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NASA NTRS2004

Underexpanded Screeching Jets From Circular, Rectangular, and Elliptic Nozzles

The screech frequency and amplitude, the shock spacing, the hydrodynamic-acoustic standing wave spacing, and the convective velocity of large organized structures are measured in the nominal Mach number range of 1.1 less than or = Mj less that or = l0.9 for supersonic, underexpanded jets exhausting from a circular, a rectangular and an elliptic nozzle. This provides a carefully measured data set useful in comparing the importance of various physical parameters in the screech generation process. The hydrodynamic-acoustic standing wave is formed between the potential pressure field of large turbulent structures and the acoustic pressure field of the screech sound. It has been demonstrated earlier that in the currently available screech frequency prediction models replacement of the shock spacing by the standing wave spacing provides an exact expression. In view of this newly found evidence, a comparison is made between the average standing wavelength and the average shock spacing. It is found that there exists a small, yet important, difference, which is dependent on the azimuthal screech mode. For example, in the flapping modes of circular, rectangular, and elliptic jets, the standing wavelength is slightly longer than the shock spacing, while for the helical screech mode in a circular jet the opposite is true. This difference accounts for the departure of the existing models from predicting the exact screech frequency. Another important parameter, necessary in screech prediction, is the convective velocity of the large organized structures. It is demonstrated that the presence of the hydrodynamic-acoustic standing wave, even inside the jet shear layer, becomes a significant source of error in the convective velocity data obtained using the conventional methods. However, a new relationship, using the standing wavelength and screech frequency is shown to provide more accurate results.

Panda, J.↗
NASA NTRS1986

Cosmic-ray shock acceleration in oblique MHD shocks

A one-dimensional, steady-state hydrodynamical model of cosmic-ray acceleration at oblique MHD shocks is presented. Upstream of the shock the incoming thermal plasma is subject to the adverse pressure gradient of the accelerated particles, the J x B force, as well as the thermal gas pressure gradient. The efficiency of the acceleration of cosmic-rays at the shock as a function of the upstream magnetic field obliquity and upstream plasma beta is investigated. Astrophysical applications of the results are briefly discussed.

Webb, G. M.↗
NASA NTRS1972

Model development of supersonic trough wind with shocks

The time dependent one dimensional hydrodynamic equations describe the evolution of the thermal plasma flow along closed magnetic field lines outside of the plasmasphere. The convection of the supersonic polar wind onto a closed fieldline results in the assumed formation of collisionless plasma shocks. These shocks move earthward as the field line with its frozen-in plasma remains fixed or contracts with time to smaller L coordinates. The high equatorial plasma temperature (of the order of electron volts) produced by the shock process decreases with time if the flow is isothermal but it will increase if the contraction is under adiabatic conditions. Assuming adiabaticity a peak in the temperature forms at the equator in conjunction with a depression in the ion density. After an initial contraction, if the flux tube drifts to higher L coordinates the direction of the shock motion can be reversed so that the supersonic region will expand along the field line towards the state characterizing the supersonic polar wind. A rapid expansion will lower the equatorial density while the temperature decreases with time under adiabatic but not isothermal conditions.

Grebowsky, J. M.↗
NASA NTRS1994

Reionization in a cold dark matter universe: The feedback of galaxy formation on the intergalactic medium

