Equilibrium and stability in a high-current discharge in a dense plasma under conditions of radiative conduction

Equilibrium and stability are examined for a high-current self-compressed discharge:in a dense, optically opaque plasma of finite conductivity, with allowance for dissipation via radiative heat transfer. If the thermal conductivity is high, the plasma temperature is virtually constant throughout the cross-section of the discharge, whereas the density and pressure fall off fairly rapidly away from the axis. The spectrum for small oscillations shows that such an equilibrium discharge is unstable with respect to short-wave hydrodynamic oscillations (bending and necking) if the plasma conductivity is low. Instability can develop only for long-wave perturbations in a cylindrical discharge, and also for a nonequilibrium discharge when the rise time is iess than the equilibration time. A planar equilibrium discharge is stable, while a cylindrical equilibrium discharge in a dense low-temperature plasma is more stable than one in a high-temperature plasma.There have been several discussions of the use of high-current discharges in dense plasmas as light sources for laser pumping. The choice of discharge dimensions is governed by the temperature T of the radiating surface, which should be 3–10 eV. Only ohmic heating can allow one to keep a plasma at such a temperature for a sufficiently long time (around 100 vsec). On the other hand, hydrodynamic instabilities (bends, necks, hot spots) can arise in a dense plasma carrying a current, which can lead to current interruption and plasma dispersal (see [1] for literature). Stability is therfore a major problem in the use of such discharges as light sources. However, it is not correct to apply the theory of [1] to such discharges, since this theory is for a not very dense, hot. transparent plasma under conditions such that radiation does not play a major part in the development of the discharge, whereas a discharge in a dense, optically opaque plasma is best as a light source. Such a plasma can have considerable radiative energy transfer, which can influence the entire character of the discharge. Moreover, effects due to the finite conductivity (diffusion of electric and magnetic fields) may play major parts at these relatively low temperatures. Here we present a theoretical discussion of the equilibrium and stability of a high-current discharge in a dense, optically opaque plasma having a finite conductivity and considerable radiative heat transfer.We are indebted to G. V. Mikhailov and V. B. Rozanov for many discussions.     

Equilibrium and stability theory of a power discharge in a dense optically transparent plasma

The equilibrium and stability of a power discharge in a dense optically transparent plasma is examined. It is shown that, contrary to the case of an optically nontransparent plasma, the temperature of a transparent discharge varies along the same characteristic scales as the other hydrodynamic quantities. Analysis of small oscillation spectra showed that such a discharge is unstable even within the framework of the geometrical optics approximation. The major portion of this paper is devoted to a study of the stability of a discharge with allowance only for bremsstrahlung; however, the conditions for the onset of instability are derived also for other types of radiation. Under the conditions studied, the general cause for the development of instabilities in a discharge in a transparent plasma is superheating that results from the inability of the weak emitted heat flux to compensate for the joule heating of the plasma. The utilization of optically nontransparent power discharges in dense plasmas as light sources for pumping lasers was discussed in [1]. In particular, the study made it possible to determine the discharge parameters for which a discharge stability sufficiently long for this purpose can be obtained for a required radiation intensity from the surface. In the present paper a theory is developed for an optically transparent plasma, in the case in which most of the radiation is transported by quanta with mean free path ecceeding the characteristic dimensions of the system. The study of the equilibrium and stability of a transparent discharge is not solely of interest as such. It contributes to a better understanding of processes occurring at the boundary of a nontransparent discharge. Owing to the drop in particle density near the boundary of the nontrans parent discharge, a transparent plasma layer is created for which the radiant (heat) transport approximation employed in [1] is no longer valid. The structure and stability of such a boundary can be analyzed on the basis of the results of this paper. Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 5, pp. 18–25, 1968.     

Toward an accurate numerical simulation of radiation hydrodynamics in laser ablation plasmas

A radiation hydrodynamics code has been developed for more accurate prediction of laser-produced low-density ablation plasmas with appropriately describing anisotropic radiation field by using Monte-Carlo technique for variable Eddington tensor with reasonable computational loads. The Eddington tensor estimated by thousand of sample particles per single fluid step can reproduce the anisotropic radiation field in the low-density region and will not result in large computational consumption. Prediction of the emitted light from ablation plasma can be corrected by the proposed method. Ablation structure sustained by a compact radiation source, which is sometimes found in experiments of collisionless shock relevant to laboratory astrophysics, may also be changed by anisotropic transfer computation in optically thin region.     

