Introduction to High Energy Density Physics (HEDP)hedpschool.lle.rochester.edu/2011SummerSchool/lectures/Drake.pdf · Introduction to High Energy Density Physics ... this plot to

Introduction to High Energy Density Physics

(HEDP)R. Paul Drake

University of MichiganSummer School on High Energy Density Physics

UCSD, July 2011

DrakeLab

Department of AtmosphericOceanic & Space Sciences

Applied Physics Program

Michigan Institute for PlasmaScience and Engineering

Center for RadiativeShock Hydrodynamics

2011 Summer School Intro to High Energy Density Physics Page 2

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


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

Image credit NNSA Nevada Site Office


We will use this plot to see aspects of high-energy-density physics (HEDP)

• HEDP parameters• Physics connections

– Strong coupling– Pressure and Fermi

degeneracy• Astrophysics

connections• Plasma physics

connections– Particles per Debye

sphere


Physics connections within and beyond HEDP

Quark-gluonplasmas

QM


HEDP plasmas can be very strongly coupled

• Γ = |qφ|/kT

X-ray Thomson scattering

ElectronTemperature

Te (eV)

Data from Glenzer & Redmer, RMP 2008


Astrophysics connections with HEDP

• Other elements of thisconnection– High Mach number

flows– Fast shocks– Ionizing– Strong B fields– Radiation matters– Plasma

hydrodynamics

Curves credit NRC report on HEDP


Perspectives on plasma physics and HEDP

• The mid-20th-Century approach to plasma physics, as seenin 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


HEDP systems often havefew particles per Debye sphere

Image credit David Montgomery

Be model

UV Thomson scattering

Data credit Riccardo Betti


Regime boundaries move as materials change

Ionization iscentrally important


The pressure often is not nkT

~ Gbar shockin Al

Data from Cauble et al, PRL 1991


HEDP theory: a fluid approach often works, butnot 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 andvariants) is important when strong waves are present at “low”density

• A single particle or a PIC (particle-in-cell) approach is needed forthe relativistic regime and may help when there are strong waves


We now discusshow to create HEDP conditions


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 speedso

– From which

T /Mi

!T 4= " T /Mi = p T /Mi /(# $1)

p = ! "1( ) Mi#T3.5

~ 20T

100 eV

$

% &

'

( )

3.5

Mbars


… or zap it with a laser

Any material

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, 0.1 TP).

This easily launches a shock.Sustaining the shock takes more laser energy.

Thicker layer fordiagnostic

Laser beamEmission From rear

Time

Momentum balance gives p ~ 3.5 I142/3 / λµm

2/3 Mbars


Perspectives on strong shocks in HEDP

• Many HEDP experiments involve at least onestrong 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

• Radiative shocks• Isentropic compression• Hydrodynamic processes

Shock in Xe clusters

Data from Ditmire et al. ApSS 2000


High Energy Lasers are key tools

• High energy lasers amplify the light energyacross a large area then compress the beam(s) inspace to create high energy density

amplify protect

Smooth(spatial filter)

amplify

vacuum

irradiate


The biggest lasers can produce 100 Mbar pressureson mm2 to cm2 areas

Target chamber at Omega laser

National IgnitionFacility

192 beams > 1 Megajoule

Omega 60 beams 30 kJ


The laser creates structure at the target surface

• The laser is absorbed at less than 1% of soliddensity

Ablation pressurefrom approximatemomentum balance:

This is a bit low; bettercalculations replace3.5 by 8.6

A pressure > 100Mbars is practical

From Drake, High-Energy-Density Physics, Springer (2006)

p ~ 3.5 I142/3 / λµm

2/3 Mbars


Hohlraums create thermal environments atmillions of degrees• Put energy inside a

high-Z enclosure

• The vacuumradiation field staysin equilibrium withthe resulting hotsurface

• One gets hightemperaturesbecause the radiationwave moves slowlyinto the material,penetrating fewmicrons

Credit LLNL

Laser spots seen through thin-walled hohlraum.

