One-dimensional Radiation Hydrodynamics Research Articles

Global Existence and blowup phenomenon for a 1D radiation hydrodynamics model problem

We consider the global existence of classical solutions and blowup phenomena for a spatially one-dimensional radiation hydrodynamics model problem, which consists of a scalar Burgers-type equation coupled with a nonlocal advection-reaction equation for radiation intensity. The model can be seen as an extension of the well-known Hamer model that includes additionally the effects of scattering. It is well-known that the initial value problem for Burgers' equation cannot be solved classically as soon as the derivative of the initial datum is negative somewhere. For our model problem, there is a critical negative number such that if the spatial derivative of the initial function is larger than this number, the associated initial-value problem admits a global classical solution. However, when the spatial derivative of the initial data is below another negative threshold number, the initial value problem can also not be solved classically. Moreover, when there does not exist a global classical solution, it is shown that the first spatial derivative of solution must blow up in finite time. The results of the paper generalize the findings of Kawashima and Nishibata for the Hamer model. Copyright © 2012 John Wiley & Sons, Ltd.

A hybrid Godunov method for radiation hydrodynamics

From a mathematical perspective, radiation hydrodynamics can be thought of as a system of hyperbolic balance laws with dual multiscale behavior (multiscale behavior associated with the hyperbolic wave speeds as well as multiscale behavior associated with source term relaxation). With this outlook in mind, this paper presents a hybrid Godunov method for one-dimensional radiation hydrodynamics that is uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds that the technique preserves certain asymptotic limits. The method incorporates a backward Euler upwinding scheme for the radiation energy density E r and flux F r as well as a modified Godunov scheme for the material density ρ, momentum density m, and energy density E. The backward Euler upwinding scheme is first-order accurate and uses an implicit HLLE flux function to temporally advance the radiation components according to the material flow scale. The modified Godunov scheme is second-order accurate and directly couples stiff source term effects to the hyperbolic structure of the system of balance laws. This Godunov technique is composed of a predictor step that is based on Duhamel’s principle and a corrector step that is based on Picard iteration. The Godunov scheme is explicit on the material flow scale but is unsplit and fully couples matter and radiation without invoking a diffusion-type approximation for radiation hydrodynamics. This technique derives from earlier work by Miniati and Colella (2007) [41]. Numerical tests demonstrate that the method is stable, robust, and accurate across various parameter regimes.

A NEW MECHANISM FOR MASS ACCRETION UNDER RADIATION PRESSURE IN MASSIVE STAR FORMATION

During the formation of a massive star, strong radiation pressure from the central star acts on the dust sublimation front and tends to halt the accretion flow. To overcome this strong radiation pressure, it has been considered that a strong ram pressure produced by a high-mass accretion rate of 10{sup -3} M{sub sun} yr{sup -1} or more is needed. We reinvestigated the necessary condition to overcome the radiation pressure and found a new mechanism for overcoming it. Accumulated mass in a stagnant flow near the dust sublimation front helps the mass accretion by its weight. This mechanism relaxes the condition for the massive star formation. We call this mechanism the 'OMOSHI effect', where OMOSHI is an acronym for 'One Mechanism for Overcoming Stellar High radiation pressure by weIght'. Additionally, in Japanese, OMOSHI is a noun meaning a weight that is put on something to prevent it from moving. We investigate the generation of the OMOSHI effect using local one-dimensional radiation hydrodynamics simulations. The radiation pressure and the gravitational force are connected through the gas pressure, and to sum up, the radiation pressure is balanced or overcome by the gravitational force. We also discuss the global structure and temporal variation ofmore » the accretion flow.« less

Shock-heating of stellar envelopes: a possible common mechanism at the origin of explosions and eruptions in massive stars

