1. 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

2. Pressure – Volume – Temperature Surface for Copper 1.0e+00 1.0e+01 1.0e+03 1.0e+00 1.0e+01 1.0e-04 1.0e-01 1.0e+02 1.0e+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

3. Povarnitsyn M. E., Khishchenko K. V., Levashov P. R. Hypervelocity impact modeling with different equations of state // Int. J. Impact Eng. 2006. V. 33. P. 625–633. Impactor - Al, velocity of impactor - 6.6 km/s, diameter of impactor - 15 mm Target - Al, thickness of target - 6.35 mm Density distribution 3.00 10 -5 2.25 1.50 0.75 Institute for High Energy Densities RAS, Moscow

4. 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

5. Pressure – Volume – Temperature Surface for Copper 1.0e+00 1.0e+01 1.0e+03 1.0e+00 1.0e+01 1.0e-04 1.0e-01 1.0e+02 1.0e+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

6. Shock-Wave Pressure in Experiments with Different Driving Systems

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

8. Multiphase Equations of State

9. 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 :

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

11. 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 :

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

13. 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).]

14. Zinc at T = 0 & 293 K

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

16. Aluminum Phase Diagram 1 - Boehler & Ross 1997 2 - Hanstrom & Lazor 2000 Density-Temperature Diagram

17. Tungsten Phase Diagram

18. Equation of State for Zinc in Shock and Release Waves

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

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

21. Radiative Opacity of Plasmas

26. 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.

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

29. 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.

30. Thank You

31. Shock Hugoniots & Release Isentropes

32. 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)]

33. Hugoniot of Tin

34. Phase Diagram of Tin

35. T = 298 K & Hugoniot of Tin

36. Phase Diagram of Tin

37. KCLCsI Phase Diagrams of KCl and CsI

38. Phase Diagram of Silica V. P. Dmitriev et al // Phys. Rev. B. 1998. V. 58. P. 11911.

39. Phase Diagram of System Quartz–Coesite–Stishovite

40. Phase Diagram of System Quartz–Coesite–Stishovite–Liquid

42. Phase Diagram of System Quartz–Stishovite–Liquid

44. Hugoniot of Titanium

46. Phase Diagram of Titanium

47. Caloric Equations of State

48. 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

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

50. 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 :

51. Equation of State for Copper

52. Shock Hugoniots & Release Isentropes PolymethylmethacrylatePolytetrafluoroethylene

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

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

55. Al impactor, Al target Caloric EOS Multiphase EOS 6.6 km/s, impactor 15 mm in diameter, plate thickness - 6.35 mm