We study the coupled evolution of the intergalactic medium (IGM) and the emerging structure in the universe in the context of the cold dark matter (CDM) model, with a special focus on the consequences of imposing reionization and the Gunn-Peterson constraint as a boundary condition on the model. We have calculated the time-varying density of the IGM by coupling our detailed, numerical calculations of the thermal and ionization balance and radiative transfer in a uniform, spatially averaged IGM of H and He, including the mean opacity of an evolving distribution of gas clumps which correspond to quasar absorption line clouds, to the linearized equations for the growth of density fluctuations in both the gaseous and dark matter components in a CDM universe. We use the linear growth equations to identify the fraction of the gas which must have collapsed out at each epoch, an approach similar in spirit to the so-called Press-Schechter formalism. We identify the IGM density with the uncollapsed baryon fraction. The collapsed fraction is postulated to be a source of energy injection into the IGM, by radiation or bulk hydrodynamical heating (e.g., via shocks) or both, at a rate which is marginally enough to satisfy the Gunn-Peterson constraint at z less than 5. Our results include the following: (1) We find that the IGM in a CDM model must have contained a substantial fraction of the total baryon density of the universe both during and after its reionization epoch. (2) As a result, our previous conclusion that the observed Quasi-Stellar Objects (QSOs) at high redshift are not sufficient to ionize the IGM enough to satisfy the Gunn-Peterson constraint is confirmed. (3) We predict a detectable He II Gunn-Peterson effect at 304(1 + z) A in the spectra of quasars at a range of redshift z greater than or approx. 3, depending on the nature of the sources of IGM reionization. (4) We find, moreover, that a CDM model with high bias parameter b (i.e., b greater than or approx. 2) cannot account for the baryon content of the universe at z approximately 3 observed in quasar absorption line gas unless Omega (sub B) significantly exceeds the maximum value allowed by big bang nucleocynthesis. (5) For a CDM model with bias parameter within the allowed range of (lower) values, the lower limit to Omega(sub B) imposed by big bang nucleosynthesis (Omega(sub B) h(sup 2) greater than or equal to 0.01) combines with our results to yield the minimum IGM density for the CDM fodel. For CDM with b = 1 (Cosmic Background Explorer (COBE) normalization), we find Omega(sub IGM)(sup min) (z approximately 4) approx. equal 0.02-0.03, and Omega(sub IGM)(sup min)(z approximately 0) approx. equal 0.005-0.03, depending upon the nature of the sources of IGM reionization. (6) In general, we find that self-consistent reionization of the IGM by the collapsed baryon fraction has a strong effect on the rate of collapse. (7) As a further example, we show that the feedback effect on the IGM of energy release by the collapsed baryon fraction may explain the slow evolution of the observed comoving QSO number density between z = 5 and z = 2, followed by the sharp decline after z = 2.

Shapiro, Paul R.↗
NASA NTRS1994

A simulation of the intracluster medium with feedback from cluster galaxies

We detail method and report first results from a three-dimensional hydrodynamical and N-body simulation of the formation and evolution of a Coma-sized cluster of galaxies, with the intent of studying the history of the hot, X-ray emitting intracluster medium. Cluster gas, galaxies, and dark matter are included in the model. The galaxies and dark matter fell gravitational forces; the cluster gas also undergoes hydrodynamical effects such as shock heating and PdV work. For the first time in three dimensions, we include modeling of ejection of processed gas from the simulated galaxies by winds, including heating and heavy element enrichment. For comparison, we employ a `pure infall' simulation using the same initial conditions but with no galaxies or winds. We employ an extreme ejection history for galactic feedback in order to define the boundary of likely models. As expected, feedback raises the entropy of the intracluster gas, preventing it from collapsing to densities as high as those attained in the infall model. The effect is more pronounced in subclusters formed at high redshift. The cluster with feedback is always less X-ray luminous, but experiences more rapid luminosity evolution, than the pure infall cluster. Even employing an extreme ejection model, the final gas temperature is only approximately 15% larger than in the infall model. The radial temperature profile is very nearly isothermal within 1.5 Mpc. The cluster galaxies in the feedback model have a velocity dispersion approximately 15% lower than the dark matter. This results in the true ratio of specific energies in galaxies to gas being less than one, beta(sub spec) approximately 0.7. The infall model predicts beta(sub spec) approximately 1.2. Large excursions in these values occur over time, following the complex dynamical history of the cluster. The morphology of the X-ray emission is little affected by feedback. The emission profiles of both clusters are well described by the standard beta-model with beta(sub fit) approximately equal to 0.7 - 0.9. X-ray mass estimates based on the assumptions of hydrostatic equilibrium and the applicability of the beta-model are quite accurate in both cases. A strong, radial iron abundance gradient is present, which develops as a consequence of the steepening of the galaxy density profile over time. Spectroscopic observations using nonimaging detectors with wide (approximately 45 min) fields of view dramatically smear the gradient. Observations with arcminute resolution, made available with the ASCA satellite, would readily resolve the gradient.