Observations of transient phenomena in the Universe reveal a spectrum of mass-ejection properties associated with massive stars, covering from Type II/Ib/Ic core-collapse supernovae (SNe) to giant eruptions of Luminous Blue Variables (LBV) and optical transients. Here, we hypothesize that a fraction of these phenomena may have an explosive origin, the distinguishing ingredient being the ratio of the prompt energy release E_dep to the envelope binding energy E_binding. Using one-dimensional one-group radiation hydrodynamics and a set of 10-25Msun, massive-star models, we explore the dynamical response of a stellar envelope subject to a strong, sudden, and deeply-rooted energy release. Following energy deposition, a shock systematically forms, crosses the progenitor envelope on a day timescale, and breaks-out with a signal of hour-to-days duration and a 10^5-10^11 Lsun luminosity. For E_dep > E_binding, full envelope ejection results with a SN-like bolometric luminosity and kinetic energy, modulations being commensurate to the energy deposited and echoing the diversity of Type II-Plateau SNe. For E_dep ~ E_binding, partial envelope ejection results with a small expansion speed, and a more modest but year-long luminosity plateau, reminiscent of LBV eruptions or so-called SN impostors. For E_dep < E_binding, we obtain a "puffed-up" star, secularly relaxing back to thermal equilibrium. In parallel with gravitational collapse and Type II SNe, we argue that the thermonuclear combustion of merely a few 0.01Msun of C/O could power a wide range of explosions/eruptions in loosely-bound massive stars, as those in the 8-12Msun range, or in more massive ones owing to their proximity to the Eddington limit and/or critical rotation.

Temperature profiles derived from transverse optical shadowgraphy in ultraintense laser plasma interactions at 6×1020 W cm−2

A variety of targets with different dimensions and materials was irradiated using the VULCAN PW laser [C. N. Danson et al., Nucl. Fusion 44, S239 (2004)]. Using transverse optical shadowgraphy in conjunction with a one-dimensional radiation hydrodynamics code it was possible to determine a longitudinal temperature gradient. It was demonstrated for thick targets with a low Z substrate and a thin higher Z tracer layer at the rear that the boundary between the two materials was Rayleigh–Taylor unstable. By including a simple bubble growth model into the calculations it was possible to correct for the associated behavior with regard to temperature. The resulting temperature gradient was in good agreement with the previously published data using two different methods of determining the temperature.

Global existence of strong solutions to the Cauchy problem for a 1D radiative gas

We consider a one-dimensional radiation hydrodynamics model in the case of the equilibrium diffusion approximation which is described by the compressible Navier–Stokes system with the additional terms in the pressure and internal energy respectively, which embody the effect of radiation. Under the physical growth conditions on the heat conductivity, we establish the existence and uniqueness of strong solutions to the Cauchy problem with large initial data, where the initial density and velocity may have differing constant states at infinity. Moreover, we show that if there is no vacuum in the initial density, then, the vacuum and concentration of the density will never occur in any finite time.

X-ray ultraviolet absorption measurements of laser-driven Au∕CH∕Al multilayers

X-ray ultraviolet absorption measurements of aluminum plasma at high temperature and high density are reported. A sample plasma was created by direct laser irradiation of a multilayered foil consisting of Au, CH, and Al. Observations were made using the method of self-backlighting spectroscopy. Simulations were performed with one-dimensional radiation-hydrodynamics code to compute the backlight profile as well as the time history of the density and temperature in the sample. By comparing the measured absorption spectra with detailed-term-accounting calculations at Te=120eV and ρ=0.1g∕cm3, it is found that the major spectral features predicted by calculations have been observed. Even better agreement between the experiment and the simulated absorption spectra was obtained by temporally averaging the radiation-hydrodynamics result over the backlight profile. This experiment shows that it is possible to measure high density and high temperature opacity by a laser-driven multilayer experiment.

Nanosecond spectroscopy of expanding laser-produced tin plasma

Time dependent behavior of laser-produced tin plasma has been investigated using gated optical emission spectroscopy. Plasma was generated by focusing 1.064 m Nd:YAG laser light onto a solid density, planar tin target in vacuum at a laser irradiance of 3.8 × 1011 W/cm2. Estimates of the electron temperature and density were made by assuming Boltzmann distributed population levels and Stark broadened singly ionized tin spectral lines, respectively. An initial temperature of 1.4 eV and density of 4.1 × 1017 cm−3 were calculated from the analysis of spectral data. Experimental data were interpreted alongside numerical results from HYADES - a onedimensional radiation hydrodynamics plasma simulation code. An energy balance was calculated to determine the fraction of incident laser energy converted to directed kinetic energy of expansion.

Simulation of the effects of X-ray emission from accretion disks on the interstellar materials

The thickness of target for X-ray sources with approximate Planck's spectral distribution from laser-produced plasmas is optimized using a one-dimensional radiation hydrodynamics code MULTI. The effect of X-ray radiation field with Planck's distribution on the processes of excitation and ionization in a plasma is stadied using a non-LTE ionized material package NIMP. These results are very important in the future experimental design to study the influence of X-ray emission from accretion disks on interstellar matter.

