Introduction to High Energy Density Physics R. Paul Drake University of Michigan

1. Introduction to High Energy Density Physics R. Paul Drake University of Michigan

2. High-Energy-Density Physics • The study of systems in which the pressure exceeds 1 Mbar (= 0.1 Tpascal = 1012 dynes/cm2), and of the methods by which such systems are produced. • In today’s introduction to this field, we will cover • Part 1: An overview of the physics • Part 2: The toys (hardware and code) • Part 3: The applications • My task is to give you a perspective and some context, within which you can better appreciate the lectures from experts you will hear this week. Inroductory Lecture

3. How is HEDP connected to other areas? Inroductory Lecture

4. The equilibrium regimes of HEDP Adapted from: National Research Council Report, 2002 “Frontiers in High Energy Density Physics: The X Games of Contemporary Science” Inroductory Lecture

5. What is Equation of State or an EOS? • Simple example: p = RT • In general an equation of state relates one of the four thermodynamic variables (, T, p, ) to two others. • Codes for HEDP often work with density and temperature(s), and thus need p(, T) and (, T). This may come in formulae or tables. • An equation of state is needed to close the fluid equations, as we will see later. • Another important example is the adiabatic EOS: p = C  •  = 5/3 for an ideal gas or a Fermi-degenerate gas •  = 4/3 for a radiation-dominated plasma •  ~ 4/3 for an ionizing plasma Inroductory Lecture

6. The EOS Landscape for HEDP • Rip Collins will discuss EOS at much more length on Thursday From Drake, High-Energy-Density Physics, Springer (2006) Inroductory Lecture

7. EOS results are often shown as the pressure and density produced by a shock wave • This sort of curve is called a Shock Hugoniot (or Rankine-Hugoniot) relation. • The other two thermodynamic variables (,T) can be inferred from the properties of shocks Pressure (GPa) Compression (density ratio) Credit: Keith Matzen, Marcus Knudson, SNLA Inroductory Lecture

8. Why do we care about EOS? • Whether we want to • make inertial fusion work, • model a gas giant planet, or • understand the structure of a white dwarf star, • we need to know how the density of a material varies with pressure • Here is one theoretical model of the structure of hydrogen Saumon et al., 2000 Inroductory Lecture

9. What is Opacity? • The spatial rate of attenuation of radiation • For radiation intensity (power per unit area per steradian) I: • The opacity has units of 1/cm or cm2/g • Opacity matters because the interaction of matter and radiation is important for much of the HEDP regime • The opacity has contributions from absorption and scattering. In HEDP absorption typically dominates. The absorption opacity is often labeled . Inroductory Lecture

10. Examples of opacity • Opacity of Aluminum • From LANL “SESAME” tables • Can see regimes affected by atomic structure From Drake, High-Energy-Density Physics, Springer (2006) Inroductory Lecture

11. One application: Cepheid variable stars • These stars have regions on uphill slopes of an opacity “mountain” • As the star contracts, increases, holding in more heat and producing a greater increase in pressure • As the star expands,  decreases, letting more radiation escape and increasing the pressure decrease Iron transmission based on Da Silva 1992 Transmission Both HEDP experiments and sophisticated computer calculations were essential to quantitative understanding Inroductory Lecture

12. X-ray absorption and emission has major implications for the universe • X-ray opacity measurements have other important applications • Understanding the universe: light curves from Type Ia supernovae • Studies of photoionized plasmas are required • To resolve discrepancies among existing models • To interpret emission near black holes regarding whether Einstein had the last word on gravity • To interpret emission near neutron stars to assess states of matter in huge magnetic fields Credit: Joe Bergeron Credit: Jha et al., Harvard cfa Inroductory Lecture

13. Many exciting phenomena in HEDP come from the dynamics • Shock waves and other hydrodynamic effects • Hydrodynamic Instabilities • Dynamics involving radiation (radiation hydrodynamics) • Radiative heat waves • Collapsing shock waves • Relativistic dynamics Inroductory Lecture

14. So how does one start HEDP dynamics? • Shoot it, cook it, or zap it • Shoot a target with a “bullet” • Pressure from stagnation against a very dense bullet ~ target (vbullet)2/2 • 20 km/s (2 x 106 cm/s) bullet at 2 g/cc stuff gives ~ 4 Mbar • Cook it with thermal x-rays • Irradiance T4 = 1013 (T/100 eV)4 W/cm2 is balanced by outflow of solid-density matter at temperature T and at the sound speed so • From which Inroductory Lecture