Metzler, Christopher A.↗
NASA NTRS2011

Simulation of Relativistic Shocks and Associated Radiation from Turbulent Magnetic Fields

Using our new 3-D relativistic particle-in-cell (PIC) code, we investigated long-term particle acceleration associated with a relativistic electron-positron jet propagating in an unmagnetized ambient electron-positron plasma. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value as predicted by hydrodynamic compression. Behind the bow shock, in the jet shock, strong electromagnetic fields are generated. These fields may lead to time dependent afterglow emission. In order to go beyond the standard synchrotron model used in astrophysical objects we have used PIC simulations and calculated radiation based on first principles. We calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We also used the technique to calculate emission from electrons based on simulations with a small system. We obtain spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability. A fully developed shock within a larger system may generate a jitter/synchrotron spectrum.

Nishikawa, K.-I.↗
NASA NTRS1988

Multistream hydrodynamic modeling of interhemispheric plasma flow

Interhemispheric plasma flow was simulated using one-stream and two-stream hydrodymic models in order to test the suggestion of Banks et al. (1971) and others that the collision of high-speed flows originating from the conjugate hemispheres will cause the formation of a pair of shocks. The single-fluid hydrodynamic equations were modified to include multiple ion streams, allowing for the possibility of counterstreaming flow. It was found that a counterstreaming of ion streams from conjugate hemispheres does occur during the early stages of the refilling of plamaspheric flux tubes, and that a pair of reverse shocks does form. These shocks form away from the equator, and their subsequent motion creates conditions similar to those predicted by the single-stream hydrodynamic models. The findings support the conclusion of earlier studies that the refilling of the plasmasphere occurs from the equatorial region downward.

Rasmussen, C. E.↗
NASA NTRS1985

Persistence of shocks to large distances in the solar wind

Present hydrodynamic models of solar wind streams predict that interactions will cause interplanetary shocks to decay and large-scale structures to coalesce and smooth out, with a decay length of 10-15 AU for moderate or small-amplitude shocks. The Pioneer 10 plasma data, extending 1-30 AU, are examined in the light of such predictions. It is found that coalescence of streams into a single stream per solar rotation does occur, in general, but that considerable structure remains by 30 AU. The leading edge of a stream often exhibits a velocity jump of greater than 20 km/s; many of these may be shocks. There is a characteristic velocity-density-temperature signature of these distant streams which differs from the close-in double-shock signature. A unique transient was seen in July 1982, at 28 AU, with a velocity jump of about 235 km/s.

Kayser, S. E.↗
NASA NTRS1987

Collapsing white dwarfs

The results of the hydrodynamic collapse of an accreting C + O white dwarf are presented. Collapse is induced by electron captures in the iron core behind a conductive deflagration front. The shock wave produced by the hydrodynamic bounce of the iron core stalls at about 115 km, and thus a neutron star formed in such a model would be formed as an optically quiet event.

Baron, E.↗
NASA NTRS1992

Time-dependent cosmic ray shocks with injection - A progress report

The study presents preliminary results of a two-fluid hydrodynamical simulation of cosmic-ray-modified shock structure by extending the steady-state calculations of Zank et al. (1991) to the time-dependent case. The present simulations model diffusive shock acceleration of the energetic particle component at planar shocks. A new model for the injection of cosmic ray particles is presented. The quadratic artificial viscosity algorithm is found to be numerically unstable and therefore unusable for strong cosmic ray shocks. There is visible ringing and overshoot in the various profiles. A large enhancement in the fluid density appears downstream of the subshock. This 'overcompression' results from the upstream fluid being compressed in the precursor, then traversing a strong shock with compression ratio near the adiabatic limit of four.

Donohue, D. J.↗
NASA NTRS1972

Model development of supersonic trough wind with shocks.

