Improved treatments of the ionizing photon mean free path in seminumerical simulations of reionization
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Frederick B Davies↗
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A Multi-Wavelength Study of the Hot Component of the Interstellar Medium
The goals of this research are as follows: (1) Using the large number of lines of sight available in the ME database, identify the lines of sight with high-velocity components in interstellar lines, from neutral species through Si VI, C IV, and N V; (2) Compare the column density of the main components (i.e. low velocity components) of the interstellar lines with distance, galactic longitude and latitude, and galactic radial position. Derive statistics on the distribution of components in space (e.g. mean free path, mean column density of a component). Compare with model predictions for the column densities in the walls of old SNR bubbles and superbubbles, in evaporating cloud boundaries and in turbulent mixing layers; (3) For the lines of sight associated with multiple high velocity, high ionization components, model the shock parameters for the associated superbubble and SNR to provide more accurate energy input information for hot phase models and galactic halo models. Thus far 49 lines of sight with at least one high velocity component to the C IV lines have been identified; and (4) Obtain higher resolution data for the lines of sight with high velocity components (and a few without) to further refine these models.
Nichols, Joy↗
Diffusive shock acceleration - Acceleration rate, magnetic-field direction and the diffusion limit
This paper reviews the concept of diffusive shock acceleration, showing that the acceleration of charged particles at a collisionless shock is a straightforward consequence of the standard cosmic-ray transport equation, provided that one treats the discontinuity at the shock correctly. This is true for arbitrary direction of the upstream magnetic field. Within this framework, it is shown that acceleration at perpendicular or quasi-perpendicular shocks is generally much faster than for parallel shocks. Paradoxically, it follows also that, for a simple scattering law, the acceleration is faster for less scattering or larger mean free path. Obviously, the mean free path can not become too large or the diffusion limit becomes inapplicable. Gradient and curvature drifts caused by the magnetic-field change at the shock play a major role in the acceleration process in most cases. Recent observations of the charge state of the anomalous component are shown to require the faster acceleration at the quasi-perpendicular solar-wind termination shock.
Jokipii, J. R.↗
Model for radon diffusion through the lunar regolith.
Description of a model for radon diffusion through the lunar regolith in which the atom migrates by random walk. The regolith is represented by a system of randomly oriented baffles in which the mean distance which the atom travels between two collisions takes on the role of a mean free path. The effective mean time between two collisions depends on two entities: the actual mean time-of-flight and the mean sticking time on grain surfaces for one collision. The latter depends strongly on the temperature and the heat of adsorption of radon on regolith materials. Both the mean free path as well as the heat of adsorption are either poorly known or unknown for the lunar regolith; hence these quantities are treated as free parameters. Because of the greatly different mean lifetimes against radioactive decay of Rn219, Rn220, and Rn222, the regolith acts as a powerful 'filter' for these species. Rn222 escape is significant (32%) even for a mean free path of 1 micron, a heat of adsorption of 7.0 kcal/mole and a regolith depth of 4 m. Calculations of radon escape from a 4 m thick regolith, using mean free paths of 1, 10, and 80 microns and heats of adsorption of 4.0, 5.2, and 7.0 kcal/mole show that the Rn222/Rn220 escape ratio can be as small as 7.7 and as large as, or larger than 47. The small value of 7.7 is of particular interest, because it is nearly equal to the escape ratio inferred by Turkevich et al. (1970) from their Surveyor 5 results.
Friesen, L. J.↗
The interplanetary transport of solar cosmic rays
Numerical solutions are presented for the propagation of solar cosmic rays in interplanetary space, including the effects of pitch-angle scattering and adiabatic focusing. The intensity-time profiles can be well fitted by a simple radial spatial diffusion equation with scattering mean-free path lambda(fit). The radial mean-free path so obtained is significantly larger than the true scattering mean-free path for low-rigidity particles due to both adiabatic focusing and the inapplicability of the diffusive approximation early in the event. The well-known discrepancy between lambda(fit) and the theoretical predictions may be resolved by these calculations.
