M. S. Tillack

Radiation-Hydrodynamic Analysis of Doped Underdense Targets for HED Studies

8 February 2005

Mechanical and Aerospace Engineering Department

and the Center for Energy Research,Jacobs School of Engineering

We are collaborating with LLNL on a 3-year study of non-LTE laser plasmas

Overall goal is to develop absolutely calibrated spectroscopic diagnostics and benchmark data from well-characterized “non-LTE” plasmas

• Address a class of problems in which temperature can not be uniquely related to energy

• Establish credibility in non-LTE calculations• Resolve long-standing problems in the literature

concerning emission from low density plasmas

TGS

“Non-LTE”: energy content and radiation emission depend on the full time-dependent set of rate equations for atomic processes

• Collisional ionization, recombination, excitation, and deexcitation

• Photoionization and stimulated recombination• Photoexcitation and stimulated emission• Spontaneous decay• Radiative recombination• Dielectronic recombination, autoionization, and electron

capture

A generic problem with laser plasmas is the large gradients and transient nature, which complicate analysis and data interpretation

Te and ne in 100 m DT film at 1 ns, 5x1014

W/cm2

Low density targets (gas bags or foams) can provide more uniform density and temperature:

1. mass limited so that all of the target mass heats

2. optical thickness comparable to target thickness at desired Te

3. larger than the hydrodynamic expansion length during the pulse >1 mm thick, 1-10 mg/cm3 for 4 ns laser

pulse

40 shots (7 days) were obtained at Nike in 2004;

Future experiments are planned at Janus

Obtained absolutely calibrated Ti L-shell emission from aerogel targets

– Measured time-resolved spectra in 470-3000 keV region covering Ti L-shell

Determined accessible plasma conditions by variation of laser parameters

– Able to heat plasma to threshold of K-shell emission (He-like Ti emission)

– Determined experimental conditions for creating L-shell emission

(135 J, 4 ns, 940 µm spot)

– Time-integrated measurements of plasma Te via Si and Ti K-shell line ratios

Examined plasma uniformity with x-ray imaging diagnostics

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are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

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Nike chamber (5 kJ)

Model predictions often disagree with data, and with each other

Non-LTE plasma simulations are computationally expensive and often not self-consistent

To model realistic plasmas, simulations must implement approximations in the atomic physics data and radiation algorithm

– A relatively complete model of a Ti ion can have

up to 20,000 levels– An approximate model of the same ion may be

reduced to ~100 levels in order to run simulations

This project is an element of the growing field of High Energy Density (HED) physics

1. Material Properties

2. Compressible Dynamics

* HED in NNSA Facilities, “Bruce Remington (LLNL), Chris Deeney (SNLA), David Hammer (Cornell),

Dick Lee (LLNL), David Meyerhofer (LLE), Dieter Schneider (LLNL), Isaac Silvera (Harvard), Bernie

Wilde (LANL),” A presentation to the High Energy Density Physics Workshop, May 24-26, 2004,

Gaithersburg, Maryland. http://www.ofes.fusion.doe.gov/More_HTML/HEDPWorkshop5-

04.html

The topic of HED on NNSA facilities is divided into 4 thrust

areas: *

Our work addresses two of

these“Compelling question” for material properties thrust area:

Can matter in the difficult warm dense matter (WDM) regime be isolated,

defining its state while measuring the material properties of interest?

3. Radiative Hydrodynamics

4. Inertial Confinement Fusion

“Compelling question” for radiation hydrodynamics area:

Can HED experimental facilities become a routine tool for testing rad-hydro

models and simulations of powerful astronomical phenomena in a scaled

laboratory setting?

The goal of the material properties thrust is to map material properties across the WDM regime

Hot Dense Matter occurs in:

• stellar interiors, accretion

disks

• laser plasmas, z-pinches

• radiatively heated foams

• ICF capsule impoded cores

Warm Dense Matter occurs in:

• cores of giant planets

• strongly shocked solids

• radiatively heated solid foils

1. Prepare the state (at desired density, temperature, etc.)

– verify that gradients are small, time-dependent effects are unimportant

2. Measure the material property of interest

– opacity, ionization state, EOS, conductivity, etc.

The methodology involves two steps:

The Radiative Hydrodynamics thrust focuses on “hot flowing matter”, where the radiation

and material flows are coupled

• Quantitative modeling of such flows is difficult; benchmark data is needed

• Examples: radiative shocks & jets, supersonic radiation flow, photoionized plasmas, radiation-dominated dynamics

• Radiative hydrodynamics abounds in astrophysical plasmas

Radiative shock in Janus

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Radiative shocks in the Cygnus loop SNR

At UCSD we are contributing to both experiments and modeling activities

• 1D LTE rad-hydro simulations using Hyades and Helios

– gray and spectrally resolved simulations– purpose is to explore and verify ne and Te behavior,

and determine whether spectral detail affects hydro

• Non-LTE simulations using Cretin and Helios-CR

• Experimental support of Te diagnostics

– Single-channel calibrated PCD detector– Multi-channel filtered diode detector

During 2004 we acquired several new modeling tools

• Cascade Applied Sciences (Jon Larsen), history of use at LLNL

• Limited capabilities for spectrally resolved opacities, LTE only

1. Hyades

• Prism Computational Sciences (MacFarlane/Golovkin), used a lot at SNLA

• Propaceos code provides spectral data, Helios-CR for non-LTE

2.

