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Introduction to High Energy Density Physics (HEDP) R. Paul Drake University of Michigan Summer School on High Energy Density Physics UCSD, July 2011 Department of Atmospheric Oceanic & Space Sciences Applied Physics Program DrakeLab Michigan Institute for Plasma Science and Engineering Center for Radiative Shock Hydrodynamics This talk will cover • Connections between HEDP and other physics • How to create HED conditions • Fundamental areas of HEDP – With some examples • Some applications of HEDP 2011 Summer School Intro to High Energy Density Physics Page 2 Precursors to high-energy-density physics • First half 20th Century: Stellar structure – Eddington, Chandrasekhar, Schwarzschild, among others • Mid-20th Century: Nuclear weapons – Oppenheimer, Sakharov, Teller, Bethe, Fermi, others • Compressible metals! – Zelʼdovich and Raizer 1966 • Physics of Shock Waves and High Temperature Phenomena • Post Mid-20th Century (1960-1980): Inertial fusion origins – Nuckolls, Basov, Emmett, others • I date HEDP as a discipline from about 1979 – Complex quantitative physics experiments became feasible – The first user facility program (NLUF at Omega) began in 1979 2011 Summer School Intro to High Energy Density Physics Image credit NNSA Nevada Site Office Page 3 We will use this plot to see aspects of highenergy-density physics (HEDP) • • HEDP parameters Physics connections – Strong coupling – Pressure and Fermi degeneracy • • Astrophysics connections Plasma physics connections – Particles per Debye sphere 2011 Summer School Intro to High Energy Density Physics Page 4 Physics connections within and beyond HEDP Quark-gluon plasmas QM 2009 Summer School Intro to High Energy Density Physics Page 5 HEDP plasmas can be very strongly coupled Electron Temperature Te (eV) • Γ = |qφ|/kT X-ray Thomson scattering 2011 Summer School Intro to High Energy Density Physics Data from Glenzer & Redmer, RMP 2008 Page 6 Astrophysics connections with HEDP • Other elements of this connection – High Mach number flows – Fast shocks – Ionizing – Strong B fields – Radiation matters – Plasma hydrodynamics 2011 Summer School Intro to High Energy Density Physics Curves credit NRC report on HEDP Page 7 Perspectives on plasma physics and HEDP • The mid-20th-Century approach to plasma physics, as seen in most textbooks, was simple – Many particles per Debye sphere often as the definition of “plasma” – Quasineutral – Only hydrogen – Spatially uniform – Maxwellian distributions – Deviations from spatial uniformity or Maxwellians drive instabilities • 21st Century plasma physics breaks these and other assumptions – An era of creation and control of systems that deviate strongly from the simple cases – High-energy-density plasmas are very much a case in point 2011 Summer School Intro to High Energy Density Physics Page 8 HEDP systems often have few particles per Debye sphere Be model UV Thomson scattering 2011 Summer School Image credit David Montgomery Intro to High Energy Density Physics Data credit Riccardo Betti Page 9 Regime boundaries move as materials change Ionization is centrally important 2011 Summer School Intro to High Energy Density Physics Page 10 The pressure often is not nkT ~ Gbar shock in Al 2011 Summer School Intro to High Energy Density Physics Page 11 Data from Cauble et al, PRL 1991 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 • 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 2011 Summer School Intro to High Energy Density Physics Page 12 We now discuss how to create HEDP conditions 2011 Summer School Intro to High Energy Density Physics Page 13 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 ~ ρtarget (vbullet)2/2 – 20 km/s (2 x 106 cm/s) bullet at 2 g/cc gives ~ 4 Mbar • Cook it with thermal x-rays – Irradiance σT4 = 1013 (T/100 eV)4 W/cm2 is balanced by outflow of solid-density matter at temperature T and at the sound speed so T / Mi !T 4 = " T / M i = p T / M i /(# $1) – From which 2011 Summer School p = (! "1) M i #T 3.5 $ T ' ~ 20& ) %100 eV ( Intro to High Energy Density Physics 3.5 Mbars Page 14 … or zap it with a laser Laser beam Any material Thicker layer for Laser: 1 ns pulse (easy) diagnostic ≥ 1 Joule (easy) Irradiance ≥ 1013 W/cm2 (implies spot size of 100 µm at 1 J, 1 cm at 10 kJ) Emission From rear Time This produces a pressure ≥ 1 Mbar (1012 dynes/cm2, 0.1 TP). Momentum balance gives p ~ 3.5 I142/3 / λµm2/3 Mbars This easily launches a shock. Sustaining the shock takes more laser energy. 