Zeus-2D Simulations of Laser-Driven Radiative Shock Experiments

A series of experiments is underway using the Omega laser to examine radiative shocks of astrophysical relevance. In these experiments, the laser accelerates a thin layer of low-Z material, which drives a strong shock into xenon gas. One-dimensional numerical simulations using the HYADES radiation hydrodynamics code predict that radiation cooling will cause the shocked xenon to collapse spatially, producing a thin layer of high density (i.e., a collapsed shock). Preliminary experimental results show a less opaque layer of shocked xenon than would be expected assuming that all the xenon accumulates in the layer and that the X-ray source is a pure Kα source. However, neither of these assumptions is strictly correct. Here we explore whether radial mass and/or energy transport may be significant to the dynamics of the system. We report the results of two-dimensional numerical simulations using the ZEUS-2D astrophysical fluid dynamics code. Particular attention is given to the simulation method.     

Density and Temperature Measurements on Laser Generated Radiative Shocks

This paper presents some recent measurements on radiative shocks generated in a xenon gas cell using high power laser. We show new results on temperature and electronic density, and on radial expansion of the shock at various initial conditions (laser energy and gas pressure). The data obtained are compared with one-dimensional and two-dimensional hydro simulations.     

Novel Diagnostic of Shock Fronts in Low-Z Dense Plasmas

We performed an experiment using high-energy protons to characterize in situ the spatial and temporal evolution of a laser-driven shock propagating through a low-Z material. Radiography of the shock propagating through the low-Z transparent material (Lexan, quartz, diamond) enabled estimation of density under compression. In order to discriminate the influence of the shocked matter on the protons trajectory, a Monte-Carlo simulation was developed. This code describes the protons trajectory through the matter, calculating the scattering angle and the loss of energy.     

Radiative bulk viscosity

Viscous resistance to changes in the volume of a gas arises when different degrees of freedom have different relaxation times. Collisions tend to oppose the resulting departures from equilibrium and, in so doing, generate entropy. Even for a classical gas of hard spheres, when the mean free paths or mean flight times of constituent particles are long we find a non-vanishing bulk viscosity. Here we apply a method recently used to uncover this result for a classical rarefied gas to radiative transfer theory, and derive an expression for the radiative stress tensor for a grey medium with absorption and Thomson scattering. We determine the transport coefficients through the calculation of the comoving entropy generation. When scattering dominates absorption, the bulk viscosity may be much larger than either the shear viscosity or the thermal conductivity.     

Laboratory Simulations of Bow Shocks and Magnetospheres

Laboratory experiments using a plasma wind generated by laser-target interaction are proposed and analyzed to investigate the creation of a shock in front of the magnetosphere and the dynamo mechanism. The proposed experiments and simulations are thought to be relevant to understanding the electron acceleration mechanisms at work in shock-driven magnetic dipole confined plasma in compact magnetized stars.     

Catastrophic cooling diagnostics

This paper presents models of optical emission line features that characterise catastrophic cooling in radiative shocks. The computations are based on a 1-D magnetohydrodynamic model. Runaway cooling results in the formation of secondary shocks which travel through the previously shocked cooling layer. Several filaments of emission with specific properties and spectral signatures are produced.     

Investigating the Astrophysical Applicability of Radiative and Non-Radiative Blast wave Structure in Cluster Media

We describe experiments that investigate the capability of an experimental platform, based on laser-driven blast waves created in a medium of atomic clusters, to produce results that can be scaled to astrophysical situations. Quantitative electron density profiles were obtained for blast waves produced in hydrogen, argon, krypton and xenon through the interaction of a high intensity (I ≈ 10¹⁷ Wcm⁻²), sub-ps laser pulse. From this we estimate the local post-shock temperature, compressibility, shock strength and adiabatic index for each gas. Direct comparisons between blast wave structures for consistent relative gas densities were achieved through careful gas jet parameter control. From these we investigate the applicability of different radiative and Sedov-Taylor self-similar solutions, and therefore the (ρ,T) phase space that we can currently access.     

Radiative transfer effects in rotationally distorted stars

A general expression for the gravity darkening of the tidally and non-uniformly rotating Roche components of close binary systems is used to calculate the uniform rotational effects on line profiles in an expanding atmosphere. We consider a non-local thermodynamic equilibrium (non-LTE) two-level atom approximation in an extended atmosphere, and use Von Zeipel's theorem for the incident radiation at the maximum optical depth  (τ=τ_max)  in the atmosphere. These calculations are performed with uniform rotational velocities of 1, 4 and 8 mtu (mean thermal units). It is found that rotation dilutes the radiation field which is similar to the expansion velocity.
We also study rotational aspects, which make the outer layers of the star distorted. The equation of line transfer is solved in the comoving frame of the expanding atmosphere of the primary using complete redistribution in the line. We use a linear law for the velocity of expansion such that the density varies as r ⁻³, where r is the radius of the star, satisfying the law of conservation of mass. It is found that rotation broadens the line profile, and P-Cygni-type line profiles are obtained.     

Radiative Transfer in Inhomogeneous Atmospheres. II

This paper is a continuation of a study of radiative transfer in one-dimensional inhomogeneous atmospheres. Two of the most important characteristics of multiple scattering in these media are calculated: the photon escape probability and the average number of scattering events. The latter is determined separately for photons leaving the medium and for photons that have undergone thermalization in the medium. The problem of finding the radiation field in an inhomogeneous atmosphere containing energy sources is also examined. It is assumed that the power of these sources, as well as the scattering coefficient, can vary arbitrarily with depth. It is shown that knowledge of the reflection and transmission coefficients of the atmosphere makes it possible to reduce all these problems to solving some first order linear differential equations with specified initial conditions. A series of new analytic results are obtained. Numerical calculations are done for two types of atmosphere with different depth dependences for the scattering coefficient. These are interpreted physically.     