Hohlraum with experiment attached on bottom

From Drake,High-Energy-DensityPhysics,Springer (2006)


Z pinches also produce high-energy-densityconditions

• Todayʼs biggest is the Z machine at Sandia, when run as aZ pinch (~ 2 MJ of x-rays)

• Z pinches exploit the attraction between parallel currents

Cylindrical wire array Implosion Stagnation

Inward J X B force Inward acceleration

Shock heating &Radiative cooling

Credit: Keith Matsen


The action is at the center of a large thoughcompact structure

Credit: Keith Matsen


Ultrafast lasers producerelativistic HED conditions• Compression in time as well as space• Hercules at U. Michigan

– The most intense laser in the world

ao = p/mc ~ 100


Located at SLAC

FFTB

e-

N=1-2·1010

!z=0.1 mm

E=30 GeV

IonizingLaser Pulse(193 nm)

Li Plasmane!6·1015 cm-3

L!30 cm

CerenkovRadiator

Streak Camera(1ps resolution)

X-RayDiagnostic

Optical TransitionRadiators Dump

25 m

"Cdt

Not to scale!

Spectrometer

25 m

Particle beam bunches can be HED systems

Slide Credit: Chan Joshi


Now we turn to the fundamental physics ofHEDP 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


Equations of State


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 varieswith pressure

• Here is one theoreticalmodel of the structure ofhydrogen

Saumon et al., 2000


[D. Saumon and T. Guillot, Ap. J. 609, 1170 (2004)]

MZ/MEarth

0 10 20 30 40

MCo

re/M

Earth

No core 0

10

20

15

5

The different EOS models for hydrogen directlyimpact whether Jupiter is predicted to have acentral dense core or not

• Outlines show range ofmodels matching Jupiterʼsproperties within 2σ ofobserved

• Cannot yet tell whetherJupiter has a core

• The predicted age ofJupiter is is also sensitiveto the H EOS, which affectsluminosity

Adapted from slide by Bruce Remington


EOS results are often shown as the pressureand density produced by a shock wave

Credit: Keith Matzen, Marcus Knudson, SNLA

Compression (density ratio)

Pressure(GPa)

• This sort of curve iscalled a ShockHugoniot (orRankine-Hugoniot)relation

• Changing curveshape comes fromchanging structure

• Other thermodynamicvariables (ε,T) can beinferred from theproperties of shocks


Equation of state experiments have been andwill be common at HED facilities

D. Hicks, et al., PHYS. REV. B 79, 014112 (2009)

Single-shock and double-shock Omega data


5 minute stretch


Radiative Shocksone topic in radiation hydrodynamics


Most HEDP dynamicsbegins 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 plasmaDenser,Hotter

Initial plasma

Shock velocity, vs

csd > vsin frameof shock

csu < vs here

upstreamdownstream

Mach number M = vs / csu


Shock waves become radiative when

• Radiative energy flux would exceed incoming material energyflux

• Where post-shock temperature is

• The ratio of these energy fluxes is proportional to us5/ρo

• Implying threshold velocities ….Material Xe Xe CHDensity 0.01 g/cc 10-5 g/cc 0.01 g/ccThreshold velocity 60 km/s 10 km/s 200 km/s

RTs=2(! "1)

(! +1)2us

2

downstreamUpstreampreheated

σTs4 > ρous

3/2


Conservation of energy forces the shock waveto develop complex structure

Shocked xenon layer Compressed 40x Traps thermal photons

Preheated regionThermal photonsescape upstream

Other funcomplications: Instabilities Wall shocks


Radiative shocks are challenging in bothastrophysics and the laboratory

• Radiative shocks– Radiation alters the structure and

dynamics of the shock– A radiation-hydrodynamic

phenomenon– Inherently nonlinear– Sometimes unstable

• Motivation from astrophysics– Supernova shocks– Stellar shocks– Some accretion phenomena

• Modeling them is difficult– Widely varying scales– Radiation transport regimes– Ionizing media and 3D effects

• Astrophysical modelerscalled for experiments in thisarea– Matching key dimensionless

parameters is what one cando

• Experiments are a majorchallenge– Novel experimental systems– Need innovation in targets

and diagnostic approaches


How to produce radiative shocks

Gas filled tubes

Laser beams launch Be pistoninto Xe or Ar gas at > 100 km/s

Piston drives shock

Diagnostics measure plasmaproperties

Gold grids provide spatialreference

Parameters1015 W/cm2

0.35 µm light1 ns pulse600 µm tube dia.

Targets: Korbie Killebrew, Mike Grosskopf,Trisha Donajkowski, Donna MarionExperiments: Amy Reighard, Tony Visco, Forrest Doss


Researchers are studying these shocks with arange of diagnostics and simulations• Radiographs • Emission

• Xray Thomson scattering

• Interferometry

Data credit: L. Boireau S. Bouquet, F. Doss M. Koenig, C. Michaut, A. Reighard, T. Visco , T. Vinci


Researchers are simulating such shocks too

Xe radiograph(of rotated output)

Level

Axial vel.