2011 Summer School Intro to High Energy Density Physics Page 15 Perspectives on strong shocks in HEDP • Many HEDP experiments involve at least one strong shock – A natural consequence of depositing kJ/mm3 in matter • Strong shocks are useful! – In Inertial Confinement Fusion – For equation of state measurements – As sources of energy or momentum Shock in Xe clusters • Radiative shocks • Isentropic compression • Hydrodynamic processes 2011 Summer School Intro to High Energy Density Physics Page 16 Data from Ditmire et al. ApSS 2000 High Energy Lasers are key tools • High energy lasers amplify the light energy across a large area then compress the beam(s) in space to create high energy density vacuum amplify protect irradiate Smooth (spatial filter) 2011 Summer School Intro to High Energy Density Physics amplify Page 17 The biggest lasers can produce 100 Mbar pressures on mm2 to cm2 areas Omega 60 beams 30 kJ Target chamber at Omega laser National Ignition Facility 192 beams > 1 Megajoule 2011 Summer School Intro to High Energy Density Physics Page 18 The laser creates structure at the target surface • The laser is absorbed at less than 1% of solid density Ablation pressure from approximate momentum balance: p ~ 3.5 I142/3 / λµm2/3 Mbars This is a bit low; better calculations replace 3.5 by 8.6 A pressure > 100 Mbars is practical From Drake, High-Energy-Density Physics, Springer (2006) 2011 Summer School Intro to High Energy Density Physics Page 19 Hohlraums create thermal environments at millions of degrees • Put energy inside a high-Z enclosure • The vacuum radiation field stays in equilibrium with the resulting hot surface Laser spots seen through thin-walled hohlraum. Credit LLNL Hohlraum with experiment attached on bottom • One gets high temperatures because the radiation wave moves slowly into the material, penetrating few microns 2011 Summer School Intro to High Energy Density Physics From Drake, High-EnergyDensity Physics, Springer (2006) Page 20 Z pinches also produce high-energy-density conditions • Todayʼs biggest is the Z machine at Sandia, when run as a Z pinch (~ 2 MJ of x-rays) • Z pinches exploit the attraction between parallel currents Cylindrical wire array Implosion Stagnation Credit: Keith Matsen Inward J X B force 2011 Summer School Inward acceleration Intro to High Energy Density Physics Shock heating & Radiative cooling Page 21 The action is at the center of a large though compact structure 2011 Summer School Intro to High Energy Density Physics Credit: Keith Matsen Page 22 Ultrafast lasers produce relativistic HED conditions • • Compression in time as well as space Hercules at U. Michigan – The most intense laser in the world ao = p/mc ~ 100 2011 Summer School Intro to High Energy Density Physics Page 23 Particle beam bunches can be HED systems Located at SLAC e- Ionizing Laser Pulse Li Plasma (193 nm) ne!6·10 15 cm-3 L!30 cm Streak Camera (1ps resolution) "Cdt N=1-2·1010 !z=0.1 mm Optical Transition Spectrometer Cerenkov E=30 GeV Radiator Radiators m 25 m 2011 Summer School Slide Credit: Chan Joshi X-Ray Diagnostic Dump Not toIntro scale! to High Energy Density Physics FFTB Page 24 Now we turn to the fundamental physics of HEDP systems • In a traditional sense HED plasma properties are weird – – – – Cannot assume Z = 1 Cannot assume the ion mass is the hydrogen mass Cannot assume only one ion species Cannot assume the plasma is always an ideal gas • This weirdness affects their Equations of State • These plasmas also exhibit a lot of