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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Electron injection and acceleration at nonlinear shocks: Results of numerical simulations

We present results of numerical simulations of electron injection and acceleration at nonlinear high Mach number shocks. The electrons are assumed to be heated at the thermal subshock to an energy E(sub inj), which is treated as a free parameter, above which they are injected by self-generated whistlers to momentum m(sub p) x V(sub A). This injection mechanism requires Mach numbers greater than (43/(beta(sub -)))(((k T(sub e))/(E(sub inj)))(exp 1/2)), where T(sub e) and beta (sub -) are the upstream electron temperature and plasma beta parameter. Above m(sub p) x V(sub A) electrons are trapped in the shock by Alfven waves. In the proton precursor region the Alfven waves are assumed to be generated by protons accelerated at the shock, and have nonlinear intensities. Below GeV, however, electrons of a given rigidity propagate faster than protons with a similar rigidity and therefore diffuse to regions ahead of the proton precursor. In those regions the Alfven waves are generated by the electrons themselves. The diffusion coefficient appears to increase with decreasing acceleration efficiency. As a result, the number of electrons accelerated to energies GeV and above and, hence, the electron to proton ratio, depend only weakly on the extent of electron heating at the subshock. The negative feedback also renders the electron spectra insensitive to shock compression ratio and smoothing length scale. The estimated e/p ratio at GeV is between approximately 1%-10%.

Levinson, Amir↗
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 NTRS1987

Energetic particle acceleration in spherically symmetric accretion flows and shocks

Steady state, spherically symmetric solutions of the cosmic-ray transport equation describing the acceleration of energetic particles in galactic accretion flows onto neutron stars, black holes, white dwarfs, and protostars are studied. The results indicate that astrophysical accretion flows can be partitioned into distinct classes depending upon whether the accretion rate lies above or below a critical value of a few times 10 to the -7th stellar masses/yr. When the particle transport is convection-dominated, both classes of accretion flows exhibit a spectral index appropriate for first-order Fermi acceleration at a plane shock in the absence of losses. As the particle transport becomes diffusion-dominated, both classes show a break and precipitous falloff in the particle spectrum due to the escape of these particles from the accretion flow. The precise nature of the spectrum depends on the relationship between the particle momentum and the spatial diffusion coefficient.

Webb, G. M.↗
NASA NTRS1994

Enhanced cosmic-ray acceleration rates in highly inclined astrophysical shocks

The theory of cosmic-ray acceleration by subluminal magnetohydrodynamics (MHD) astrophysical shocks according to the test particle approximation is extended to highly oblique shocks where flow speeds which appear nonrelativistic in the shock rest frame appear on transformation to the de Hoffmann-Teller or E identically equal to 0 frame to have upstream flow speeds approaching c. Monte Carlo simulation shows that relative to the predictions of diffusion theory, as the upstream E identically equal to 0 frame velocity approaches c, flatter spectra and faster acceleration rates occur. These spectral and acceleration time changes are similar to those found for relativistic, parallel MHD shocks and may affect all nonthermal active galactic nuclei emission from relativistic electrons. Also there is an additional means of increasing the upper limit of the cosmic-ray spectrum expected from active galactic nuclei, although the approximation used may not accurately reproduce the spectral shape.

Lieu, R.↗
DOE OSTI2021

Aero-Thermal Characterization of Accelerating and Diffusing Passages Downstream of Rotating Detonation Combustors

Cycle benefits of rotating detonation engines show up to five percentage points of efficiency gain for low-pressure ratio engines. An optimal integration between the combustor and the turbine needs to be guaranteed to realize this potential gain. The rotating detonation combustor (RDC) exhausts transonic flow with shocks rotating at frequencies ranging from a few to tens of kilohertz depending on the number of present waves. Hence, the turbine design requires precise knowledge of the fluctuations and losses downstream of the combustor. This paper focuses on the quantification of fluctuations and losses for accelerating and diffusing passages. The analysis of the combustor is performed via reactive unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. The unsteady RANS equations are solved via CFD++ from Metacomp with a one-step reaction mechanism for an H2-air mixture. The resolving of the boundary layer is achieved with a structured mesh of around 36 million cells. Inlet pressure of 10 bar and two different back pressures are applied to the combustor to model the interconnection with downstream turbines. Finally, we present and assess a methodology to reduce the computational time to model these passages ten times.

Braun, James↗
NASA NTRS1994

Model images of radio halos around supernova remnants

I present model calculations of profiles and two-dimensional images of the radio synchrotron emission of young supernova remnants, concentrating on observable effects of relativistic eletrons diffusing upstream of the shock wave. If the preshock electron scattering mean free path is sufficiently long, observable synchrotron halos outside the bulk of the radio emission can potentially result; their absence can constrain the mean free path from above. If scattering is primarily due, as expected, to Alfven waves with amplitude detla(B), the halo is expected to extend a distance of order r(sub g)c(delta(B)/B)(exp 2)/v(sub s) beyond the shock, where r(sub g) is the gyroradius of the electrons emitting at the observed frequency, B is the upstream magnetic field strength, v(sub s) is the shock velocity, and the amplitude delta(B) refers to wave with wavelength comparable to r(sub g), of order 10(exp 13) cm for typical supernova-remnant parameters. However, the detailed geometry of the halo varies with the assumptions about particle acceleration in the shock wave. I present an atlas of model profiles and images as a function of preshock diffusion length, of aspect angle between the magnetic field and the line of sight, and of other relevant parameters.