Non-LTE radiation transport in high radiation plasmas

A primary goal of numerical radiation transport is obtaining a self-consistent solution for both the radiation field and plasma properties, which requires consideration of the coupling between the radiation and the plasma. The different characteristics of this coupling for continuum and line radiation have resulted in two separate sub-disciplines of radiation transport with distinct emphases and computational techniques. LTE radiation transfer focuses on energy transport and exchange through broadband radiation, primarily affecting temperature and ionization balance. Non-LTE line transfer focuses on narrowband radiation and the response of individual level populations, primarily affecting spectral properties. Many high energy density applications, particularly those with high-Z materials, incorporate characteristics of both these regimes. Applications where the radiation fields play an important role in the energy balance and include strong line components require a non-LTE broadband treatment of energy transport and exchange.We discuss these issues and present a radiation transport treatment which combines features of both approaches by explicitly incorporating the dependence of material properties on both temperature and radiation fields. The additional terms generated by the radiation dependence do not change the character of the system of equations and can easily be added to a numerical transport implementation. A numerical example from a Z-pinch application demonstrates that this method improves both the stability and convergence of the calculations. The information needed to characterize the material response to radiation is closely related to that used by the linear response matrix (LRM) approach to near-LTE simulation, and we investigate the use of the LRM for these calculations.     

Advances in NLTE modeling for integrated simulations

The last few years have seen significant progress in constructing the atomic models required for non-local thermodynamic equilibrium (NLTE) simulations. Along with this has come an increased understanding of the requirements for accurately modeling the ionization balance, energy content and radiative properties of different atomic species for a wide range of densities and temperatures. Much of this progress is the result of a series of workshops dedicated to comparing the results from different codes and computational approaches applied to a series of test problems. The results of these workshops emphasized the importance of atomic model completeness, especially in doubly-excited states and autoionization transitions, to calculating ionization balance, and the importance of accurate, detailed atomic data to producing reliable spectra.We describe a simple screened-hydrogenic model that calculates NLTE ionization balance with sufficient accuracy, at a low enough computational cost for routine use in radiation-hydrodynamics codes. The model incorporates term splitting, Δn = 0 transitions, and approximate UTA widths for spectral calculations, with results comparable to those of much more detailed codes. Simulations done with this model have been increasingly successful at matching experimental data for laser-driven systems and hohlraums.Accurate and efficient atomic models are just one requirement for integrated NLTE simulations. Coupling the atomic kinetics to hydrodynamics and radiation transport constrains both discretizations and algorithms to retain energy conservation, accuracy and stability. In particular, the strong coupling between radiation and populations can require either very short time steps or significantly modified radiation transport algorithms to account for NLTE material response. Considerations such as these continue to provide challenges for NLTE simulations.     

Equilibrium and stability of a cylindrical linear pinch with a homogeneous temperature distribution

The equilibrium and stability of a high-current discharge have been theoretically investigated in a dense optically gray plasma. The plasma is assumed to be completely opaque to longwave photons and completely transparent to short-wave photons. The threshold frequency is determined by setting the diameter of the plasma pinch equal to the mean free path of the photons. We solve the equations of magnetohydrodynamics together with the equation of radiative transfer. We show that in a gray plasma an equilibrium state can exist with a practically homogeneous temperature distribution over the discharge cross section. Temperature homogeneity is ensured by the large radiant thermal conductivity, which is related to the longwave radiation. The radiant thermal conductivity also causes the discharge to be stable with respect to superheating. We analyze the possibility of using such a discharge for the energy pumping of a laser. We show that for discharge currents of order 10⁶ A, the efficiency of a gray discharge exceeds the efficiency of an opaque discharge by a factor of three.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 33–39, January–February, 1971.     