crazy dynamics – – – – – Shock waves and things they make happen Plasma wakes and things they make happen Gigagauss magnetic field generation Self-organized completely kinetic stationary states Among many others 2011 Summer School Intro to High Energy Density Physics Page 25 Equations of State 2011 Summer School Intro to High Energy Density Physics Page 26 We care about the Equation of State (EOS). Why? • In order to – make inertial fusion work – model a gas giant planet – understand the structure of a white dwarf star – understand warm dense matter • 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 2011 Summer School Intro to High Energy Density Physics Page 27 MCore/MEarth The different EOS models for hydrogen directly impact whether Jupiter is predicted to have a central dense core or not 20 • Outlines show range of models matching Jupiterʼs properties within 2σ of observed • Cannot yet tell whether Jupiter has a core • The predicted age of Jupiter is is also sensitive to the H EOS, which affects luminosity 15 10 5 0 No core 0 10 20 30 40 MZ/MEarth [D. Saumon and T. Guillot, Ap. J. 609, 1170 (2004)] 2011 Summer School Intro to High Energy Density Physics Adapted from slide by Bruce Remington Page 28 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 Pressure (GPa) • Changing curve shape comes from changing structure • Other thermodynamic variables (ε,T) can be inferred from the properties of shocks Compression (density ratio) Credit: Keith Matzen, Marcus Knudson, SNLA 2011 Summer School Intro to High Energy Density Physics Page 29 Equation of state experiments have been and will be common at HED facilities Single-shock and double-shock Omega data D. Hicks, et al., PHYS. REV. B 79, 014112 (2009) 2011 Summer School Intro to High Energy Density Physics Page 30 5 minute stretch 2011 Summer School Intro to High Energy Density Physics Page 31 Radiative Shocks one topic in radiation hydrodynamics 2011 Summer School Intro to High Energy Density Physics Page 32 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. 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 downstream 2011 Summer School csd > vs in frame of shock Shock velocity, vs csu < vs here Initial plasma Intro to High Energy Density Physics upstream Mach number M = vs / csu Page 33 Shock waves become radiative when • Radiative energy flux would exceed incoming material energy flux σTs4 > ρous3/2 Upstream preheated downstream • Where post-shock temperature is • The ratio of these energy fluxes is proportional to us5/ρo • Implying threshold velocities …. RTs = 2(! " 1) 2 us 2 (! + 1) Material Xe Xe CH Density 0.01 g/cc 10-5 g/cc 0.01 g/cc Threshold velocity 60 km/s 10 km/s 200 km/s 2011 Summer School Intro to High Energy Density Physics Page 34 Conservation of energy forces the shock wave to develop complex structure Shocked xenon layer Compressed 40x Traps thermal photons Preheated region Thermal photons escape upstream Other fun complications: Instabilities Wall shocks 2011 Summer School Intro to High Energy Density Physics Page 35 Radiative shocks are challenging in both astrophysics and the laboratory • Radiative shocks • – Radiation alters the structure and dynamics of the shock – A radiation-hydrodynamic phenomenon – Inherently nonlinear – Sometimes unstable – Matching key dimensionless parameters is what one can do • • Motivation from astrophysics – Supernova shocks – Stellar shocks – Some accretion phenomena • Astrophysical modelers called for experiments in this area Experiments are a major challenge – Novel experimental systems – Need innovation in targets and diagnostic approaches Modeling them is difficult – Widely varying scales – Radiation transport regimes – Ionizing media and 3D effects 2011 Summer School Intro to High Energy Density Physics Page 36 How to produce radiative shocks Laser beams launch Be piston into Xe or Ar gas at > 100 km/s Gas filled tubes Piston drives shock Diagnostics measure plasma properties Gold grids provide spatial reference Parameters 1015 W/cm2 0.35 