Radial vel.

Density

Pressure

Te

Tr

The agreementhere is too good

CRASH 1.0 2D Simulation


Next directions in the study of radiative shocks

shock

Reighard Omega experiment

Omega scale:Determine structureand dynamicsBoth axial and lateralCreate more complexsystems

Target for ViscoX-ray Thomsonscatteringexperiment

Omega has the potential to doother radiation hydrodynamics

NIF can go further

Continuously radiating shockproduces dense xenon layer at> 30 times initial density.


Applications ofHigh Energy Density Physics


Why did the US Congress fund HED machines?

•They were developed for inertial confinement fusion (ICF)


In ICF one first compresses the fuel using anablatively driven implosion• This turns out to be necessary to avoid blowing up the lab

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

An ablatively driven implosion

ICF fusion Capsule


After compression, one has to make the ICFfuel burn by fusion• Two approaches

This is the traditional approach

Design the central hot spotso it ignites the fuel

Let the central hot spot bemuch smaller and rapidlyignite the compressed fuel

Options: lasers, particles, slugs

This is called fast ignition


HED experimental astrophysics is emerging

• New tools enable new science,and create new sciences

e.g., Hubble diagram

Spectroscopy enabledand created astrophysics

Astronomy: the human eye and brain

• High Energy Density facilitiesare new tools …..


core

zoneradiative

convectivezone

2007 Don Dixon / cosmographica.com

Predictions of solar structure do notagree with observations (13 σ CZproblem)

Solar structure depends on opacities thathave never been measured

Challenge: create and diagnose stellarinterior conditions on earth

Z opacity experiments reach T ~ 156 eV

High T enables first studies of transitionsimportant in stellar interiors

Laboratory experiments test opacity modelsthat are crucial for stellar interior physics

λ (Angstroms)

trans

miss

ion

8.0 10.0 12.0 14.0

Fe / Mg transmission at T ~ 156 eV

Laboratory experiments test opacity modelsthat are crucial for stellar interior physics

Slide credit: James Bailey


Magnetically-driven z-pinch implosions provide one means todo studies like this, requiring bright x-ray sources

Current

B-Field

JxB Force

StagnationImplosionInitiation

kinetic and electrical energy

internal (shock heating)

x rays

electrical energy

kinetic energy• Energy: 1.5 MJ x-ray ≈ 15%

of stored electrical• Power: 200 TW x-ray



Opacity and photoionization experiments, relevant to stellarinteriors and accretion powered objects, have been done atZ and could be done at Omega

The importance of radiation for creation and diagnosis is a unifying themefor these very different plasmas

Fe + Mg transmission Te ~ 156 eV, ne ~ 1022 cm-3

Ne transmission at Te ~ 25 eV, ne ~ 1019 cm-3

photoionization sampleradiation effects in

plasma surroundingblack hole

opacity sample -same chargestates in sun

Zx-ray

source1-2 MJ

2·1014 W

X-rays

λ

λ

[Jim Bailey, PRL (2007); and PoP 13, 056301 (2006)]



There are three key dimensionless parametersfor radiative shocks

• The ratio radiation flux at the initial postshock temperature tothe incoming material energy flux

• The upstream optical depth• The downstream optical depth

Density

TemperatureUpstream ρo,To,po

(Ignoring ion-electron decoupling near the density jump)

Initial post-shock state ρi,Ti,pi

Downstream final state ρf,Tf,pf

Cooling layer

! T 4

"ous

3/ 2


Shocks in SNe pass through the regime of ourexperiments as they emerge

• 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 thinregion

Ensman and Burrows, ApJ., 393,742-755,1992

1987A simulation Xe experiment simulation

A.B. Reighard, Ph.D. Thesis, 2007


The fluid energy equation has a number ofterms that often donʼt matter• General Fluid Energy

Equation:

!!t

"# +"u2

2+ ER

$

% &

'

( ) + * + "u # +

u2

2

$

% &

'

( ) + pu

,

- .

