfson, R. S.↗