µm light 1 ns pulse 600 µm tube dia. 2011 Summer School Intro to High Energy Density Physics Experiments: Amy Reighard, Tony Visco, Forrest Doss Page 37 Targets: Korbie Killebrew, Mike Grosskopf, Trisha Donajkowski, Donna Marion Researchers are studying these shocks with a range of diagnostics and simulations • Radiographs 2011 Summer School • Emission • Xray Thomson scattering Intro to High Energy Density Physics • Interferometry Page 38 Data credit: L. Boireau S. Bouquet, F. Doss M. Koenig, C. Michaut, A. Reighard, T. Visco , T. Vinci Researchers are simulating such shocks too Level CRASH 1.0 2D Simulation Axial vel. Xe radiograph (of rotated output) Radial vel. Density Pressure Te 2009 Summer School Intro to High Energy DensityTr Physics The agreement here is too good Page 39 Next directions in the study of radiative shocks Omega scale: Determine structure and dynamics Both axial and lateral Create more complex systems Reighard Omega experiment Target for Visco X-ray Thomson scattering experiment shock Continuously radiating shock produces dense xenon layer at > 30 times initial density. 2011 Summer School Omega has the potential to do other radiation hydrodynamics NIF can go further Intro to High Energy Density Physics Page 40 Applications of High Energy Density Physics 2011 Summer School Intro to High Energy Density Physics Page 41 Why did the US Congress fund HED machines? •They were developed for inertial confinement fusion (ICF) 2011 Summer School Intro to High Energy Density Physics Page 42 In ICF one first compresses the fuel using an ablatively driven implosion • This turns out to be necessary to avoid blowing up the lab ICF fusion Capsule An ablatively driven implosion Fuel layer is first compressed by shocks. Then the shell is accelerated inward by high-pressure, low-density corona. Stagnation creates a central hot spot surrounded by cold dense fuel 2011 Summer School Intro to High Energy Density Physics Page 43 After compression, one has to make the ICF fuel burn by fusion • Two approaches Design the central hot spot so it ignites the fuel Let the central hot spot be much smaller and rapidly ignite the compressed fuel Options: lasers, particles, slugs This is the traditional approach 2011 Summer School This is called fast ignition Intro to High Energy Density Physics Page 44 HED experimental astrophysics is emerging • New tools enable new science, and create new sciences Astronomy: the human eye and brain Spectroscopy enabled and created astrophysics e.g., Hubble diagram • High Energy Density facilities are new tools ….. 2011 Summer School Intro to High Energy Density Physics Page 45 Laboratory Laboratoryexperiments experimentstest testopacity opacitymodels models that thatare arecrucial crucialfor forstellar stellarinterior interiorphysics physics Predictions of solar structure do not agree with observations (13 σ CZ problem) Solar structure depends on opacities that have never been measured convective zone Challenge: create and diagnose stellar interior conditions on earth radiative zone Z opacity experiments reach T ~ 156 eV core High T enables first studies of transitions important in stellar interiors 2007 Don Dixon / cosmographica.com Slide credit: James Bailey 2011 Summer School transmission Fe / Mg transmission at T ~ 156 eV 8.0 10.0 12.0 λ (Angstroms) Intro to High Energy Density Physics 14.0 Page 46 Magnetically-driven z-pinch implosions provide one means to do studies like this, requiring bright x-ray sources Current B-Field JxB Force kinetic and electrical energy electrical energy internal (shock heating) kinetic energy x rays • • Initiation Implosion Energy: 1.5 MJ x-ray ≈ 15% of stored electrical Power: 200 TW x-ray Stagnation Slide credit: James Bailey 2011 Summer School Intro to High Energy Density Physics Page 47 Opacity and photoionization experiments, relevant to stellar interiors and accretion powered objects, have been done at Z and could be done at Omega opacity sample same charge states in sun X-rays Fe + Mg transmission