15. … or zap it with a laser • The laser is absorbed at less than 1% of solid density Bill Kruer will explain laser-plasma interactions tomorrow morning From Drake, High-Energy-Density Physics, Springer (2006) Inroductory Lecture

16. We can estimate the laser ablation pressure from momentum balance • Temperature from energy balance • Irradiance IL = 1014 I14 W/cm2 is carried away by flowing electrons • Energy balance is with f ~ 0.1 and • One finds • Pressure from momentum balance (p = momentum flux) • This is a bit low; the flow is actually faster (3.5 -> 8.6) Inroductory Lecture

17. Most HEDP dynamics begins with a shock wave • If I push a plasma boundary forward at a speed below cs, sound waves move out and tell the whole plasma about it. • If I push a plasma boundary forward at a speed above cs, a shock wave is driven into the plasma. • In front of the shock wave, the plasma gets no advance warning. • The shock wave heats the plasma it moves through, increasing cs behind the shock. • Behind the shock, the faster sound waves connect the entire plasma Denser, Hotter Shock velocity, vs upstream downstream csd > vs here csu < vs here Mach number M = vs / csu Initial plasma Inroductory Lecture

18. Much of the excitement in HEDP comes from the dynamics Shock waves establish the HEDP regime of an experiment Inroductory Lecture

19. HEDP theory: a fluid approach often works, but not always • Most phenomena can be grasped using a single fluid • with radiation, • perhaps multiple temperatures • perhaps heat transport, viscosity, other forces, and • A multiple fluid (electron, ion, perhaps radiation or other ion) approach is needed at “low” density • Magnetic fields sometimes matter • Working with particle distributions (Boltzmann equation and variants) is important when strong waves are present at “low” density • A single particle or a PIC (particle-in-cell) approach is needed for the relativistic regime and may help when there are strong waves Inroductory Lecture

20. Most phenomena can be seen with a single-fluid approach • Continuity Equation • Momentum Equation • Density , velocity , pressure , radiation pressure • Viscosity tensor , other force densities • Hydrodynamics is complicated because the nonlinear terms in these equations matter essentially Inroductory Lecture

21. The energy equation has a number of terms that often don’t matter • General Fluid Energy Equation: Material Energy Flux m Smaller or Hydro-like Typ. small Or Ideal MHD Inroductory Lecture

22. So let’s discuss dynamic phenomena We start with hydrodynamics • Sound waves w = cs k or f (Hz) = cs / l • Shock waves • Rarefactions • Instabilities Inroductory Lecture

23. It’s easy to make a shock wave with a laser Emission From rear Laser beam Any material Thicker layer for diagnostic Laser: 1 ns pulse (easy) ≥ 1 Joule (easy) Irradiance ≥ 1013 W/cm2 (implies spot size of 100 µm at 1 J, 1 cm at 10 kJ) This produces a pressure ≥ 1 Mbar (1012 dynes/cm2, .1 TP). This easily launches a shock. Sustaining the shock takes more laser energy. Time Inroductory Lecture

24. Astrophysical jets and supernovae make shocks too Supernova Remnant Astrophysical Jet J. Hester Burrows et al. Inroductory Lecture

25. We analyze shocks in a frame of reference where the shock is at rest Matter comes in at velocity of shock in lab frame, vs Matter leaves at slower velocity, vd Denser, Hotter Density ru here Density rd here From continuity equation: From momentum and energy equations: For strong shocks Marcus Knudson will tell you much more about shocks Inroductory Lecture

26. Where the density drops, plasmas undergo rarefactions • The outward flow of matter with a density decrease is a rarefaction • Rarefactions can be steady • Steady (more or less) • The Sun emits the solar wind • Rarefactions can be abrupt • When shock waves or blast waves emerge from stars or dense plasma, a rarefaction occurs Inroductory Lecture

27. Many HEDP experiments have both shocks and rarefactions Sketch of Experiment SN 1987A Radiographic data at 8 ns R.P. Drake, et al. ApJ 500, L161 (1998) Phys. Rev. Lett. 81, 2068 (1998) Phys. Plasmas 7, 2142 (2000) This experiment to reproduce the hydrodynamics of supernova remnants has both shocks and rarefactions Inroductory Lecture

