Equation of state of fluid helium at high temperatures and densities

Hugoniot curves and shock temperatures of gas helium with initial temperature 293 K and three initial pressures 0.6, 1.2, and 5.0 MPa were measured up to 15000 K using a two-stage light-gas gun and transient radiation pyrometer. It was found that the calculated Hugoniot EOS of gas helium at the same initial pressure using Saha equation with Debye-Hückel correction was in good agreement with the experimental data. The curve of the calculated shock wave velocity with the particle velocity of gas helium which is shocked from the initial pressure 5 MPa and temperature 293 K, i.e., theD ≈u relation,D=C ₀+λu (u<10 km/s, λ=1.32) in a low pressure region, is approximately parallel with the fittedD ≈u (λ=1.36) of liquid helium from the experimental data of Nellis et al. Our calculations show that the Hugoniot parameter λ is independent of the initial density p{in0}. TheD≈u curves of gas helium will transfer to another one and approach a limiting value of compression when their temperature elevates to about 18000 K and the ionization degree of the shocked gas helium reaches 10⁻³.     

Equation of state of fluid helium at high temperatures and densities

Helium, hydrogen, and their isotopes are the simplest monoatomic and diatomic molecules. It is relatively easy to describe their properties using the basic principles of quantum mechanics. In condensed matter physics, hydrogen and helium serve as the models for the condensed matter properties at extreme conditions so that both experi- mental and theoretical physicists pay much attention to the study of their properties[1], especially the insulator-metal transition of hydrogen[2]. The aim to st…     

Simulations of shock waves in solids

Molecular dynamic shock wave simulations have been carried out for face centered cubic (f.c.c.) and body centered cubic (b.c.c.) solids using Lennard-Jones and Morse potentials for the interatomic interactions. The Hugoniot conservation relations were accurately obeyed in all of these calculations. The shock wave profiles may vary with the interatomic potential and the crystal structure, effects most clearly shown by the temperature profile near the shock front. The Lennard-Jones solids are intensitive to a change in structure but the Morse solids appear sensitive to crystal structure, at least in comparing b.c.c. with f.c.c. It was shown that the average shock wave temperature can be calculated from a combination of the Hugoniot conservation relations and the Mie-Grüneisen equation of state. The temperature calculated this way is in good agreement with the average shock wave temperature obtained in the computer simulations.     

A caloric equation of state of a condensed medium derived based on generalized Hugoniot curves

The caloric equation of state, which expresses the internal energy through the volume and pressure is required in analyzing and calculating shock-wave processes in reacting media. The present work develops a method for constructing such an equation for condensed media on the basis of generalized Hugoniot curves. Expressions approximating the dependence of the Grüneisen coefficient and pressure on the volume along the Hugoniot curve. Formulas for calculating detonation Hugoniot curves from the shock Hugoniot curve of the condensed reaction products. The expressions obtained can be applied to approximate calculations of shockwave processes (for example, gasless detonation) in reacting condensed media. If necessary, such calculations can be performed with the use of physical quantities from standard handbooks.     

Electron kinetics in collisionless shock waves

We study the kinetic model of the formation of the energy spectrum of nonthermal electrons near the front of a quasilongitudinal, supercritical, collisionless shock wave. Nonresonant interactions of the electrons and the fluctuations generated by kinetic instabilities of the ions in the transition region inside the shock front play the main role in the heating and preacceleration of electrons. We calculate the electron energy spectrum in the vicinity of the shock wave and show that the heating and preacceleration of electrons occur on a scale of the order of several hundred ion inertial lengths in the vicinity of the viscous discontinuity. Although the electron distribution function is significantly nonequilibrium near the shock front, its low-energy part can be approximated by a Maxwellian distribution. The effective electron temperature T _eff ² behind the front, obtained in this manner, increases with the Mach number of the shock wave slower than it would if it followed the Hugoniot adiabat. We determine the condition under which the electron heating is ineffective but the electrons are effectively accelerated to high energies. The high-energy asymptotic behavior of the distribution function is that of a power law, with the exponent determined by the total compression ratio of the plasma, as in the case of acceleration by the first-order Fermi mechanism. The model is used to describe the case (important for applications) of acceleration of electrons by shock waves with large total Mach numbers, with the structure of these waves modified by the nonlinear interaction of nonthermal ions and consisting of an extended prefront with a smooth variation of the macroscopic parameters and a viscous discontinuity in speed with a moderate value of the Mach number. Zh. éksp. Teor. Fiz. 115, 846–864 (March 1999)     