The time-dependent one dimensional hydrodynamic equations describe the evolution of the thermal plasma flow along closed magnetic field lines outside of the plasmasphere. The convection of the supersonic polar wind onto a closed field line results in the assumed formation of collisionless plasma shocks. These shocks move earthward as the field line with its 'frozen-in' plasma remains fixed or contracts with time to smaller L coordinates. The high equatorial plasma temperature (of the order of electron volts) produced by the shock process decreases with time if the flow is isothermal, but it will increase if the contraction is under adiabatic conditions. Assuming adiabaticity a peak in the temperature forms at the equator in conjunction with a depression in the ion density. After an initial contraction, if the flux tube drifts to higher L coordinates, the direction of the shock motion can be reversed so that the supersonic region will expand along the field line toward the state characterizing the supersonic polar wind.

Grebowsky, J. M.↗
NASA NTRS1992

Effects of equatorially trapped ions on refilling of the plasmasphere

The kinetic aspects of shock formation in response to the equatorial heating of ions are reported by means of small-scale kinetic simulations of countersteaming plasma flows along a spatially varying magnetic field having the features of the dipolar magnetic field lines. Attention is given to the trapping of the field-aligned flowing ions in response to the simulated equatorial heating of ions and the associated self-consistent structures in the electric potentials and the f-plasma flow pattern. Trapping is found to lead to the formation of electrostatic shocks, which propagate away from the 'equator' as seen in the hydrodynamic model of Singh and Torr (1990). The shocks form near the mirror points of the 'equatorially' heated ions. The second stage of the refilling with equatorially trapped ions is reported. A variety of structures in density and temperature distributions as the refilling proceeds slowly is found.

Singh, Nagendra↗
NASA NTRS1995

Motion of the Termination Shock in Response to an 11 Year Variation in the Solar Wind

A two-dimensional hydrodynamic numerical model has been used to study the motion of the termination shock in response to an 11 year variation in the solar wind ram pressure. For a total variation in the ram pressure by a factor of 2, a termination shock at 89 AU moves inward and outward about +/- 8 percent of its distance with a typical velocity of 12 km/s.

solar↗
NASA NTRS1994

Shock propagation and the generation of magnetohydrodynamic wave fields in inhomogeneous molecular clouds

We develop a simple one-dimensional model for the interaction of a steady, thin, planar shock wave with a nonrigid cloud which may be in motion relative to the surrounding medium, and we apply the model to shocks impinging on, and propagating through, molecular clouds. Both 'adiabatic' (gamma = 5/3) and radiative (gamma = 1) shocks are considered and we allow for the presence of a uniform magnetic field directed either parallel or perpendicular to the shock normal. The former field orientation is equivalent to the hydrodynamic case, and the latter involves only fast MHD shocks. We focus on the manner in which such shocks can generate internal kinetic motions in the cloud on a range of size and density scales through the direct acceleration of cores and clumps by shocks transmitted into them and through the generation of an MHD wavefield via the reflection of the incident shock at clump boundaries. We find that stronger incident Mach numbers and smaller density contrasts lead to more efficient cloud acceleration, as do isothermal intercloud shocks and small intercloud magnetic field strengths. The acceleration efficiency is insensitive to the adiabatic index and the magnetic field strength in the cloud itself. For typical parameter choices, the direct acceleration of clouds and clumps by strong shocks is found to be substantial and could at least in part account for their observed velocity dispersions. If the shocks are moderately weak, the final velocity of the cloud is linearly related to its initial velocity, with higher acceleration giving shallower slopes (i.e., final velocity distributions which are less sensitive to the initial distribution). Compared to the kinetic energy of the postshock cloud, the energy given to the wavefield at each encounter is small, and the heating of the interclump medium by the dissipation of this wavefield is found to be insufficient to balance the cooling rate in the cloud as a whole (although it may be important in particular regions), even if this medium is warm, unless it is also extremely tenuous (n approximately less than 0.1/cu cm). Nevertheless, the correction for the velocity imparted to the cloud leads to a substantial increase in the critical incident Mach numner for wave emission over that reported by Spitzer for the rigid case. The implications of our model for shock-induced star formation are discussed briefly.