Te ~ 156 eV, ne ~ 1022 cm-3 λ Z x-ray source 1-2 MJ 2·1014 W photoionization sample radiation effects in plasma surrounding black hole Ne transmission at Te ~ 25 eV, ne ~ 1019 cm-3 λ The importance of radiation for creation and diagnosis is a unifying theme for these very different plasmas [Jim Bailey, PRL (2007); and PoP 13, 056301 (2006)] 2011 Summer School Intro to High Energy Density Physics Slide credit: James Bailey Page 48 There are three key dimensionless parameters for radiative shocks • • • The ratio radiation flux at the initial postshock temperature to the incoming material energy flux 4 The upstream optical depth The downstream optical depth Cooling layer Density Downstream final state ρf,Tf,pf Temperature !T 3 " ou s / 2 Initial post-shock state ρi,Ti,pi Upstream ρo,To,po (Ignoring ion-electron decoupling near the density jump) 2011 Summer School Intro to High Energy Density Physics Page 49 Shocks in SNe pass through the regime of our experiments as they emerge 1987A simulation • Xe experiment simulation Core collapse SNe shock passing through outer layers becomes radiative – Once radiation ahead of the shock can escape • Associated with luminosity burst; radiation escaping to optically thin region 2011 Summer School Intro to High Energy Density Physics A.B. Reighard, Ph.D. Thesis, 2007 Page 50 Ensman and Burrows, ApJ., 393,742-755,1992 The fluid energy equation has a number of terms that often donʼt matter • General Fluid Energy Equation: Material Energy Flux Γm , $ / ' u2 ' !$ "u 2 + E R ) + * + ."u&# + & "# + ) + pu1 = !t % 2 2( ( - % 0 2J • E + Fother • u 2 * • [FR + ( pR + E R )u + Q 2 (3 v • u)] ! ei ~1 " pe Or Ideal MHD 2011 Summer School Typ. small !m = PeRad " rad !m " hydro Smaller or Hydro-like !m Pe !m Re This enables scaled astrophysical hydrodynamics experiments when Re, Pe, and PeRad are >> 1 Intro to High Energy Density Physics Page 51 Destruction of clumps in post-shock flow has been a research area with impact Chandra data Well scaled experiment Klein et al., ApJ 2003 Robey et al., PRL 2002 • • • Experimental results used to help interpret Chandra data from the Puppis A supernova remnant Well-scaled experiments have deep credibility Una Hwang et al., Astrophys. J. (2005) 2011 Summer School Intro to High Energy Density Physics Page 52 How shock-clump experiments are done • … but not in a way that lets one diagnose details • The experiment involves blast-wave-driven mass stripping from a sphere • Early experiments used Cu in plastic; recent experiments use Al in foam 2011 Summer School Intro to High Energy Density Physics Page 53 Observations of the Al/foam case continued until mass stripping had destroyed the cloud • Hansen et al., ApJ 2007, PoP 2007 2011 Summer School Intro to High Energy Density Physics Page 54 The stripping is clearly turbulent, consistent with the necessary conditions Hansen et al., ApJ 2007 Remaining Mass (µg) • The turbulent model is based on “Spaldingʼs law of the wall”, Spalding (1961) • Parameters Re ~ 105 to 106 U ~ 10 km/s ν ~ 10-5 to 10-6 m2/s δ ~ Sphere ~ 60 µm radius • δ /U ~ 6 ns ~ rollup time (data) • Robey/Zhou time is ~ 1 ns Time (ns) 2011 Summer School Intro to High Energy Density Physics Page 55 Perspectives on relativistic HEDP • • The development of Chirped Pulse Amplification in the 1980ʼs soon enabled the production of high-field HEDP conditions and relativistic electrons Intense particle beams also are HED media • • Much interesting dynamics occurs Much of this produces relativistic distributions of particles – Often exponential in energy – Energy scales of a few to many MeV • Pursuit of acceleration in plasma wakes has led to discovering organized behavior with the production of quasi-monoenergetic electron beams 2011 Summer School Intro to High Energy Density Physics Page 56 Wakes are common in fluid disturbances • • To experience acceleration on a wake, go wakeboarding or surfing A wakeboarder can surf the wake on a boat… gaining momentum http://www.nickandjulz.com/pro/photos/wake/ 2011 Summer School Intro to High Energy Density Physics Page 57 To accelerate lots of electrons, take them surfing too • Electrons can surf the wake on a pressure pulse in a plasma Plasma Wake Laser pulse Electrons • The pressure pulse can be produced by one or more laser beams or by an electron bunch. This is wakefield acceleration. 