反向碰撞法测量Bi的低压Hugoniot数据

在火炮和二级轻气炮上利用反向碰撞技术,通过测量飞片击靶速度以及飞片/窗口的界面粒子速度,获得了金属铋(Bi)在10-45 GPa压力范围内的Hugoniot数据. 该方法克服了电探针法在测量低压Hugoniot数据时由于导通一致性差而不能准确得到冲击波速度的难题,同时又避免了精确测量样品中冲击波走时的问题. 实验获得的冲击波速度(D)-波后粒子速度(u)Hugoniot数据表明,Bi在粒子速度u=0.9 km/s附近D-u曲线发生了明显拐折,产生这一拐折的原因推测与冲击导致的Bi的固-液相变有关. 关键词： Hugoniot数据 反向碰撞 冲击相变 铋     

Effect of radiation on compressibility of hot dense sodium and iron plasma using improved screened hydrogenic model with l splitting

High pressure investigations of matter involve the study of strong shock wave dynamics within the materials which gives rise to many thermal effects leading to dissociation of molecules, ionization of atoms, and radiation emission, etc.The response of materials experiencing a strong shock can be determined by its shock Hugoniot calculations which are frequently applied in numerical and experimental studies in inertial confinement fusion, laboratory astrophysical plasma,etc. These studies involve high energy density plasmas in which the radiation plays an important role in determining the energy deposition and maximum compressibility achieved by the shock within material. In this study, we present an investigation for the effect of radiation pressure on the maximum compressibility of the material using shock Hugoniot calculations. In shock Hugoniot calculations, an equation of state(EOS) is developed in which electronic contributions for EOS calculations are taken from an improved screened hydrogenic model with-l splitting(I-SHML) [High Energy Density Physics(2018) 26 48] under local thermodynamic equilibrium(LTE) conditions. The thermal ionic part calculations are adopted from the state of the art Cowan model while the cold ionic contributions are adopted from the scaled binding energy model. The Shock Hugoniot calculations are carried out for sodium and iron plasmas and our calculated results show excellent agreement with published results obtained by using either sophisticated self-consistent models or the first principle study.     

Hugoniot curve of urea

Various approaches to describing the Hugoniot curve for urea were considered. A satisfactory agreement with experimental data was obtained under the assumption that a polymorphous transformation of urea occurred behind the shock wave front.     

Superelasticity and the propagation of shock waves in crystals

The separation of a shock wave into an elastic precursor and a plastic wave is a characteristic phenomenon occurring only in solid media. The existence of the elastic shock wave at pressures p ≈ 10 GPa, which is one or two orders of magnitude higher than the dynamic elastic limit, has been detected in recent numerical calculations and a femtosecond laser experiment. The plastic shock wave has no time to be formed in these ultrashort waves at p ≈ 10 GPa. The processes of the formation and propagation of the elastic and plastic waves in aluminum at higher pressures obtained by means of femtosecond lasers have been analyzed in this work. It has been found that the elastic precursor survives even under the conditions when the pressure behind the plastic front reaches a giant value p ∼ 1 Mbar at which the melting of the metal begins. It has been shown that superelasticity should be taken into account to correctly interpret the preceding laser experiments.     

冲击加载下Zr51Ti5Ni10Cu25Al9金属玻璃的塑性行为

进行了10—27 GPa应力范围内Zr₅₁Ti₅Ni₁₀Cu₂₅Al₉金属玻璃的平面冲击实验以研究其高压-高应变率加载下的塑性行为.由样品自由面粒子速度剖面的分析获得了冲击加载过程的轴向应力,并通过轴向应力与静水压线的比较获得剪应力.实验结果表明,尽管存在明显的松弛效应,但Zr基金属玻璃的Hugoniot弹性极限随着冲击应力的增加而增加.然而,塑性波阵面上的剪应力则显示先硬化而后软化现象,而且软化的幅度随冲击应力的增加而增加.冲击加载下Zr基金属玻璃的上述剪应力变化特征与分子动力学模拟结果比较一致,但与压剪实验结果和一维应力冲击实验结果明显不同.     