/

0 1 =

2J•E + Fother •u2* • FR + pR + ER( )u+Q 2 3 v •u( )[ ]

Material Energy Flux Γm

!m

Pe

!m

Re

!m

PeRad=

" rad

" hydro

!m

Smalleror Hydro-like

! ei

" pe

~ 1Typ. small

OrIdealMHD

This enables scaledastrophysical hydrodynamicsexperiments whenRe, Pe, and PeRad are >> 1


Destruction of clumps in post-shock flow hasbeen a research area with impact

• Experimental results used to help interpret Chandra data from the PuppisA supernova remnant

• Well-scaled experiments have deep credibility• Una Hwang et al., Astrophys. J. (2005)

Klein et al., ApJ 2003Robey et al., PRL 2002

Well scaled experimentChandra data


How shock-clump experiments are done

• … but not in a way that letsone diagnose details

• The experiment involvesblast-wave-driven massstripping from a sphere

• Early experiments used Cuin plastic; recentexperiments use Al in foam


Observations of the Al/foam case continueduntil mass stripping had destroyed the cloud

• Hansen et al., ApJ 2007, PoP 2007


The stripping is clearly turbulent, consistentwith the necessary conditions

• The turbulent model is basedon “Spaldingʼs law of thewall”, Spalding (1961)

• ParametersRe ~ 105 to 106

U ~ 10 km/sν ~ 10-5 to 10-6 m2/sδ ~ Sphere ~ 60 µm radius

• δ /U ~ 6 ns ~ rollup time (data)

• Robey/Zhou time is ~ 1 ns

RemainingMass (µg)

Time (ns)

Hansen et al., ApJ 2007


Perspectives on relativistic HEDP

• The development of Chirped Pulse Amplification in the1980ʼs soon enabled the production of high-field HEDPconditions 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 todiscovering organized behavior with the production ofquasi-monoenergetic electron beams


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/


To accelerate lots of electrons,take them surfing too

• Electrons can surf the wake on a pressure pulse in aplasma

• The pressure pulse can be produced by one or more laserbeams or by an electron bunch. This is wakefield acceleration.

Credit: LBL OASIS Group

Laser pulse

Electrons

Plasma Wake


In 1979, Tajima and Dawson published theinvention of wakefield acceleration

• A Simple notion

• Complex implementation– Through the 1990ʼs this required convincing some plasma

waves to evolve to a final, desired, very nonlinear state

λp Wake phase velocity

vph = ωpe/kp=ωpeλp/(2π)

Choose ωpe, λp so vph = c


In 2002, Pukhov and Meyer-ter-Vehn identifiedthe “bubble regime”


Helium Gas Jet

Laser-Plasma Electron Accelerator

Laser Pulse Focuses

Ionize Gas & Make Wave

Gas Jet Fires

Wave Captures and Accelerates Electrons

about3 mm

Tajima & Dawson, Phys. Rev. Lett. 43, 267 (1979)

INVISIBLE

slide courtesy Mike Downer, UT-Austin


First GeV Electron Beam from LWFA

• Laser: a0 ~ 1.46 (40 TW, 37 fs)• Capillary: D = 312 µm; L = 33 mm

Credit: W.P. Leemans et. al, Nature Physics 2 (2006) 696; *Simulation using VORPAL

1 GeV beam

0

250

500

0.9 1.1

[GeV]

[pC/GeV]

expt.

sim.*

Sim ExptQ (pC) 25-60 35E (GeV) 1.0 1.1dE/E RMS (%) 4 2.5div. (mrad) 2.4 1.6


single shot frequencydomain holography

Magnetic field measurementsof the electron beam

(wavebreaking diagnostic)

Researchers have developed advanceddiagnostic techniques for plasma accelerators

Data credits: Mike Downer, Kaluza et al. ( submitted ), Michigan/Texas collaboration, Matlis et al., Nature Physics 2006


Energy Doubling of42 Billion VoltElectrons Using an 85 cm LongPlasma WakefieldAccelerator

Nature v 445,p741 (2007)

42 GeV 85GeV

Slide Credit: Chan Joshi


RAL

LBLOsaka

UCLA

E164X

ILC

Plasma Accelerator Progress“Accelerator Moore’s Law”

E167

LBNL

Working MachinesDoing physics

Max.Energy inPlasma Experiments


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]


High-energy-density physics is exciting!

Radiating shocks

Toward TeV beamsSelf-organized states

With applications fromsupernovae to medicine

Credits: Karl Krushelnick, Bedros Afeyan


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 HEDplasmas?

• 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 ofhigh 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 warmdense matter?

Documents

Introduction to High Energy Density Physics (HEDP)hedpschool.lle.rochester.edu/2011SummerSchool/lectures/Drake.pdf · Introduction to High Energy Density Physics ... this plot to