Gombosi, T. I.↗
Numerical study of solar flare particle propagation in the heliosphere
Numerical solutions are presented for the propagation of solar cosmic rays in interplanetary space, including the effects of pitch-angle scattering and adiabatic focusing. The intensity-time profiles can be well fitted by a simple radial spatial diffusion equation. For low-rigidity particles the radial mean free path so obtained is significantly larger than the mean free path calculated from the scattering coefficient due to the inapplicability of the diffusive approximation early in the event. The well-known discrepancy between the scattering mean free path and the theoretical predictions may be resolved by these calculations.
Gombosi, T. I.↗
Uncertainty quantification for neutrino opacities in core-collapse supernovae and neutron star mergers
We perform an extensive study of the correlations between the neutrino-nucleon inverse mean free paths (IMFPs) and the underlying equation of states (EoSs). Strong interaction uncertainties in the neutrino mean free path are investigated in different density regimes. The nucleon effective mass, the nucleon chemical potentials, and the residual interactions in the medium play an important role in determining neutrino-nucleon interactions in a density-dependent manner. Here we study how the above quantities are constrained by an EoS consistent with (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. We then study the uncertainties of both the charged current and the neutral current neutrino-nucleon inverse mean free paths due to the variation of these quantities, using the Hartree-Fock+random phase approximation method. Finally, we calculate the Pearson correlation coefficients between (i) the EoS-based quantities and the EoS-based quantities; (ii) the EoS-based quantities and the IMFPs; (iii) the IMFPs and the IMFPs. We find a strong impact of residual interactions on neutrino opacity in the spin and spin-isospin channels, which are not well constrained by current nuclear modelings.
79 ASTRONOMY AND ASTROPHYSICS↗
Seismic codas on the earth and the moon - A comparison
The seismic codas, representing that part of the seismogram following the arrival of the surface waves or the direct S waves, characteristic of the earth and moon are compared with regard to the implications of coda characteristics for scattering and attenuation. Scattering models based on single S-S scatter theory, in which seismic energy in the coda is assumed to be S waves that have undergone only one scattering without conversion, and on diffusion theory, which assumed that energy in the coda has been scattered many times, are examined, and situations where the single-scattering and multiple-scattering theories are applicable are distinguished by the ratio of attenuation distance to the scattering mean free path. Values of the attenuation distance and the mean free path derived from coda studies for the earth and moon are compared, and it is found that for the frequency range 0.5-10 Hz, diffusion scattering is important in lunar codas, while at frequencies from 1 to 25 Hz single scattering is important in terrestrial codas. It is pointed out that attenuation acts to eliminate scattering paths much longer than the attenuation length. The observed differences between terrestrial and lunar codas are thus attributed to lesser attenuation and greater scattering on the moon.
Dainty, A. M.↗
Ion Viscosity Mediated by Tangled Magnetic Fields: An Application to Black Hole Accretion Disks
We examine the viscosity associated with the shear stress exerted by ions in the presence of a tangled magnetic field. As an application, we consider the effect of this mechanism on the structure of black hole accretion disks. We do not attempt to include a self-consistent description of the magnetic field. Instead, we assume the existence of a tangled field with coherence length lambda(sub coh), which is the average distance between the magnetic 'kinks' that scatter the particles. For simplicity, we assume that the field is self-similar, and take lambda(sub coh) to be a fixed fraction zeta of the local disk height H. Ion viscosity in the presence of magnetic fields is generally taken to be the cross-field viscosity, wherein the effective mean free path is the ion Larmor radius lambda(sub L), which is much less than the ion-ion Coulomb mean free path A(sub ii) in hot accretion disks. However, we arrive at a formulation for a 'hybrid' viscosity in which the tangled magnetic field acts as an intermediary in the transfer of momentum between different layers in the shear flow. The hybrid viscosity greatly exceeds the standard cross-field viscosity when (lambda/lambda(sub L)) much greater than (lambda(sub L)/lambda(sub ii)), where lambda = ((lambda(sub ii)(sup -1) + lambda(sub (coh)(sup -1))(sup -1) is the effective mean free path for the ions. This inequality is well satisfied in hot accretion disks, which suggests that the ions may play a much larger role in the momentum transfer process in the presence of magnetic fields than was previously thought. The effect of the hybrid viscosity on the structure of a steady-state, two-temperature, quasi-Keplerian accretion disk is analyzed. The hybrid viscosity is influenced by the degree to which the magnetic field is tangled (represented by zeta = lambda(sub coh)), and also by the relative accretion rate M/M(sub E), where M(sub E) = L(sub E)/c(sup 2) and L(sub E) is the Eddington luminosity. We find that ion viscosity in the presence of magnetic fields (hybrid viscosity) can dominate over conventional magnetic viscosity for fields that are tangled on sufficiently small scales.
