Magnetohydrodynamic scaling: From astrophysics to the laboratory

During the last few years, considerable progress has been made in simulating astrophysical phenomena in laboratory experiments with high-power lasers. Astrophysical phenomena that have drawn particular interest include supernovae explosions; young supernova remnants; galactic jets; the formation of fine structures in late supernovae remnants by instabilities; and the ablation-driven evolution of molecular clouds. A question may arise as to what extent the laser experiments, which deal with targets of a spatial scale of ∼100 μm and occur at a time scale of a few nanoseconds, can reproduce phenomena occurring at spatial scales of a million or more kilometers and time scales from hours to many years. Quite remarkably, in a number of cases there exists a broad hydrodynamic similarity (sometimes called the “Euler similarity”) that allows a direct scaling of laboratory results to astrophysical phenomena. A discussion is presented of the details of the Euler similarity related to the presence of shocks and to a special case of a strong drive. Constraints stemming from the possible development of small-scale turbulence are analyzed. The case of a gas with a spatially varying polytropic index is discussed. A possibility of scaled simulations of ablation front dynamics is one more topic covered in this paper. It is shown that, with some additional constraints, a simple similarity exists. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71174/2/PHPAEN-8-5-1804-1.pd

Predicting the safety and efficacy of butter therapy to raise tumour pHe: an integrative modelling study

Background: Clinical positron emission tomography imaging has demonstrated the vast majority of human cancers exhibit significantly increased glucose metabolism when compared with adjacent normal tissue, resulting in an acidic tumour microenvironment. Recent studies demonstrated reducing this acidity through systemic buffers significantly inhibits development and growth of metastases in mouse xenografts.\ud \ud Methods: We apply and extend a previously developed mathematical model of blood and tumour buffering to examine the impact of oral administration of bicarbonate buffer in mice, and the potential impact in humans. We recapitulate the experimentally observed tumour pHe effect of buffer therapy, testing a model prediction in vivo in mice. We parameterise the model to humans to determine the translational safety and efficacy, and predict patient subgroups who could have enhanced treatment response, and the most promising combination or alternative buffer therapies.\ud \ud Results: The model predicts a previously unseen potentially dangerous elevation in blood pHe resulting from bicarbonate therapy in mice, which is confirmed by our in vivo experiments. Simulations predict limited efficacy of bicarbonate, especially in humans with more aggressive cancers. We predict buffer therapy would be most effectual: in elderly patients or individuals with renal impairments; in combination with proton production inhibitors (such as dichloroacetate), renal glomular filtration rate inhibitors (such as non-steroidal anti-inflammatory drugs and angiotensin-converting enzyme inhibitors), or with an alternative buffer reagent possessing an optimal pK of 7.1–7.2.\ud \ud Conclusion: Our mathematical model confirms bicarbonate acts as an effective agent to raise tumour pHe, but potentially induces metabolic alkalosis at the high doses necessary for tumour pHe normalisation. We predict use in elderly patients or in combination with proton production inhibitors or buffers with a pK of 7.1–7.2 is most promising

The time scale for the transition to turbulence in a high Reynolds number, accelerated flow

An experiment is described in which an interface between materials of different density is subjected to an acceleration history consisting of a strong shock followed by a period of deceleration. The resulting flow at this interface, initiated by the deposition of strong laser radiation into the initially well characterized solid materials, is unstable to both the Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) instabilities. These experiments are of importance in their ability to access a difficult experimental regime characterized by very high energy density (high temperature and pressure) as well as large Reynolds number and Mach number. Such conditions are of interest, for example, in the study of the RM/RT induced mixing that occurs during the explosion of a core-collapse supernova. Under these experimental conditions, the flow is in the plasma state and given enough time will transition to turbulence. By analysis of the experimental data and a corresponding one-dimensional numerical simulation of the experiment, it is shown that the Reynolds number is sufficiently large (Re>105)(Re>105) to support a turbulent flow. An estimate of three key turbulence length scales (the Taylor and Kolmogorov microscales and a viscous diffusion scale), however, shows that the temporal duration of the present flow is insufficient to allow for the development of a turbulent inertial subrange. A methodology is described for estimating the time required under these conditions for the development of a fully turbulent flow. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70243/2/PHPAEN-10-3-614-1.pd

Modified Bell-Plesset Effect with Compressibility: Application to Double-Shell Ignition Target Designs

The effect of spherical convergence on the fluid stability of collapsing and expanding bubbles was originally treated by Bell [Los Alamos Scientific Laboratory Report No. LA-1321 (1951)] and Plesset [J. Appl. Phys. 25, 96 (1954)]. The additional effect of fluid compressibility was also considered by Bell but was limited to the case of nonzero density on only one side of a fluid interface. A more general extension is developed which considers distinct time-dependent uniform densities on both sides of an interface in a spherically converging geometry. A modified form of the velocity potential is used that avoids an unphysical divergence at the origin [Goncharov et al., Phys. Plasmas 7, 5118 (2000); Lin et al., Phys. Fluids 14, 2925 (2002)]. Two consequences of this approach are that an instability proposed by Plesset for an expanding bubble in the limit of large interior density is now absent and application to inertial confinement fusion studies of stability becomes feasible. The model is applied to a proposed ignition double-shell target design [Amendt et al., Phys. Plasmas 9, 2221 (2002)] for the National Ignition Facility [Paisner et al., Laser Focus World 30, 75 (1994)] for studying the stability of the inner surface of an imploding high-Z inner shell. Application of the Haan [Phys. Rev. A 39, 5812 (1989)] saturation criterion suggests that ignition is possible

