introduction to high energy density physics r. paul drake university of michigan
DESCRIPTION
Introduction to High Energy Density Physics R. Paul Drake University of Michigan. High-Energy-Density Physics. The study of systems in which the pressure exceeds 1 Mbar (= 0.1 Tpascal = 10 12 dynes/cm 2 ), and of the methods by which such systems are produced. - PowerPoint PPT PresentationTRANSCRIPT
Introduction to High Energy Density Physics
R. Paul Drake University of Michigan
2003 HEDP Class Inroductory Lecture Page 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.
2003 HEDP Class Inroductory Lecture Page 3
How is HEDP connected to other areas?
2003 HEDP Class Inroductory Lecture Page 4
The equilibrium regimes of HEDPAdapted from:
National Research Council Report, 2002
“Frontiers in High Energy Density Physics: The X Games
of Contemporary Science”
2003 HEDP Class Inroductory Lecture Page 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
2003 HEDP Class Inroductory Lecture Page 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)
2003 HEDP Class Inroductory Lecture Page 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
Credit: Keith Matzen, Marcus Knudson, SNLA
Compression (density ratio)
Pressure (GPa)
2003 HEDP Class Inroductory Lecture Page 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
2003 HEDP Class Inroductory Lecture Page 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 .
€
dI
dx= −χI = −ρχ mI
2003 HEDP Class Inroductory Lecture Page 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)
2003 HEDP Class Inroductory Lecture Page 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 onDa Silva 1992
Transmission
Both HEDP experiments and sophisticated computer calculations were essential to quantitative understanding
€
∝ e-χd
2003 HEDP Class Inroductory Lecture Page 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
2003 HEDP Class Inroductory Lecture Page 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
2003 HEDP Class Inroductory Lecture Page 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 €
T /M i
€
T 4 = ε T /M i = p T /M i /(γ −1)
€
p = γ −1( ) M iσT3.5 ~ 20
T
100 eV
⎛
⎝ ⎜
⎞
⎠ ⎟3.5
Mbars
2003 HEDP Class Inroductory Lecture Page 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)
2003 HEDP Class Inroductory Lecture Page 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)
€
~ 1.5ncritkBT ~ 2.6 ×105 TkeV
λ μ2
J
cm3
€
IL ~ fε T /me
€
T ~ 2 I14λ μ2
( )2 / 3
keV
€
p = M i
kBT
M i
×ncrit
kBT
M i
= ncritkBT = 3.5I14
2 / 3
λ μ2 / 3
Mbars
2003 HEDP Class Inroductory Lecture Page 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
Initial plasma
Shock velocity, vs
csd > vs here
csu < vs here
upstreamdownstream
Mach number M = vs / csu
2003 HEDP Class Inroductory Lecture Page 18
Much of the excitement in HEDP comes from the dynamics
Shock waves establish the HEDP regime of an experiment
2003 HEDP Class Inroductory Lecture Page 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
2003 HEDP Class Inroductory Lecture Page 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
€
∂∂t
= −∇ • ρu( )
€
∂u∂t
+ ρ u • ∇( )u = −∇p−∇pR −∇ • σ +Fother
€
€
u
€
p
€
pR
€
€
Fother
2003 HEDP Class Inroductory Lecture Page 21
The energy equation has a number of terms that often don’t matter
• General Fluid Energy Equation:
€
∂∂t
ρε +ρu2
2+ ER
⎛
⎝ ⎜
⎞
⎠ ⎟+∇ ⋅ ρu ε +
u2
2
⎛
⎝ ⎜
⎞
⎠ ⎟+ pu
⎡
⎣ ⎢
⎤
⎦ ⎥=
−J • E+ Fother • u−∇ • FR + pR + ER( )u+Q − σ v • u( )[ ]
Material Energy Flux m
€
m
Pe
€
m
Re
€
m
PeRad
=
τ rad
τ hydro
Γm
Smalleror Hydro-like
€
ν ei
ωpe
~ 1 Typ. small
Or Ideal MHD
2003 HEDP Class Inroductory Lecture Page 22
So let’s discuss dynamic phenomena We start with hydrodynamics
• Sound waves = cs k or f (Hz) = cs /
• Shock waves
• Rarefactions
• Instabilities
2003 HEDP Class Inroductory Lecture Page 23
It’s easy to make a shock wave 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, .1 TP).
This easily launches a shock.
Sustaining the shock takes more laser energy.