Subramanian, Prasad↗
Implications of the reported low energy electron gradients
A recently reported measurement of a small electron gradient in the energy range from 1.9 to 8.4 MeV by Webber et al. (1973) is interpreted in terms of a large local value of the scattering mean free path for these particles. The possibility that the scattering mean free path may be large throughout the modulation region is then investigated under the assumption of an azimuthally symmetric modulation region of 5 AU extent, the applicability of the diffusion-convection-adiabatic energy loss transport equation, and a galactic origin for the low-energy electrons. The implications for the solar modulation of electrons and the interstellar electron spectrum are discussed.
Lezniak, J. A.↗
Fracture, failure, and fragmentation
A general approach is required for describing matter of behavior when the failure is likely to involve growth and coalescence of a large number of fractures. Failures of this kind appear frequently in rapid dynamic processes, particularly in the formation of spall fragments. An approach to formulating constitutive relations that accounts for the opening, shear and growth of an ensemble of cracks is discussed. The approach accounts for plastic flow accompanying fragmentation. The resulting constitutive relations were incorporated into a Lagrangian computer program. A theoretical approach to coalescence is described. The simplest formulation uses a linear Liouville equation, with crack growth limited by the mean free path of cracks, assumed constant. This approach allows for an anisotropic distribution of cracks. An alternative approach in which the decrease of the mean free path with increasing crack size is accounted for, but the crack distribution is assumed isotropic is described. A reduction of the governing Liouville equation to an ordinary differential equation of third order is possible, and the result can be used to determine how mean free path decreases with increasing crack size.
Dienes, J. K.↗
On the radiative damping of atmospheric waves
General expressions for computing time constants for radiative decay of harmonic temperature perturbations in planetary atmospheres are developed. Four spatial scales are shown to be generally important: the scale height of the atmospheric absorber, the absorption mean free path for thermal radiation, the altitude above the planetary surface, and the wavelength of the temperature perturbation. Atmospheric inhomogeneity is particularly important when the radiation mean free path and the vertical wavelength divided by 2 pi both exceed the absorber scale height. The surface is very important for wave decay at altitudes less than a few radiation mean free paths, and its effect depends on a comparison of the surface response time and the lifetime of the atmospheric perturbation. The surface response time depends on the conducting and emitting properties of the surface material and on the strength of turbulence in the planetary boundary layer. The additional influence of chemical reactions and phase changes on radiative damping is discussed, and several assumptions inherent in the development of the general expressions for time constants are evaluated. Terrestrial examples are used for purposes of illustration, but the development is kept sufficiently general so that the results remain applicable to most situations on other planets.
Prinn, R. G.↗
Full Inversion of Solar Relativistic Electron Events Measured by the Helios Spacecraft
The Parker Solar Probe and the incoming Solar Orbiter mission will provide measurements of solar energetic particle (SEP) events at close heliocentric distances from the Sun. Up to present, the largest data set of SEP events in the inner heliosphere are the observations by the two Helios spacecraft. Aims.We re-visit a sample of 15 solar relativistic electron events measured by the Helios mission with the goal of better characterizing the injection histories of solar energetic particles and their interplanetary transport conditions at heliocentric distances <1AU. Methods. The measurements provided by the E6 instrument on board Helios provide us with the electron directional distributionsin eight di erent sectors that we use to infer the detailed evolution of the electron pitch-angle distributions. The results of a Monte Carlo interplanetary transport model, combined with a full inversion procedure, were used to fit the observed directional intensities in the 300–800 keV nominal energy channel. Unlike previous studies, we have considered both the energy and angular responses of the detector. This method allowed us to infer the electron release time profile at the source and determine the electron interplanetary transport conditions. Results. We discuss the duration of the release time profiles and the values of the radial mean free path, and compare them with thevalues reported previously in the literature using earlier approaches. Five of the events show short injection histories (<30 min) at the Sun and ten events show long-lasting (>30 min) injections. The values of mean free path range from 0.02AU to 0.27AU.Conclusions. The inferred injection histories match with the radio and soft X-ray emissions found in literature.We find no dependence of the radial mean free path on the radial distance. In addition, we find no apparent relation between the strength of interplanetary scattering and the size of the solar particle release.