Miesch, Mark S.↗
NASA NTRS1986

The special relativistic shock tube

The shock-tube problem has served as a popular test for numerical hydrodynamics codes. The development of relativistic hydrodynamics codes has created a need for a similar test problem in relativistic hydrodynamics. The analytical solution to the special relativistic shock-tube problem is presented here. The relativistic shock-jump conditions and rarefaction solution which make up the shock tube are derived. The Newtonian limit of the calculations is given throughout.

Thompson, Kevin W.↗
NASA NTRS1986

The clumpy circumstellar medium around young supernova remnants

Each of the youngest supernova remnants known in the Milky Way, Cas A, Kepler's SNR, and Tycho's SNR, shows a different morphological structure caused by different conditions in the progenitor stars and their surroundings. In all three cases, however, the observed shells have a thickness of about 1/4 the radius, a sharp outer edge, and significant brightness irregularities. These features require that the circumstellar medium be highly clumped. To investigate the phenomenon, models of the expansion have been constructed using a one-dimensional spherical hydrodynamic code. As a supernova shock moves down the external density gradient of the star, material behind the shock begins to go into free expansion. Then as surrounding material is encountered a reverse shock moving back into the ejectum will be formed. Until the expansion has swept up about eight times the ejected mass when the situation can be considered as a point explosion in its surroundings, the dynamics are controlled by conditions between the shocks. The region is also where the synchrotron radio emission from relativistic electrons trapped in magnetic fields arises. Initial particles and fields are accelerated and amplified by eddy motion at the interface between the ejected and swept-up material and at the boundaries of clumps. Polarimetry shows that these SNR have a net radial orientation of their magnetic fields apparently from stretching by Rayleigh-Taylor instabilities at the contact surfaces. Without clumps the observed shell is much too narrow and steep on the inside.

Dickel, J. R.↗
NASA NTRS1992

A semikinetic model for early stage plasmasphere refilling. I - Effects of Coulomb collisions

A collisionless, time-dependent, kinetic plasma model is applied to the problem of baseline plasmasphere refilling of an initially depleted flux tube, without regard for the effects of wave-particle interactions. Refilling calculations for various flux tubes and for different ionospheric plasma fluxes and temperatures are performed. In each case considered, the same set of events occurs. Initially, two polar wind outflows develop from each hemisphere and set up counterstreaming beams. With time the vacant phase space region between these beams fills, primarily because of collision-induced particle diffusion but also because of lowering ambipolar potential drops from the increasing density in the plasmasphere. In contrast to all previous hydrodynamic approaches, no formation of shocks was found. The plasma first evolves an isotropic, nearly Maxwellian velocity distribution in a region that starts near the ionosphere and moves outward toward the equator. For reasonable topside ionospheric temperatures and fluxes, the thermal plasma all along an L shell is found to become nearly isotropic in 6 to 30 hr, consistent with the observations of Horwitz et al. (1984).

Wilson, G. R.↗
NASA NTRS1994

Studies on equatorial shock formation during plasmaspheric refilling

Investigations based on small-scale simulations of microprocesses occurring when a magnetic flux tube refills with a cold plasma are summarized. Results of these investigations are reported in the following attached papers: (1) 'Numerical Simulation of Filling a Magnetic Flux Tube with a Cold Plasma: The Role of Ion Beam-Driven Instabilities'; and (2) 'Numerical Simulation of Filling a Magnetic Flux Tube with a Cold Plasma: Effects of Magnetically Trapped Hot Plasma'. Other papers included are: 'Interaction of Field-Aligned Cold Plasma Flows with an Equatorially-Trapped Hot Plasma: Electrostatic Shock Formation'; and 'Comparison of Hydrodynamic and Semikinetic Treatments for a Plasma Flow along Closed Field Lines'. A proposal for further research is included.

Singh, N.↗