利用多层阻抗梯度飞片产生准等熵压缩的理论解析

基于冲击波理论对多层阻抗梯度飞片击靶过程波系的相互作用做了理论分析，计算表明在多层阻抗梯度飞片的撞击下，样品的压缩线是一组通过不同初始状态点的冲击压缩线的连线, 它位于冲击压缩(hugoniot)线与等熵压缩线之间. 所以通过飞片层数的设计,可获得介于冲击压缩线与等熵线之间的任意状态点,这就为以后偏冲击压缩(off-hugoniot)状态方程的实验研究提供了理论参考. 实验测量的样品/窗口界面速度与理论计算的一致性支持上述结论的可靠性与准确性. 关键词： 准等熵压缩 多层阻抗梯度飞片 理论解析     

JB-9001钝感炸药冲击Hugoniot关系测试

 利用“压力对比法”实验技术，通过锰铜压力计测试待测炸药样品和LY12铝样品在LY12铝飞片的同时撞击下的界面压力p_exp和p_Al，从冲击波关系式和正交回归直线拟合分析，确定了JB-9001钝感炸药的冲击Hugoniot关系。     

冲击加载下20钢中弹性前驱波衰减与应力松弛行为实验研究

 通过改变样品厚度，对平面冲击加载下20钢的弹性前驱波的波幅衰减和应力松弛进行了实验研究。采用激光速度干涉测速仪（VISAR）实测了样品后自由面速度历史，采样频率达到1 ns，保证了实验结果的准确性。实验结果显示：Hugoniot弹性极限随着传播距离呈指数衰减，在所研究的样品厚度范围内，Hugoniot弹性极限减小了44%；应力松弛行为和弹性前驱波的上升沿时间也依赖于传播距离；冲击加载的强度对材料动态屈服行为的影响很小。     

Effects of the diffusive acceleration of particles by shock waves in the primordial matter of the solar system

The effects of the shock wave diffusive acceleration of particles are considered in the case of formation of isotopic relations of the anomalous Xe-HL component of xenon in relic grains of nanodiamonds in chondrites. It is shown that this component could be formed and captured simultaneously with the nanodiamond synthesis in the conditions of the explosive shock wave propagation from supernova outbursts. The specificity of isotopic composition of Xe-HL is due to the high hardness of the spectrum of nuclear-active particles at the shock wave front and its enrichment with heavy isotopes. The spallogenic nature of both the anomalous and normal components of xenon is ascertained, and the role of the subsequent evolutionary processes in the change of their isotopic systems is shown. Experimental evidence of the formation of the power law spectrum of particles with the spectral index γ ∼ 1 by the supersonic turbulence during the carbon-detonation supernova SnIa explosion is obtained; this perhaps opens new perspectives in studying the problem of the origin of cosmic rays. It is shown that at the stage of free expansion of the explosive shock wave, the degree of compression of the matter at the wave front was σ = 31 (the corresponding Mach number M ∼ 97); this led to a 31-fold increase of the magnetic field as well as of the maximum energy of accelerated particles, so that even the energy of protons reached ∼ 3 × 10¹⁵ eV, i.e., the “knee” region.     

Shear strength of metals behind shock fronts

Results are presented from a numerical modeling of experiments, conducted by J. Lipkin, R. Asay, L. Chabildas, and J. Wise, in which shock-compressed aluminum and polycrystalline beryllium were loaded again by shock waves. Reproduction of the experimental structures of the impulses in the calculations made it possible to determine the stresses acting in the materials during the primary and secondary shock loading, as well as to study the dynamics of the secondary shock load. It is shown that resistance to plastic strain is maintained in aluminum and beryllium behind the front of weak shock waves with intensities up to 10 GPa. The shear strength of the material behind the front does not correspond to the shear stresses at the Hugoniot elastic limit. For aluminum alloy 6061-T6 and beryllium, shear strength behind the fronts of shock waves with amplitudes up to 10 GPa is lower than in the elastic precursor but is greater than the static yield point of the material in the initial state.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 62–66, October, 1995.     

