Wide-range Multiphase Equations of State and Radiative Opacity of Substances at High Energy Densities Konstantin V. Khishchenko, Nikolay Yu. Orlov Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia EMMI Workshop on Plasma Physics with Intense Ion and Laser Beam, November 21-22, 2008, GSI, Darmstadt, Germany

Pressure – Volume – Temperature Surface for Copper 1.0e e e e e e e e e+05 V, cm 3 /g T, kK P, GPa LIQ.+GAS GAS PLASMA LIQ. MELTING IEX CRYSTALL LM H CP S HPHP H - principal Hugoniot H P - porous Hugoniots S - release isentropes IEX - isobaric expansion

Povarnitsyn M. E., Khishchenko K. V., Levashov P. R. Hypervelocity impact modeling with different equations of state // Int. J. Impact Eng V. 33. P. 625–633. Impactor - Al, velocity of impactor km/s, diameter of impactor - 15 mm Target - Al, thickness of target mm Density distribution Institute for High Energy Densities RAS, Moscow

Modeling of Laser-Matter Interaction by Mikhail E. Povarnitsyn et al. Images of the shockwave in the ambient gas (at normal conditions) and the ejected material after irradiation of the aluminum target with pulse parameters:  L = 20 ns, R = 0.96, opt = 200 nm, I L = 5x10 8 W/cm 2, t 0 =  L r L = 300 mm

Pressure – Volume – Temperature Surface for Copper 1.0e e e e e e e e e+05 V, cm 3 /g T, kK P, GPa LIQ.+GAS GAS PLASMA LIQ. MELTING IEX CRYSTALL LM H CP S HPHP H - principal Hugoniot H P - porous Hugoniots S - release isentropes IEX - isobaric expansion

Shock-Wave Pressure in Experiments with Different Driving Systems

Direct (a) and Indirect (b) Laser Driven Shock Wave Setups Alessandra Benuzzi et al., Phys. Rev. E 54 (1996) 2162

Multiphase Equations of State

Equation of State Model General form Solid phase. Elastic component (EOS at T = 0 K) at V < V 0c : at V > V 0c : at V = V 0c :

Equation of State Model General form Solid phase. Thermal lattice components

Equation of State Model General form Fluid phase. Elastic component (EOS at T = 0 K) at V < V m0 : at V m0 < V < V cr : at V cr < V :

Equation of State Model General form Fluid phase. Thermal atomic components

Equation of State Model General form Thermal electron component is from Ref. [A. V. Bushman, V. E. Fortov, G. I. Kanel’, A. L. Ni, Intense Dynamic Loading of Condensed Matter (Taylor & Francis, Washington, 1993).]

Zinc at T = 0 & 293 K

Aluminum at P = 1 bar Specific heat capacity of the solid phase under normal pressure Thermal expansion of the solid and liquid phases

Aluminum Phase Diagram 1 - Boehler & Ross Hanstrom & Lazor 2000 Density-Temperature Diagram

Tungsten Phase Diagram

Equation of State for Zinc in Shock and Release Waves

Pressure of Shock Compression of a Sample to Be Achieved for Critical Point Investigation in Isentropic Release Waves

Equation of State for PMMA Comparison with Temperature Data Р = 1 barHugoniot

Radiative Opacity of Plasmas

Fig. 1. The spectral coefficient for X-rays absorption K(x) (cm 2 /g) calculated for alloy (Ni80%/Cr20%) (black line) and for the composition Alloy 188 (Cr21.72%/Ni22.92%/Fe2.24%/Co39%/W13.93%) (red line) at the temperature T=1 keV and the density.

Orlov N. Yu., et al., Laser and Particle Beams 25 (2007)

1. The Ion Model provides reliable quantum mechanical calculations of the radiative opacity over a wide range of plasma temperature and density. 2. The Ion Model can be used to give theoretical explanations of experimental results at high energy density in plasmas.

Thank You

Shock Hugoniots & Release Isentropes

Aluminum Phase Diagram 1 - Sinko & Smirnov 2002Density-Temperature Diagram Critical point (CP) parameters are from Ref. [V. E. Fortov, A. N. Dremin, A. A. Leont'ev, Teplofiz. Vys. Temp. 13(5), 1072 (1975)]

Hugoniot of Tin

Phase Diagram of Tin

T = 298 K & Hugoniot of Tin

Phase Diagram of Tin

KCLCsI Phase Diagrams of KCl and CsI

Phase Diagram of Silica V. P. Dmitriev et al // Phys. Rev. B V. 58. P

Phase Diagram of System Quartz–Coesite–Stishovite

Phase Diagram of System Quartz–Coesite–Stishovite–Liquid

Phase Diagram of System Quartz–Stishovite–Liquid

Hugoniot of Titanium

Phase Diagram of Titanium

Caloric Equations of State

Pressure – Volume – Internal Energy Surface for Polytetrafluoroethylene C — cold curve at T = 0 K, H & H p — principal and porous Hugoniots, R — double shock compression curve, S — release isentrope

Caloric Equation of State Model E = E(V, P) or P = P(V, E) General form Thermal component (according to Bushman & Lomonosov 1989)

Equation of State Model General form Elastic component (EOS at T = 0 K) at V < V 0c : at V > V 0c : at V = V 0c :

Equation of State for Copper

Shock Hugoniots & Release Isentropes PolymethylmethacrylatePolytetrafluoroethylene

Shock Hugoniots of Aromatic Polymers Polyimidea — Polyamide, b — Polystyrene

Shock Hugoniots of Polyamide (PA), Polystyrene (PS) & Polyimide (PI)

Al impactor, Al target Caloric EOS Multiphase EOS 6.6 km/s, impactor 15 mm in diameter, plate thickness mm