2011 Summer School Credit: LBL OASIS Group Intro to High Energy Density Physics Page 58 In 1979, Tajima and Dawson published the invention of wakefield acceleration • A Simple notion λp Wake phase velocity vph = ωpe/kp=ωpeλp/(2π) Choose ωpe, λp so vph = c • Complex implementation – Through the 1990ʼs this required convincing some plasma waves to evolve to a final, desired, very nonlinear state 2011 Summer School Intro to High Energy Density Physics Page 59 In 2002, Pukhov and Meyer-ter-Vehn identified the “bubble regime” 2011 Summer School Intro to High Energy Density Physics Page 60 Laser-Plasma Electron Accelerator Tajima & Dawson, Phys. Rev. Lett. 43, 267 (1979) INVISIBLE Gas Jet Fires about 3 mm Laser Pulse Focuses Ionize Gas & Make Wave Helium Gas Jet Wave Captures and Accelerates Electrons 2009 Summer School slide courtesy Mike Downer, UT-Austin Intro to High Energy Density Physics Page 61 First GeV Electron Beam from LWFA • Laser: a0 ~ 1.46 (40 TW, 37 fs) • Capillary: D = 312 µm; L = 33 mm [pC/GeV] 500 1 GeV beam expt. 250 sim.* 0 0.9 2011 Summer School Sim Expt Q (pC) 25-60 35 E (GeV) 1.0 1.1 dE/E RMS (%) 4 2.5 div. (mrad) 2.4 1.6 1.1 [GeV] Intro to High Energy Density Physics Credit: W.P. Leemans et. al, Nature Physics 2 (2006) 696; *Simulation using VORPAL 62 Researchers have developed advanced diagnostic techniques for plasma accelerators Magnetic field measurements of the electron beam (wavebreaking diagnostic) 2011 Summer School single shot frequency domain holography Intro to High Energy Density Physics Page 63 Data credits: Mike Downer, Kaluza et al. ( submitted ), Michigan/Texas collaboration, Matlis et al., Nature Physics 2006 Energy Doubling of 42 Billion Volt Electrons Using an 85 cm Long Plasma Wakefield Accelerator 42 GeV 85GeV Nature v 445,p741 (2007) 2011 Summer School Slide Credit: Chan Joshi Intro to High Energy Density Physics Page 64 Plasma Accelerator Progress “Accelerator Moore’s Law” ILC Working Machines Doing physics E167 E164X LBNL RAL Max.Energy in Plasma Experiments 2011 Summer School UCLA Intro to High Energy Density Physics LBL Osaka Page 65 For a deeper fundamental background in HEDP • Come next summer to the next offering of – Foundations of High Energy Density Physics • A thorough introduction to the foundations of this subject – Taught by one lecturer (me) to provide a continuous discussion with common notation based on a book – A two week course • Past students have been enthused – Otherwise I would not be doing this again! – Contact [email protected] 2011 Summer School Intro to High Energy Density Physics Page 66 High-energy-density physics is exciting! Radiating shocks Self-organized states Toward TeV beams With applications from supernovae to medicine 2011 Summer School Credits: Karl Krushelnick, Bedros Afeyan Intro to High Energy Density Physics Page 67 Forefront fundamental areas of HEDP • High energy density hydrodynamics – How do the distinct properties of high energy density systems alter hydrodynamic behavior? • Radiation-dominated dynamics and material properties – What are the unique properties of radiation-dominated HED plasmas? • Magnetized HED dynamics – How do magnetic fields form, evolve, and affect the properties of high energy density plasmas? • Nonlinear optics of HED plasmas – How does high-intensity coherent radiation alter the behavior of high energy density plasmas? • Relativistic high energy density plasma physics – How do plasmas with relativistic temperatures or relativistic flows behave? • Warm dense matter physics – What are the state, transport, and dynamic properties of warm dense matter? 2011 Summer School Intro to High Energy Density Physics Page 68