钽铌合金材料的冲击压缩特性研究

 对一种新型的钽铌合金材料进行了冲击压缩特性实验研究，通过超声测量得到了其常态下的横波和纵波声速，进而计算得到了其相关的一些静态力学参量。通过二级轻气炮加载技术，得到其在60~196 GPa压力范围内的冲击Hugoniot线。这一测量结果与混合物叠加法估算的结果符合较好，并将这种新型合金材料的力学特性与两种钨合金材料进行了简单对比。比较结果显示，Ta-Nb合金材料是一种具有较好工程应用前景的材料。     

Gold under high pressure

Abstract

First principle predictions for the equation of state of gold using solid and liquid state theories are compared up to combined pressures and temperatures of 600 GPa and 17 000 K with static diamond anvil cell compression, ultrasonic measurements and shock Hugoniot data which include a recent laser driven shock Hugoniot points at 600 GPa. Excellent agreement between theoretical and experimental data is observed. The theoretically estimated 300 K isotherm agrees to within 2 GPa with the isotherm that has been measured to 70 GPa using the diamond anvil cell. The structural energy estimates show that the normal f.c.c. phase remains stable under pressure. The estimate of the shock Hugoniot temperature of gold at 600 GPa based on a liquid state model is consistent with the measurements of laser induced shock luminescence, which in fact provides an experimental determination of the temperature of gold above its Hugoniot melting point. The powerful means provided by theory in the prediction of material properties of gold at ultra high pressures and temperatures is significant because gold is an efficient converter of laser energy into soft X-rays and is a potential candidate as a standard for high pressure, high temperature work.     

Dissipative Instability of Shock Waves

A new condition is obtained for the linear instability of a plane front of an intense shock wave in an arbitrary medium, which is determined by the finiteness of the viscosity. It is shown that the shock front instability occurs due to dissipative instability of the flow behind the front, which is analogous to the flow instability in the boundary layer. It is found that in the low-viscosity limit, one-dimensional longitudinal perturbations increase much faster than two-dimensional (corrugation) perturbations. The results are compared with the available data of experimental observation and numerical simulation of instability of shock waves. The comparison shows a better agreement between the new absolute shock instability as compared to the condition of such instability in the classical D’yakov theory disregarding viscosity.     

液氘Hugoniot曲线的理论计算

 用液体变分微扰理论加量子力学修正和指数6（EXP-6）相互作用势，计算了液氘的一次和二次冲击压力为0～80 GPa范围Hugoniot曲线。计算结果表明：冲击压力与实验符合较好。但冲击温度明显高于实验值，对其偏高的原因进行了探讨。     

Equation of state of initially liquid carbon monoxide and nitrogen mixture

The modified liquid perturbation variational theory and the improved vdW-1f model were applied to calculating the equation of the state of liquid CO-N₂ mixture with the ratio of 1:1, 4:1 and 1:4, respectively, in the shock pressure range of 9–49 GPa. It was shown that the calculated result for CO-N₂ mixture with the ratio of 1:1 is well consistent with the earlier experimental data. The thermodynamics equilibrium, chemical equilibrium and phase equilibrium were all considered in detail. It was found that Hugoniot of liquid CO-N₂ mixture is moderately softened in the pressure range of 20–30 GPa and 30–49 GPa for different initial proportions, and that the Hugoniot is more softened in the latter pressure range, which means that the structural phase transition occurs near 20 GPa and 30 GPa. Since the shock productions may absorb a plenty of systematic energy, the shock temperature and pressure decline compared with the case of no chemical reaction. Pressures and temperatures increase gradually with the increase in the mole fraction of nitrogen composition. The results for the 1:1 CO-N₂ mixture lie in the middle of two others. Therefore, it was shown that the modified Lorentz-Berthelor rule used in the scheme is effective to study shock-compression properties of liquid CO-N₂ mixture under high temperatures and high pressures. Supported by the National Natural Science Foundation of China (Grant No. 10576020)