Helios

• Lagrangian grid, flux limited, diffusion approximationStandard 1D rad-hydro codes

• 3D non-LTE collisional-radiative rate equation solver (Howard Scott)Cretin

HULLAC• Parametric potential method to generate atomic data (Klapisch/Busquet)

Cases were examined using Hyades at high and low density, high and low intensity, with and without

doping

Case # Description Ti wt% SiO2 density(mg/cm3)

laser intensity(TW/cm2)

0 modeling base case 0 2 4.91 experimental base case 2 2 4.92 high Ti dopant case 6 2 4.93 high SiO2 density case 2 8 4.94 thin target case 2 2 4.95 high laser intensity case 2 2 3706 high intensity, high doping 6 2 370

t

I 3.6 ns

4 ns

All cases used a 4-ns flat-top intensity profile at 248 nm

An unfeathered grid with 50 zones was used to simplify graphical interpretation (constant mass per zone)

Base case temperature evolution (5x1012 W/cm2, SiO2, 2 mg/cm3 )

Spatial profile at 2.5 ns

~50 eV

~1/2 ns

Base case density evolution

Spatial profile at 2.5 ns

(note: ncr=16x1021/cm3)

Charge state, target expansion, laser absorption

(nodes 25-50)

(100 nodes)

(Denavit, PoP 1994)

Two key physical processes are involved in underdense laser plasma energy transfer

= 10–16 Te–3/2 Z ln (ne

2/ncr)

1. Laser absorption in underdense plasma (inverse bremsstrahlung)

2. Emission and absorption of thermal radiation

L = 1 mm

The radiation absorption wave propagates more slowly at higher density (8 mg/cm3)

Scaling depends on opacity rather than inverse

bremsstrahlung

~50 eV

... but the final temperature, density and charge state are remarkably

similar

At 4x1014 W/cm2, the plasma is fully stripped and expands more rapidly

This plasma becomes transparent; the density is initially uniform, but is quickly lost due to

expansion

0.E+00

1.E+20

2.E+20

3.E+20

4.E+20

5.E+20

6.E+20

7.E+20

8.E+20

0 10 20 30 40 50

Zone index

Electron density, cm

-3

increasing time

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 50

Zone index

Temperature, keV

increasing time

Properly modeling opacities is challenging

Planck averaging:

Rosseland averaging:

SiO2

We tried several variations to explore the influence of opacity models on the results

• Sesame data in Hyades

• Built-in multi-group model in Hyades

• Propaceos (spectral) data averaged and imported into Hyades

• Propaceos (spectral) data used in Helios

• Sesame data used in Helios

• Reduced frequency group (averaged) modeling with Helios

Due to problems implementing multi-group radiation

transport in Hyades, we relied upon Helios to study the

effect of doping

Unfortunately, temperatures from Hyades and Helios do not agree very

well

Hyade

s

Helios

spatial profiles at 2.5

ns

Opacity data is surely part of the reason

• Helios plasmas are much more opaque

• Which is correct?

range of interest

Comparison of spectrally averaged opacities

The energy balance looks completely different

Helios stores ~50% of the energy, whereas Hyades promptly radiates 90%. Helios plasma is far more opaque.

2 kJ/cm2

7 kJ/cm2

8 kJ/cm2

16 kJ/cm2

The effect of 6% Ti dopant on Te (using Helios)

The doped case cools faster and is less uniform

base case

6% Ti

The effect of 6% Ti dopant on ne (using Helios)

The lower temperature leads to slightly lower density

base case

6% Ti

Summary

• Plasmas with uniform ne and “relatively” uniform

Te were obtained and parametrically studied in the

range 5x1012–5x1014 W/cm2; not quite good enough yet

• The best results seem to occur when the target is

optically thick to the laser

• Codes disagree, even with single-group opacities.

Hyades needs more work to produce accuratespectrally resolved results

• Doping significantly affects temperatures (based on Helios simulations); makes them

worse!

Our plans in 2005-06 include more modeling and experimental

collaborations

• Further optimization of rad hydro

• Increased use of Cretin to study non-LTE

emissions

• Explore atomic data for non-LTE work

Hullac, Propaceos, new averaging schemes, ...

• Development of PCD detectors for Te

measurements

– single, calibrated diamond diode

– filtered diode array

• Experiments at Janus