超高速碰撞产生的电磁辐射

超高速碰撞产生的电磁辐射是固体物质在强冲击作用下的重要物理响应,在深空探测、航天器对空间碎片的防护设计、武器毁伤评估应用广泛。本文中概述了超高速碰撞产生的电磁辐射现象,总结了不同碰撞条件下,超高速碰撞产生微波和闪光的时频特性;从超高速碰撞产生材料破碎和产生等离子体两个方面,分析了超高速碰撞产生微波的辐射模型;归纳了超高速碰撞下的发光机理,并阐述了超高速碰撞产生连续光谱和线谱的辐射模型,指出了超高速碰撞产生电磁辐射研究存在的不足与发展趋势。     

一种基于图乘的变刚度直杆位移计算折算技巧1)

为解决图乘法计算变截面杆件位移时分割图形数目多,计算容易出错这一问题,提出了一种刚度折算的方法,把长度已知的变截面杆件等价转换为两个一定长度的等截面杆件,通过刚度与位移的关系进行折算,然后叠加即可得到正确结果。可显著减少图乘次数,降低计算量,提高计算效率和正确率,值得推广。     

Opacity calculation for target physics using the ABAKO/RAPCAL code

Radiative properties of hot dense plasmas remain a subject of current interest since they play an important role in inertial confinement fusion (ICF) research, as well as in studies on stellar physics. In particular, the understanding of ICF plasmas requires emissivities and opacities for both hydro-simulations and diagnostics. Nevertheless, the accurate calculation of these properties is still an open question and continuous efforts are being made to develop new models and numerical codes that can facilitate the evaluation of such properties. In this work the set of atomic models ABAKO/RAPCAL is presented, as well as a series of results for carbon and aluminum to show its capability for modeling the population kinetics of plasmas in both LTE and NLTE regimes. Also, the spectroscopic diagnostics of a laser-produced aluminum plasma using ABAKO/RAPCAL is discussed. Additionally, as an interesting application of these codes, fitting analytical formulas for Rosseland and Planck mean opacities for carbon plasmas are reported. These formulas are useful as input data in hydrodynamic simulation of targets where the computation task is so hard that in line computation with sophisticated opacity codes is prohibitive.     

Mathematical analysis of the radiation from a magnetic line source on a cylindrically capped wedge covered by a plasma sheath

Summary Radial eigenfunctions appropriate for the dielectric (or plasma) layered medium and air are used to obtain an exact solution of the problem of radiation from a magnetic line source (or a slotted antenna) on a conducting infinite wedge with a cylindrical cap covered by a dielectric (or plasma) sheath. In order to satisfy the boundary conditions at the interfaces between the dielectric (or plasma) and the air, it is necessary to expand the radial eigenfunctions of one medium in terms of those of the other.This method can be used to solve any other two dimensional diffraction or radiation problem involving a cylindrically capped wedge surrounded by a dielectric (or plasma) sheath.     

Relationship between multibody dynamics computation and nonlinear vibration theory

This paper presents the ground-work of implementing the multibody dynamics codes to analyzing nonlinear coupled oscillators. The recent developments of the multibody dynamics have resulted in several computer codes that can handle large systems of differential and algebraic equations (DAE). However, these codes cannot be used in their current format without appropriate modifications. According to multibody dynamics theory, the differential equations of motion are linear in the acceleration, and the constraints are appended into the equations of motion through Lagrange's multipliers. This formulation should be able to predict the nonlinear phenomena established by the nonlinear vibration theory. This can be achieved only if the constraint algebraic equations are modified to include all the system kinematic nonlinearities. This modification is accomplished by considering secondary nonlinear displacements which are ignored in all current codes. The resulting set of DAE are solved by the Gear stiff integrator. The study also introduced the concept of constrained flexibility and uses an instantaneous energy checking function to improve integration accuracy in the numerical scheme. The general energy balance is a single scalar equation containing all the energy component contributions. The DAE solution is then compared with the solution predicted by the nonlinear vibration theory. It also establishes new foundation for the use of multibody dynamics codes in nonlinear vibration problems. It is found that the simulation CPU time is much longer than the simulation of the original equations of the system.     

New parametrization for differences between plasma kinetic codes

Validation and verification of plasma kinetics codes requires the development of quantitative methods and techniques for code comparisons. We describe two parameters that can be used for characterization of differences between such codes. It is shown that these parameters, which are determined from the most general results of kinetic codes, can provide important information on the differences between the basic rate coefficients employed. Application of this method is illustrated by comparisons of some results from the 3rd NLTE Code Comparison Workshop for carbon, germanium, and gold plasmas.     