Thicker layer for diagnostic
Laser beam
Emission From rear
Time
2003 HEDP Class Inroductory Lecture Page 24
Astrophysical jets and supernovae make shocks too
Supernova RemnantAstrophysical Jet
Burrows et al. J. Hester
2003 HEDP Class Inroductory Lecture Page 25
We analyze shocks in a frame of reference where the shock is at rest
Denser,Hotter
Matter comes in at velocity of shock in lab frame, vs
Density d here Density u here
Matter leaves at slower velocity, vd
From continuity equation:
From momentum and energy equations:
vd =vs
ρuρd For strong shocks
ρdρu
=γ+1( )M 2
γ−1( )M 2 +2 ≈
γ+1( )γ−1( )
pdpu
=2γM2 − γ−1( )
γ+1( ) ≈
2γγ+1( )
M 2
Marcus Knudson will tell you much more about shocks
2003 HEDP Class Inroductory Lecture Page 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
Density
Position
• Rarefactions can be abrupt – When shock waves or blast
waves emerge from stars or dense plasma, a rarefaction occurs
2003 HEDP Class Inroductory Lecture Page 27
Many HEDP experiments have both shocks and rarefactions
SN 1987ASketch of
ExperimentRadiographic 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
2003 HEDP Class Inroductory Lecture Page 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)
2003 HEDP Class Inroductory Lecture Page 29
Hydrodynamic instabilities are common
• Three sources of structure
– Buoyancy-driven instabilities (e.g. Rayleigh-Taylor)
– Lift-driven instabilities (e.g. Kelvin-Helmholtz)
– Vorticity effects (e.g. Richtmyer-Meshkov)
Instability in a simulation of supernova remnant
Chevalier, et al. ApJ 392, 118 (1992)
2003 HEDP Class Inroductory Lecture Page 30
Buoyancy-driven instabilities are very important
• The most important are bouyancy-driven– Rayleigh Taylor
– “Entropy mode” or “Convective mode”
• Examples of this:
http://www.chaseday.com/PHOTOSHP/2JUL76/01-cbnw.JPG
Convective cloud formation
Rayleigh Taylor
Average density determines pressure gradient
Local density determines local gravitational force Net upward force = (<> - )g
2003 HEDP Class Inroductory Lecture Page 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
€
n ≈kg
1+ kL−βkvAblation
Remington et al. Phys. Fl. B 1993
2003 HEDP Class Inroductory Lecture Page 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
2003 HEDP Class Inroductory Lecture Page 33
Supernova remnants produce the Rayleigh-Taylor driven by plasma flow in simulation, …
• 1D profile and 2D simulations
Chevalier, et al. ApJ 392, 118 (1992)
In supernova remnants
and supernovae
Kifonidis, et al.
2003 HEDP Class Inroductory Lecture Page 34
.. in observation, and in lab experiment
Supernova Remnant E0102- 72 from Radio to X- Ray Credit: X- ray (NASA/C XC/ SAO); optical (NASA/HST); radio: (ATNF/ ATCA) http://antwrp.gsfc.nasa.gov/apod/ap00 0414.html
Blast-wave driven labresult
RemnantE0102
Dmitri Ryutov will tell you more….
2003 HEDP Class Inroductory Lecture Page 35
Here’s how we do such experiments
• Precision structure inside a shock tube • Interface with 3D
modulations
From Drake et al. Phys. Plas. 2003
2003 HEDP Class Inroductory Lecture Page 36
The second major instability driver is lift
Airplane wing
Rippled interface
Flow
Flow
Kelvin-Helmholtz Instability
U
U
2003 HEDP Class Inroductory Lecture Page 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
€
n = −ikx
A
2ΔU +
kxΔU
2
2 ρ aρ b
(ρ a + ρ b )Wave
propagates If A ≠ 0
Wave Grows for all kx
€
∂δx s
∂t+ u • ∇δx s = us
2003 HEDP Class Inroductory Lecture Page 38
Kelvin-Helmholtz makes mushrooms on Rayleigh-Taylor spike tips
Supernova simulation by Kifonidis et al. Lab simulation: Miles et al.
Data in Robey et al.
But not so much along the stems.
A big difference among codes is how much “hair” they grow on the stems.
2003 HEDP Class Inroductory Lecture Page 39
Instead, “vortex shedding” is important in clump destruction
Simulation of 1987A ejecta-ring collision
QuickTime™ and aGIF decompressorare needed to see this picture.
Clump destruction by blast wave (Robey et al. PRL)
Clump destruction by steady flow (Kang et al. PRE)
This process is also driven by lift
2003 HEDP Class Inroductory Lecture Page 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).
€
=∇×u
€
∂∂t
=∇ × (u×ω) + ν∇ 2ω
2003 HEDP Class Inroductory Lecture Page 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
2003 HEDP Class Inroductory Lecture Page 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