Reynolds, Stephen P.↗
NASA NTRS1981

Energetic particle spectra in finite shocks - The earth's bow shock

Particle acceleration and escape at the earth's bow shock wave are discussed in order to account for reported exponential fast particle spectra. A model is presented of particle acceleration in a finite two-dimensional shock perpendicular to the magnetic field, with particle parallel and perpendicular diffusion coefficients inversely proportional to each other. It is shown that the exponential particle energy per unit charge spectra observed by Ipavich et al. (1979) for the case of a radial solar wind magnetic field may be obtained if the fast particles escape the shock by means of resonant diffusion to unconnected field lines. The calculated e-folding value of the energy/charge ratio is found to be independent of the level of turbulence near the shock and in good agreement with observations. For the case of a nonradial solar wind magnetic field, the model is noted to predict that convection may be the dominant means of escape. It is also pointed out that the parallel and perpendicular diffusion coefficients may be measured indirectly at the bow shock.

Eichler, D.↗
NASA NTRS1994

Ion injection and acceleration at quasi-perpendicular shocks

We present and discuss results of a new model for ion injections and acceleration at quasi-perpendicular collisionless shocks. We use the one-dimensional hybrid simulation (kinetic ions/fluid electrons) and impose an assumption on the ion motion so that diffusion across the magnetic field (normal to the shock front) is possible. These motions are otherwise suppressed by both one- and two-dimensional simulations. We find that, even in strictly perpendicular shocks, when scattering normal to the field is included, a fraction of the incident ions are accelerated to suprathermal energies. When reasonable scattering times are considered, only pickup ions are injected, whereas thermal solar wind ions are not. The acceleration of these ions is very rapid. We have found that a few of the initially low-energy pickup ions can reach many tens to a few hundred times the plasma ramming energy in less than 100 gyroperiods. Furthermore, highly field aligned energetic ions are found to exist upstream of the slightly oblique shock. The most direct applications of this study is toward the interpretation of observations of both solar wind and interstellar pickup ion distributions in the vicinity of interplanetary shocks which are most often quasi-perpendicular. This work also directly addresses a fundamental issue with regard to our current understanding of the anomalous component of cosmic rays.

Giacalone, J.↗
NASA NTRS1986

Coupled hydromagnetic wave excitation and ion acceleration upstream of the Jovian bow shock

We extend the Lee (1982) self-consistent theory of upstream wave excitation and particle energization to address observations by Voyager 2 of sunward propagating MHD waves and diffuse suprathermal particle populations upstream of the Jovian bow shock. Two new ideas are incorporated into the theory. First, the interplanetary seed wave population is taken to be an equal admixture of waves propagating both toward and away from the shock parallel to the interplanetary magnetic field. Second, finite connection times are incorporated approximately into the theory in an effort to understand whether the particle spectra at high energy are limited by particle escape or finite connection time. It is found that finite connection times dominate the particle distribution at energies above 40 keV. In this manner the suprathermal proton distributions can be accounted for by a multiple reflection, shock acceleration theory. We find that the theory can also account for the low-frequency waves observed upstream of the shock in conjunction with the suprathermal ions.

Smith, C. W.↗
DOE OSTI2021

A High Resolution Simulation of a Single Shock-Accelerated Particle

We report particle drag models, which capture macroviscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a two-dimensional axisymmetric Navier–Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted using the hydrocode FLAG. FLAGs capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated—a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAGs Navier–Stokes and heat diffusion solutions and to provide a rationale for recent experimental particle drag measurements.

42 ENGINEERING↗
NASA NTRS1981

Monte Carlo simulation of charged particles upstream of the earth's bow shock

A simple model of the earth's bow shock is presented and compared with ISEE-1 observations of diffuse ions upstream of the shock. Ion behavior is modeled in a test particle simulation using Monte Carlo techniques for a plane parallel shock at which cold solar wind ions are heated sufficiently to allow diffusion back upstream. Fitting of the model to the observations indicates that the diffusion coefficient must increase faster than linearly with velocity, and provides an upper limit to the acceleration efficiency defined as the proportion of incoming solar wind ions accelerated and observed upstream. Results suggest that astrophysical shocks are capable of accelerating ions directly from the thermal plasma without the need for a distinct preenergizing injection stage.