28. When rarefactions overtake shocks, “blast waves” form • Planar blast wave produced by a 1 ns laser pulse on plastic From Drake, High-Energy-Density Physics, Springer (2006) Inroductory Lecture

29. Hydrodynamic instabilities are common Chevalier, et al. ApJ 392, 118 (1992) Instability in a simulation of supernova remnant • Three sources of structure • Buoyancy-driven instabilities (e.g. Rayleigh-Taylor) • Lift-driven instabilities (e.g. Kelvin-Helmholtz) • Vorticity effects (e.g. Richtmyer-Meshkov) Inroductory Lecture

30. Buoyancy-driven instabilities are very important Convective cloud formation • The most important are bouyancy-driven • Rayleigh Taylor • “Entropy mode” or “Convective mode” • Examples of this: Rayleigh Taylor Average density determines pressure gradient http://www.chaseday.com/PHOTOSHP/2JUL76/01-cbnw.JPG Local density determines local gravitational force Net upward force = (<> - )g Inroductory Lecture

31. Two mechanisms reduce Rayleigh-Taylor in HEDP experiments • Approximate exponential growth rate • Gradient scale length (L) reduces growth rate • Ablation removes material at a speed vAblation, stabilizing Rayleigh-Taylor at large k • There is an interplay of initial conditions and allowable growth • Riccardo Betti will discuss the ICF case Thursday • Experiments have gone beyond ICF-compatible growth Remington et al. Phys. Fl. B 1993 Inroductory Lecture

32. Rayleigh-Taylor also occurs in flow-driven systems • Ejecta-driven systems • Rarefactions drive nearly steady shocks • Supernova remnants • Experiments • Rarefactions often evolve into blast waves A rarefaction can produce flowing plasma that can drive instabilities Inroductory Lecture

33. Supernova remnants produce the Rayleigh-Taylor driven by plasma flow in simulation, … • 1D profile and 2D simulations In supernova remnants Chevalier, et al. ApJ 392, 118 (1992) and supernovae Kifonidis, et al. Inroductory Lecture

34. .. in observation, and in lab experiment Remnant E0102 Blast-wave driven lab result Dmitri Ryutov will tell you more…. Inroductory Lecture

35. Here’s how we do such experiments • Precision structure inside a shock tube From Drake et al. Phys. Plas. 2003 • Interface with 3D modulations Inroductory Lecture

36. The second major instability driver is lift U Flow Rippled interface Flow U Airplane wing Kelvin-Helmholtz Instability Inroductory Lecture

37. For simple abrupt velocity shear the theory is simple • Start with Euler equations • Plus continuity of the interface: • For abrupt shear flow (i.e., velocity difference) at an interface, find Kelvin Helmholtz instability growth rate • However, velocity gradients with scale length Lu stabilze modes with k > ~ 2/ Lu Wave propagates If A ≠ 0 Wave Grows for all kx Inroductory Lecture

38. Kelvin-Helmholtz makes mushrooms on Rayleigh-Taylor spike tips Lab simulation: Miles et al. Supernova simulation by Kifonidis et al. But not so much along the stems. A big difference among codes is how much “hair” they grow on the stems. Data in Robey et al. Inroductory Lecture

39. Instead, “vortex shedding” is important in clump destruction Clump destruction by blast wave (Robey et al. PRL) Clump destruction by steady flow (Kang et al. PRE) Simulation of 1987A ejecta-ring collision This process is also driven by lift Inroductory Lecture

40. This is a natural entry to the third category:vorticity effects • Vorticity is defined as • Volumetric vorticity corresponds to swirling motions • Shear flows generate surface vorticity • Volumetric vorticity is transported like magnetic fields in plasmas • Vortex motion can produce large structures in systems that are not technically “unstable” (as they have no feedback loop). Inroductory Lecture

41. A major vorticity effect in astro & ICF is the Richtmyer-Meshkov “instability” • Richtmyer Meshkov occurs when a shock crosses a rippled interface. • Related processes happen with a rippled shock reaches any interface. The shear flow across the interface drives it to curl up. The ripple may or may not invert in phase, depending on details. The modulations grow at most linearly in time Inroductory Lecture

42. Richtmyer Meshkov can produce spikes and bubbles like those from Rayleigh-Taylor • Strong-shock case • The vorticity deposited by a shock on a rippled interface causes the denser material to penetrate to the shock • From Glendinning et al., Phys. Plas. 2003 Inroductory Lecture