Pacheco, D.↗
Quasi-linear theory and transport theory
The theory of energetic particle scattering by magnetostatic fluctuations is reviewed in so far as it fails to produce the rigidity-independent mean-free-paths observed. Basic aspects of interplanetary magnetic field fluctuations are reviewed with emphasis placed on the existence of dissipation range spectra at high wavenumbers. These spectra are then incorporated into existing theories for resonant magnetostatic scattering and are shown to yield infinite mean-free-paths. Nonresonant scattering in the form of magnetic mirroring is examined and offered as a partial solution to the magnetostatic problem. In the process, mean-free-paths are obtained in good agreement with observations in the interplanetary medium at 1 AU and upstream of planetary bow shocks.
Smith, Charles W.↗
Thermodynamics and transport in molten chloride salts and their mixtures
Relationship between thermophysical properties and phonon mean free path. Heat capacity, viscosity, and thermal conductivity in ionic liquids decrease as mean free path decreases and dynamics become less “solid-like” and collect motion diminishes.
Cockrell, C. [Nuclear Futures Institute, Bangor Un↗
Theoretical analysis of low-energy proton and helium anisotropies in the outer heliosphere
Expressions for streaming components are considered along with aspects of azimuthal anisotropy, taking into account a calculation of mean free paths and a comparison with corotation conditions. Questions of polar anisotropy are also taken into account. It is found that the azimuthal anisotropy of 30 - 56 MeV protons near the ecliptic plane at 12 AU in 1977 was consistent with corotation, or slightly faster. This implies that the mean free path is approximately 16 AU. The azimuthal anisotropy of the anomalous 10-21 and 30 - 56 MeV/nucleon helium at the same time and place was an order of magnitude less than the corotation value. This implies a mean free path of approximately 5 AU.
Forman, M. A.↗
Spatially Dependent Seismic Wavefield Scattering from an Underground Chemical Explosion: Analysis of the Source Physics Experiment Dry Alluvium Geology Large- N Array
Explosion sources have been observed to generate significant shear‐wave energy despite their isotropic nature. To investigate this phenomenon, we conduct an analysis of the seismic data collected as part of the Source Physics Experiment (SPE): Dry Alluvium Geology (DAG) and investigate the generation of shear‐wave energy via scattering. The data were produced by three underground chemical explosions and consist of three‐component seismograms, which were recorded by the DAG Large‐N array. Synthetic tests suggest that for the DAG experiments, small‐scale stochastic heterogeneities, defined as features with correlation lengths of 10–100s of meters, are more effective than large‐scale geologic structure (scales >1–10 km) at reproducing the scattering of explosion generated wavefields observed at DAG. We analyze the seismic data for spatially variable ratios between transversely and radially polarized seismic energy, and then estimate the mean free path of P and S waves. All analyses are conducted within a frequency band of 5–50 Hz. The ratio of transversely to radially polarized energy is the highest in the east and west portion of the Large‐N array. In addition, the magnitude of the estimated S‐wave mean free path is shorter in the eastern portion of the Large‐N array. This variation indicates that the eastern area of the DAG array is where more scattering is occurring, suggesting azimuthal dependence of P‐to‐P and P‐to‐S scattering. Furthermore, this azimuthal dependence of P‐to‐S scattering can have implications for explosion discrimination based on spectral ratios of seismic wave types, because the general assumption is that explosions do not generate shear‐wave energy. Synthetic tests modeling only larger‐scale geologic structure had lower transversely polarized energy (only four stations showing a transversely to radially polarized energy ratio greater than 1) and fewer stations (<10) displaying shorter (<300 m) mean free paths than what was observed in the DAG data results.
Darrh, Andréa Nicole↗
A collision-based hybrid method for the BGK equation
In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.
97 MATHEMATICS AND COMPUTING↗