Radiative Transfer in Inhomogeneous Atmospheres. I

This series of papers is devoted to multiple scattering of light in plane parallel, inhomogeneous atmospheres. The approach proposed here is based on Ambartsumyan's method of adding layers. The main purpose is to show that one can avoid difficulties with solving various boundary value problems in the theory of radiative transfer, including some standard problems, by reducing them to initial value problems. In this paper the simplest one dimensional problem of diffuse reflection and transmission of radiation in inhomogeneous atmospheres with finite optical thicknesses is considered as an example. This approach essentially involves first determining the reflection and transmission coefficients of the atmosphere, which, as is known, are a solution of the Cauchy problem for a system of nonlinear differential equations. In particular, it is shown that this system can be replaced with a system of linear equations by introducing auxiliary functions P and S. After the reflectivity and transmissivity of the atmosphere are determined, the radiation field in it is found directly without solving any new equations. We note that this approach can be used to obtain the required intensities simultaneously for a family of atmospheres with different optical thicknesses. Two special cases of the functional dependence of the scattering coefficient on the optical thickness, for which the solutions of the corresponding equations can be expressed in terms of elementary functions, are examined in detail. Some numerical calculations are presented and interpreted physically to illustrate specific features of radiative transport in inhomogeneous atmospheres.     

Radiative Transfer in Inhomogeneous Atmospheres. III

The approach proposed in the previous parts of this series of papers is used to solve the radiative transfer problem in scattering and absorbing multicomponent atmospheres. Linear recurrence relations are obtained for both the reflectance and transmittance of these kinds of atmospheres, as well as for the emerging intensities when the atmosphere contains energy sources. Spectral line formation in a one-dimensional inhomogeneous atmosphere is examined as an illustration of the possibility of generalizing our approach to the matrix case. It is shown that, in this case as well, the question reduces to solving an initial value problem for linear differential equations. Some numerical calculations are presented.     

Radiative Shocks in Astrophysics and the Laboratory

This paper explores the variations in radiative shock behavior originating from the properties of the system containing the shock. Specifically, the optical depth of the upstream region and the downstream region both affect the behavior of radiative shocks. Optically thick systems such as stellar interiors or supernovae permit only limited shock-induced increases in density. At the other limit, the radiation and shock dynamics in optically thin systems permits the post-shock density to reach arbitrarily large values. The theory of the shock structure is summarized for systems in which the upstream region is optically thin, common to some astrophysical systems and a number of experiments.     

Numerical Treatment of Radiative Transfer

We present a numerical treatment of radiative transfer in three dimensions. The radiation is modeled by the grey moment M ₁ system. The introduced scheme is able to compute accurate numerical solutions over a broad class of regimes from the transport to the diffusive limit. We discuss numerical issues concerning the resolution and the parallelization of this scheme for multi-dimensional simulations. Several numerical results are then presented, which show that this approach is robust and have the correct behavior in both the diffusive and free-streaming limits. We also present a comparison in two dimensions of our code with a Monte-Carlo transfer code.     

Hybrid Simulation of Collisionless Shock Formation in Support of Laboratory Experiments at Unr

The problem of producing collisionless shocks in the laboratory is of great interest for space and astrophysical plasmas. One approach is based on the idea of combining strong magnetic field (up to 100 Tesla) created during a Z-pinch discharge with a plasma flow produced in the process of the interaction of a laser pulse with a solid target. In support of laboratory experiments we present hybrid simulations of the interaction of the plasma flow with frozen in it magnetic field, with the spherical obstacle. Parameters of the flow correspond to a laser plasma ablation produced in the laboratory during irradiation of the target by a 3 J laser. Magnetic fields in the plasma flow and around the obstacle are created by the currents produced by the pulse power ZEBRA voltage generator. With the appropriate set of initial conditions imposed on the flow collisionless shocks can be created in such a system. Using independent generators for plasma flow and magnetic field allows for the exploration of a wide range of shock parameters. We present simulations of the formation of supercritical collisionless shock relevant to the experiment, performed with the 2D version of the hybrid code based on the CAM-CL algorithm [Planet. Space Sci. 51, 649, 2003].     

Density Measurements of Shock Compressed Matter Using Short Pulse Laser Diagnostics

In this paper, experimental results on X-ray and proton radiography of shock compressed matter are presented. It has been performed at the Rutherford Appleton Laboratory (RAL) using three long pulse beams to generate a shock wave in a multi-layer foil and a short pulse beam to create either an X-ray or protons source for a transverse radiography. Depending on the probe material (aluminium or carbon foam) a Molybdenum Kα source or a proton beam are used. Density data of the shocked aluminium, in the multimagabar regime are presented.     

Structure of Radiative Shock Waves in Stellar Atmospheres

A global iteration method to determine the self-consistent structure of steady plane-parallel radiative shock waves is shown to converge to the stable solution with upstream front velocities of 15 km/s ≤ U ₁≤ 60 km/s and for hydrogen gas of unperturbed temperature T= 3000 K and density ρ = 10⁻¹⁰gcm⁻³. This revised version was published online in July 2006 with corrections to the Cover Date.