3. Launching the New Enterprise

As the academic year of 1945-46 approached, the intensity of activity in preparation for actually opening the school in the fall term became overwhelming. Incredible though it may seem, Ives and Day were able in a period of a few weeks to assemble the nucleus of a faculty, several of whom formed a continuing source of counsel and advice both during the school’s formative years and thereafter. Includes: The First Dean and the School’s Dedication; A Participant’s View of the Early Years; Ives Moves On; Several Views of Martin P. Catherwood; The Founders

Spatial Resolution of Gated X-Ray Pinhole Cameras

The new camera FXI was investigated. Spatial resolution, or its Fourier transform, the modulation transfer function (MTF), is critical for quantitative interpretation of recent hydrodynamic instability data taken on the Nova laser. We have taken data corresponding to backlit straight edges, pinholes, and grids, both on the bench and {ital in}{ital situ} on Nova. For both the pinhole and edge data, the MTF at all wavelengths of interest can be deduced from a single image. Grids are of more limited usefulness, giving the MTF value only at the spatial period of the grid. These different techniques for characterizing the MTF of gated x-ray pinhole cameras are discussed, with results specific to the FXI presented

Numerical simulation of supernova-relevant laser-driven hydro experiments on OMEGA

In ongoing experiments performed on the OMEGA laser [J. M. Soures et al., Phys. Plasmas 5, 2108 (1996)] at the University of Rochester Laboratory for Laser Energetics, nanosecond laser pulses are used to drive strong blast waves into two-layer targets. Perturbations on the interface between the two materials are unstable to the Richtmyer–Meshkov instability as a result of shock transit and the Rayleigh–Taylor instability during the deceleration-phase behind the shock front. These experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen–helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. The authors are, at present, particularly interested in the development of the Rayleigh–Taylor instability through the late nonlinear stage, the transition to turbulence, and the subsequent transport of material within the turbulent region. In this paper, the results of numerical simulations of two-dimensional (2D) single and multimode experiments are presented. These simulations are run using the 2D Arbitrary Lagrangian Eulerian radiation hydrodynamics code CALE [R. T. Barton, Numerical Astrophysics (Jones and Bartlett, Boston, 1985)]. The simulation results are shown to compare well with experimental radiography. A buoyancy-drag model captures the behavior of the single-mode interface, but gives only partial agreement in the multimode cases. The Richtmyer–Meshkov and target decompression contributions to the perturbation growth are both estimated and shown to be significant. Significant dependence of the simulation results on the material equation of state is demonstrated, and the prospect of continuing the experiments to conclusively demonstrate the transition to turbulence is discussed. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71253/2/PHPAEN-11-7-3631-1.pd

Transition to turbulence and effect of initial conditions on three-dimensional compressible mixing in planar blast-wave-driven systems

Perturbations on an interface driven by a strong blast wave grow in time due to a combination of Rayleigh–Taylor, Richtmyer–Meshkov, and decompression effects. In this paper, results from three-dimensional (3D) numerical simulations of such a system under drive conditions to be attainable on the National Ignition Facility [E. M. Campbell, Laser Part. Beams 9, 209 (1991)] are presented. Using the multiphysics, adaptive mesh refinement, higher order Godunov Eulerian hydrocode, Raptor [L. H. Howell and J. A. Greenough, J. Comput. Phys. 184, 53 (2003)], the late nonlinear instability evolution, including transition to turbulence, is considered for various multimode perturbation spectra. The 3D post-transition state differs from the 2D result, but the process of transition proceeds similarly in both 2D and 3D. The turbulent mixing transition results in a reduction in the growth rate of the mixing layer relative to its pretransition value and, in the case of the bubble front, relative to the 2D result. The post-transition spike front velocity is approximately the same in 2D and 3D. Implications for hydrodynamic mixing in core-collapse supernovae are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87764/2/056317_1.pd

Experiment on mass-stripping of interstellar cloud following shock passage

The interaction of supernova shocks and interstellar clouds is an important astrophysical phenomenon which can lead to mass-stripping (transfer of material from cloud to surrounding flow, ''mass-loading'' the flow) and possibly increase the compression in the cloud to high enough densities to trigger star formation. Our experiments attempt to simulate and quantify the mass-stripping as it occurs when a shock passes through interstellar clouds. We drive a strong shock using 5 kJ of the 30 kJ Omega laser into a cylinder filled with low-density foam with an embedded 120 {micro}m Al sphere simulating an interstellar cloud. The density ratio between Al and foam is {approx} 9. Time-resolved x-ray radiographs show the cloud getting compressed by the shock (t {approx} 5 ns), undergoing a classical Kelvin-Helmholtz roll-up (12 ns) followed by a Widnall instability (30 ns), an inherently 3d effect that breaks the 2d symmetry of the experiment. Material is continuously being stripped from the cloud at a rate which is shown to be inconsistent with laminar models for mass-stripping (the cloud is fully stripped by 80 ns-100 ns, ten times faster than the laminar model). We present a new model for turbulent mass-stripping that agrees with the observed rate and which should scale to astrophysical conditions, which occur at even higher Reynolds numbers than the current experiment. The new model combines the integral momentum equations, potential flow past a sphere, flat plate skin friction coefficients, and Spalding's law of the wall for turbulent boundary layers