Emission-line-profile variability as a contraint on the structure and dynamics of hot star winds

We present theoretical calculations of emission-line-profile variability (LPV), based on radiation hydrodynamics simulations of the infamous radiative instability of hot star winds. We demonstrate that spherically symmetric wind structures (shells) cannot account for the observed profile variability at line center. Hence, we resort to a model that breaks-up the wind volume into a number of independent star-centered cones. The essential approximation made here is that each of these cones can be described by a structure calculated with a one-dimensional (1d) radiation hydrodynamics model. Such pseudo-3d ‘patch’-method leads to a satisfactory reproduction of the fundamental characteristics of LPV observed in O-type and Wolf-Rayet star optical spectra: the low-level fluctuations in the profile centre region, a migration of variable sub-peaks from line center to edge, that mimics the underlying wind acceleration. Our method highlights the correlation between the velocity scale of profile sub-peaks at line center and the lateral extent of wind structures, while at line edge it reflects the intrinsic radial velocity dispersion of emitting clumps. However, our model fails to reproduce the increase in this characteristic velocity scale from line center to edge, which we believe is a shortcoming of our purely 1d hydrodynamics approach.

Numerical study of fast ignition of ablatively imploded deuterium–tritium fusion capsules by ultra-intense proton beams

Compression and ignition of deuterium–tritium fuel under conditions relevant to the scheme of fast ignition by laser generated proton beams [Roth et al., Phys. Rev. Lett. 86, 436 (2001)] are studied by numerical simulation. Compression of a fuel containing spherical capsule driven by a pulse of thermal radiation is studied by a one-dimensional radiation hydrodynamics code. Irradiation of the compressed fuel by an intense proton beam, generated by a target at distance d from the capsule center, and subsequent ignition and burn are simulated by a two-dimensional code. A robust capsule, absorbing 635 kJ of 210 eV (peak) thermal x rays, with fusion yield of almost 500 MJ, has been designed, which could allow for target gain of 200. On the other hand, for a reasonable proton spectrum the required proton beam energy Eig, exceeds 25 kJ (for d=4 mm), even neglecting beam losses in the hohlraum and assuming that the beam can be focused on a spot with radius of 10 μm. The effects of proton range lengthening due to the increasing plasma temperature and of beam temporal spread caused by velocity dispersion are discussed. Ways to reduce Eig to about 10 kJ are discussed and analyzed by simulations.

ICF target ignition studies in planar, cylindrical, and spherical geometries

A model for nonlocal α particle transport is implemented in a one-dimensional radiation hydrodynamics code and applied for typical directly and indirectly driven ICF target simulations. Ignition criteria are compared for four configurations; spherical, cylindrical, planar with a central hot spot, and another planar configuration with a hot spot on one side. This last planar configuration is then used for fast ignitor studies, since it is able to simulate hot spot formation by direct laser heating and free expansion towards the incoming beam. Ignition requirements as a function of laser intensity and pulse length, taking into account the relationship between intensity, hot electron temperature, and range, are then determined.

Developing a Radiative Shock Experiment Relevant to Astrophysics.

We report on the initial results of experiments being developed on the Falcon laser to simulate radiative astrophysical shocks. Cylindrically diverging blast waves were produced in low-density ( approximately 1018 cm-3), high-Z gas by laser-irradiating Xe gas jets containing atomic clusters. The blast-wave trajectory was measured by Michelson interferometry. The velocity for the blast wave is slightly less than the adiabatic Sedov-Taylor prediction, and an ionization precursor is observed ahead of the shock front. This suggests energy loss through radiative cooling and reduced compression due to preheat deposited ahead of the shock, both consistent with one-dimensional radiation hydrodynamics simulations.

Two-dimensional simulations of KALIF beam–target interactions

Beam–target interaction experiments performed at the Karlsruhe Light Ion Facility (KALIF) have previously been simulated by one-dimensional (1D) radiation hydrodynamics in slab geometry, which implies a spacially homogeneous beam power distribution. In this paper the consequences of a non-homogeneous beam power distribution are studied by 2D hydrodynamical simulations. It is shown that – for conditions valid at KALIF – time and space resolved measurements of the target back surface velocity can be used to deduce information on the spacial beam profile.