Ellison, D. C.↗
NASA NTRS1987

Voyager 2 plasma wave observations at Uranus

At Uranus, the Voyager 2 plasma wave investigation observed very significant phenomena related to radio emissions, dust impacts, and magnetospheric wave-particle interactions. On January 19, 1986 (R = 270 R-sub U) the plasma wave investigation detected an intense radio burst at 31 and 56 kHz, and this provided the first indication that Uranus had a magnetosphere. During the encounter, more of these sporadic bursts were observed along with relatively continuous radio emissions extending down to 10 kHz, and a sporadic narrowband radio signal with f near 5 kHz. As Voyager passed through the ring plane, the plasma wave investigation recorded a large number of dust impacts. The Voyager 2 plasma wave instrument also detected many strong electromagnetic and electrostatic plasma waves, with intensity peaks in the region within 12 Uranus radii. These waves have characteristics that can interact strongly with the local plasma and with the trapped energetic particles, leading to precipitation into the atmosphere, charged particle acceleration, and charged particle diffusion. In addition, strong wave activity was detected in the region of the bow and shock and moderate levels in the magnetic tail.

Scarf, F. L.↗
NASA NTRS1994

Statistical analysis of diffuse ion events upstream of the Earth's bow shock

A statistical study of diffuse energetic ion events and their related waves upstream of the Earth's bow shock was performed using data from the Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM) satellite over two 5-month periods in 1984 and 1985. The data set was used to test the assumption in the self-consistent model of the upstream wave and particle populations by Lee (1982) that the particle acceleration through hydromagnetic waves and the wave generation are directly coupled. The comparison between the observed wave power and the wave power predicted on the observed energetic particle energy density and solar wind parameters results in a high correlation coefficient of about 0.89. The intensity of diffuse ions falls off approximately exponentially with the distance upstream from the bow shock parallel to the magnetic field with e-folding distances which vary from approximately 3.3 R(sub E) to approximately 11.7 R(sub E) over the energy range from 10 keV/e to 67.3 keV/e for both protons and alpha particles. After normalizing the upstream particle densities to zero bow shock distance by using these exponential variations, a good correlation (0.7) of the density of the diffuse ions with the solar wind density was found. This supports the suggestion that the solar wind is the source of the diffuse ions. Furthermore, the spectral slope of the diffuse ions correlates well with the solar wind velocity component in the direction of the interplanetary magnetic field (0.68 and 0.66 for protons and alpha particles) which concurs with the notion that the solar wind plays an important role in the acceleration of the upstream particles.

Trattner, K. J.↗
NASA NTRS1989

Seed population for about 1 MeV per nucleon heavy ions accelerated by interplanetary shocks

Data obtained between 1977 and 1982 by the ISEE 1 and ISEE 3 satellites on the composition of heavy ions of about 1 MeV per nucleon, accelerated in interplanetary shock events which followed solar flare events, are examined. It was found that the average relative abundances for C, O, and Fe in the shock events were very close to those found for energetic ions in the solar flares, suggesting that, at these energies, the shock accelerated particles have the solar energetic particles as their seed population. This hypothesis is supported by the fact that the Fe/O ratio in the solar particle events is very strongly correlated with the Fe/O ratio in associated diffusive shock events.

Tan, L. C.↗
NASA NTRS1985

Time-dependent nonlinear cosmic ray shocks confirming abstract

Numerical studies of time dependent cosmic ray shock structures in planar geometry are interesting because analytical time-independent solutions are available which include the non-linear reactions on the plasma flow. A feature of these time asymptotic solutions is that for higher Mach numbers (M approximately 5) and for a low cosmic ray upstream pressure the solution is not uniquely determined by the usual conservation laws of mass, momentum and energy. These numerical solutions clearly indicate that much work needs to be done before we understand shock acceleration as a time dependent process. The slowness of the process is possibly due to the fact that there is a diffusive flux into the downstream region in addition to the usual advective losses. Analytic investigations of thie phenomenon are required.

Dorfi, E. A.↗
NASA NTRS1991

Gamma-rays from cosmic ray interactions in supernova shells

A model is presented for the transport and interaction of cosmic rays accelerated by a pulsar and confined inside an expanding supernova remnant. Assuming that protons are accelerated at the reverse shock in the confined pulsar wind and convected into the shell via the Rayleigh-Taylor instability, the diffusion and interaction of these protons in the expanding envelope is modeled. The resulting gamma-ray flux is lower than previous estimates due primarily to the inclusion of proton adiabatic losses in the expanding pulsar wind. Energy-dependent diffusion causes the higher energy gamma-ray light curves to decay faster than those at lower energy. The predicted flux from SN1987A, for proton luminosity less than 10 exp 40 erg/s, is below the present detector sensitivities at both GeV and TeV energies, although supernovae occurring within the Galaxy may be detectable.

Harding, A. K.↗
NASA NTRS1993

Prependicular transport in 1- and 2-dimensional shock simulations

We consider the foundations of 1- and 2-dimensional shock simulations in which the physical quantities are independent of a coordinate which is not parallel to the magnetic field. We show analytically that in such simulations the ions are effectively tied to the convected magnetic lines of force because of the presence of an ignorable spatial coordinate. This conclusion has important consequences. In particular we conclude that the acceleration of energetic charged particles at quasi-perpendicular shocks cannot be properly studied in such simulations because the role of perpendicular diffusion cannot be properly evaluated.

Jokipii, J. R.↗