铰接门式刚架柱的计算长度系数

采用中性平衡法分析了5榀铰接门式刚架的稳定性,通过理论分析和规范方法计算了刚架柱的计算长度系数. 计算结果表明: 中性平衡法分析结果与有限元法的结果一致;按规范规定,摇摆柱的计算长度系数为1,但分析结果都大于1;对刚架柱,各规范或规程的计算结果不仅相差较大,而且与中性平衡法的分析结果相差也比较大. 说明规范方法并不适用计算铰接门式刚架的稳定性,对于此类刚架应该通过稳定分析获得刚架柱计算长度系数.     

From lasers to the universe: Scaling laws in laboratory astrophysics

In this work scaling laws in laboratory astrophysics are studied. It is shown that mathematical models governing radiation hydrodynamics-driven phenomena are invariant under the homothetic group transformation and can be rescaled according to several types of scaling laws. This property is valid for both optically thick and optically thin materials and it allows a correct and rigorous connection between astrophysical objects or phenomena and laboratory experiments. This approach is applied to astrophysical jets and radiative shocks where advantages as well as difficulties are pointed out.     

Buckling of sandwich wide columns

The paper deals with the theoretical prediction of buckling loads for sandwich columns with metallic and laminated facings and foam or honeycomb core. The loading is a uniform axial compression, applied statically (very slowly) and suddenly with constant magnitude and infinite duration (step loading). The effect of length and boundary conditions is assessed and results are presented for the following cases: for a cantilever column, a simply supported column and a clamped column, for several lengths. Several fiber materials are used in the laminated facings. Two types of core were examined: alloy-foam or hexagonal glass/phenolic honeycomb. The facings are Boron/Epoxy, Graphite/Epoxy and Kevlar/Epoxy laminates with 0° orientation with respect to the column axis and a metallic one made out of aluminum. These various materials are employed to provide comparative data that can be used in design. Results, for the static case are generated by computer codes as well as by the use of closed form theoretical solutions. For the dynamic case, results are generated by the DYNA3D code.     

Development of co-current air–water flow in a vertical pipe

Measurements of the cross-sectional distribution of the gas fraction and bubble size distributions were conducted in a vertical pipe with an inner diameter of 51.2 mm and a length of about 3 m for air/water bubbly and slug flow regimes. The use of a wire-mesh sensor obtained a high resolution of the gas fraction data in space as well as in time. From this data, time averaged values for the two-dimensional gas fraction profiles were decomposed into a large number of bubble size classes. This allowed the extraction of the radial gas fraction profiles for a given range of bubble sizes as well as data for local bubble size distributions. The structure of the flow can be characterized by such data. The measurements were performed for up to 10 different inlet lengths and for about 100 combinations of gas and liquid volume flow rates. The data is very useful for the development and validation of meso-scale models to account for the forces acting on a bubble in a shear liquid flow and models for bubble coalescence and break-up. Such models are necessary for the validation of CFD codes for the simulation of bubbly flows.     

Approximate analysis for transient heat conduction with radiation in a slab

In an attempt to minimize the numerical computations associated with the solution of transient heat conduction with radiation in a slab, a perturbation type of analysis is being applied to the temperature field and radiation heat flux simultaneously. The resulting partial differential equations for the perturbation functions for the temperature are solved in explicit forms by use of the energy integral methods, while the radiation heat flux is determined by an appropriate scheme of approximating the temperature distribution in the slab. Included in the analysis are the effects of the parameters: the optical thickness, the ratio of conduction transport to radiation and the wall emissivity. It is found that, in a wide range of these governing parameters, the results compare very favorably with those obtained by the numerical solution of the formulated integro-differential equation. With the present analysis, the temperature, conduction and radiation heat fluxes can be predicted without resorting to lengthy numerical analysis.     

Prigogine theorem of minimum entropy production applied to the average-atom model

Thermodynamics of irreversible processes is applied to study the interaction of matter and a radiation field in non-local thermodynamic equilibrium within the framework of the average-atom model. The rate of entropy production of matter and the radiation field, in contact with a free electron reservoir in local thermodynamic equilibrium, is obtained using conjugates of the state variables. The average-atom one-electron populations are determined by minimizing the rate of entropy production at fixed electronic density, electronic temperature, and radiation field. Numerical results and comparisons with experiment for a photoionized iron plasma are presented and discussed. Our approach, which is based on first principles, can be used in a large variety of non-local thermodynamic equilibrium situations.