Numerical simulation of ultra-short laser pulse energy deposition and bulk transport for material processing

We have extended the physics of the one-dimensional radiation hydrodynamics simulation code HYADES to include processes important for studying laser–matter interaction with dielectrics and metals in the eV and sub-eV electron temperature range. Ultra-short laser pulses (USLP) are advantageous in many material processing situations where most of the absorbed laser energy appears in mass motion, and little appears as thermal energy. Major additions to the code include (1) the transport, reflection and absorption of laser light, (2) thermal energy transport and improved shockwave physics, and (3) improved models for the equation of state (EOS), strength of materials, and fracture. Examples from material processing and plasma generation were chosen for simulation. Our numerical simulations include the effects of radiation transport, hydrodynamic expansion and shockwave phenomena.

Energetics and symmetry of hohlraum targets driven by ion beam pulses with simple time shape

The energetics of hohlraum targets for inertial fusion are studied by means of one-dimensional radiation hydrodynamics simulations, assuming that a pulse of thermal X-rays with a simple time shape is fed into the cavity. A fusion yield E fus = 160–250 MJ is released by a capsule with fuel mass m DT = 3.3 mg, driven by a two-step pulse. The required input energy is E x ≈ 3.4 MJ for a hohlraum area ratio a = 9 and 6.6 MJ for a = 20, corresponding to gains of G x = E fus/ E x = 50–73 and 25–35 respectively. Higher gains are obtained by three-step pulses. Targets with m DT = 0.4 mg require better-shaped pulses, with at least three steps. Driven by E x = 0.85−1.7 MJ, they release E fus = 8–10 MJ. Symmetry aspects of axially symmetric hohlraums driven by heavy ion beams are studied by a viewfactor code, employing wall motion and re-emissivities provided by the one-dimensional hydro-simulations. The dependence of the capsule irradiation asymmetry on the hohlraum aspect ratio, area ratio and fill density is analyzed. Reductions of wall motion and converter expansion, and the use of shields appear necessary to allow for the use of a moderate area ratio a ≈ 10–15.

HYADES—A plasma hydrodynamics code for dense plasma studies

The one-dimensional radiation hydrodynamics code HYADES was originally developed to simulate laboratory experiments on dense plasmas driven by intense sources of energy. The code was constructed with the objectives of providing a tool that is (1) “easy to use” by an experimentalist, (2) formulated using simple yet accurate numerical approximations to the physics models, (3) easy to modify and extend with new models, and (4) run on a variety of computers including PCs and Macs. Improvements have been made to several of the physics packages, especially the atomic physics and opacity models. Recent additions and modifications have been made to allow more realistic simulations of materials at temperatures below a few eV. These include models for materials with strength, yield, and linear heat conduction. Examples of simulations of two recent laboratory experiments demonstrates the utility of the code.

Thermal X-ray emission from ion-beam-heated matter

The conversion of ion beam energy into thermal x-ray radiation by means of stretched cylindrical plasma volumes is studied by analytic modeling and numerical simulation. The analysis is restricted to one-dimensional radiation hydrodynamics. Scaling relations for different materials are derived. Due to equation-of-state properties, high-Z material turns out superior for achieving high conversion efficiency. The paper provides practical answers for thermal x-ray generation with intense heavy ion beams. Deposition powers in the order of 10 16 W/g are required for applications to ion beam inertial confinement fusion.

Thermal X-Ray Emission from Ion-Beam-Heated Matter

The conversion of ion beam energy into thermal x-ray radiation by means of stretched cylindrical plasma volumes is studied by analytic modeling and numerical simulation. The analysis is restricted to one-dimensional radiation hydrodynamics. Scaling relations for different materials are derived. Due to equation-of-state properties, high-Z material turns out superior for achieving high conversion efficiency. The paper provides practical answers for thermal x-ray generation with intense heavy ion beams. Deposition powers in the order of 10l6 W/g are required for applications to ion beam inertial confinement fusion.

MULTI — A computer code for one-dimensional multigroup radiation hydrodynamics

The basic physical equations as well as a computer code for the simulation of one-dimensional radiation hydrodynamics are described. The hydrodynamic equations are combined with a multigroup method for the radiation transport. The code, written in standard FORTRAN-77, is characterized by one-dimensional planar geometry with multilayer structure. A time-splitting schema has been adopted with implicit finite-differencing formulation (including the hydrodynamics), and Lagrangian coordinates. Tabulated equations of state and opacities are used.