Optimization of plasma uniformity in laser-irradiated underdense targets

M. S. Tillack, K. L. Sequoia, B. O’Shay

University of California, San Diego9500 Gilman DriveLa Jolla, CA 92093-0438USA

H. A. Scott

Lawrence Livermore National LaboratoryP.O. Box 808Livermore, CA 94561USA

C. A. Back

General AtomicsP.O. Box 85608San Diego, CA 92186-5608USA

Objectives:

Studies of atomic processes in laser plasma require uniform conditions:

a) Predict the degree of uniformity in ne and Te for directly-heated underdense (non-LTE) targets

b) Explore the impact of physics models on the results

c) Propose design solutions to improve the uniformity

Under conditions of direct heating, the value of absorption coefficient is critical

If t<1 mm or I>1014 W/cm2, the targets expand too quickly

Key Physics Issue: Choice of Opacity and Ionization Models

Inverse bremsstrahlung, non-LTEIntroduction

Inverse bremsstrahlung in Hyades

Comparison with experiment

Hyades (Cascade Applied Sciences)1D rad-hydroGray (Sesame) or multi-group diffusionSaha or average atom ionization modelHelios

(Prism Computational Sciences)1D rad hydro5000-group computed opacities

Numerical Simulation

Experimental Geometry

(NIKE)1.6 kJ, 248 nm4 ns12˚ cone angle5x1012–5x1014 W/cm2

McWhirter condition

The density is uniform when Zeff is near a maximum and hydro expansion is small

(I<1014, t>1 mm)

Density uniformity

(ne>1.4x1014 Te1/2(E)3 cm–

3)

It’s difficult to achieve optically thin plasma with 2 mg/cc (5x1020) SiO2 targets 1 mm thick @ Te<300 eV

(note: ncr=16x1021/cm3)

Pillbox Target

Most of the plasma is non-LTE

Cases analyzed• 0– 6 at% Ti dopant

• 2–8 mg/cc

• 1–2.2 mm thickness

• 5x1012 – 4x1014 W/cm2

Experimental

Parameters:

High Fluence:

• 2.2 mm

• 3% Ti dopant

• 2.7 mg/cc

• 5.7x1013 W/cm2 (248 nm)

Low Fluence:

• 1 mm

• 6% Ti dopant

• 2.5 mg/cc

• 4.6x1012 W/cm2 (248 nm)

LTE

non-LTE

2.5 ns

Non-LTE ionization balance of Ti in 2 mg/cc SiO2 (Cretin)

2 ns

data courtesy of Prism Comp. Sci.

(2.5 at%)

The radiation mean free path at 150 eV is several

mm

Hyades 35-group, non-LTE avg. atom

Helios predicts much higher temperatures

Double-Sided Illumination

1 mm thick2.6 mg/cc SiO2

Same total laser input(2 x 2.5e12 or 2 x 3e13)

2-sided illumination provides a more uniform temperature profile at lower intensity

I=6x1013 W/cm2

Te,

eV

Time, ns

I=5x1012 W/cm2

Time, ns

Indirect radiation heating from end zones also can produce uniform temperature and

density

3 mg/cc SiO2

2.6 mg/cc SiO2 3% Ti

3 mg/cc SiO2Laser Laser

0 1 mm 2

0

20

40

60

80

100

120

140

160

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

R, cm

Te, eV

1 ns

2 ns

3 ns

4 ns

Time, ns

R,

cm

Ne,

10

20

cm

-3

Time, ns

Time, ns

Te,

eV

2 ns

35 photon energy groups

Doping affects rad-hydroOpacity and Ionization Options in Hyades (pure

SiO2)

High Fluence Modeling Results

High IntensityBase Case Results

I=6x1013 W/cm2

Zeff

Time, ns

Higher laser intensity gives higher, slightly flatter temperature and faster, stronger

ionization

2.5 ns

2.5 ns

Conclusions:

• In this regime, results are sensitive to models used

• LTE and non-LTE results are quite different

• Doping has a significant effect on the radiation hydrodynamics

• Double-sided and indirect illumination both show promise

• More data are needed to help understand the underlying physics

SiO2 aerogel

with Ti dopant

}

Energy Balance

2.5 ns

Zeff

5x1012 W/cm2

Time, ns

Zon

e C

oord

inate

, cm

6x1013 W/cm2

Time, ns

Zon

e C

oord

inate

, cm