This work was performed under the auspices of the U.S. Department of Energy by the University of CaliforniaLawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.

Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551-0808

UCRL-PRES-204413

Simulations of Electron Transport Experiments for Fast Ignition using LSP

Presented to:15th International Symposium on

Heavy Ion Inertial FusionPrinceton University, NJ

Richard P. J. TownAX-Division

Lawrence Livermore National LaboratoryJune 7, 2004

UCRL-PRES-204413-2

The LSP code has been used to study fast ignition relevant transport experiments

• A critical issue for Fast Ignition is understanding the transport of the ignitor electrons to the fuel.

• Experiments have shown a rapid increase in beam width followed by reasonable collimation with a 20° half angle.

• We have used the LSP code to:– generate simulated K images; – model XUV images; and– model cone focus experiments.

• The LSP code has been used to study the effect on beam transport of:– non-Spitzer conductivity; and– the initial beam divergence.

UCRL-PRES-204413-3

A critical issue for fast ignition is understanding the transport of the ignitor electrons to the fuel

Rbeam

Rcore

Laser couples efficientlyto the core

Laser couples inefficientlyto the core

corebeam

2

core

beamminlaser RR for

RREE

1.1x1021cm-3 1026cm-3

This is a major driver on the short-pulse laser specification.This is a major driver on the short-pulse laser specification.

UCRL-PRES-204413-4

The XUV image can be used to estimate the temperature of the rear surface

XUV image • A series of LASNEX calculations of isochorically heated Al targets establishes the relationship between temperature and intensity.

UCRL-PRES-204413-5

Stephens et al.1 used a Bragg crystal mirror to image a Cu fluor layer embedded in Al with a CCD camera• Fast electron transport is diagnosed by burying a layer of of high-Z

(e.g., Cu or Ti) material within a low-Z plasma matrix (e.g., Al or CH).

• Electrons reaching the layer cause K-shell ionization and the emitted photons are imaged with a camera, thus characterizing energy transport within a dense plasma.

CCD camera

Bragg crystal mirror

Laser

electrons

K fluorescence layer

1R.B. Stephens, et al, to appear in Phys. Rev. E.

UCRL-PRES-204413-6

Experiments on MeV electron transport have been performed by researchers around the world

• Experimental data1 show:– a rapid increase in beam size in the first few microns; and– a fairly collimated (20º half angle) beam in the bulk of the

material.

1M. H. Key, et al, 5th Workshop on Fast Ignition of Fusion Targets (2001).

0 200 400

200

50

250

150

100

Thickness (m)

Spot

Rad

ius

(m

) X-ray (CH)

X-ray (Al)

XUVK fluorescenceLaser spot

UCRL-PRES-204413-7

LSP1 is a hybrid particle code used extensively in the ion beam community• Performed simulations using 2-D in cylindrical (r-z) geometry.

• Employs a “direct implicit” energy conserving electromagnetic algorithm.

• Hybrid fluid-kinetic descriptions for electrons with dynamic reallocation.

• Scattering between the beam and background plasma included.– Ionization and excitation ignored.

• LSP has been coupled to ITS to enable the generation of K images to enable direct comparison with experimental data.

• Beam created by injection at the target boundary or by promotion within the plasma.

1D. R. Welch, et al, Nucl. Inst. Meth. Phys. Res. A464, 134 (2001).

UCRL-PRES-204413-8

We have performed simulations of generic electron transport experiments• The targets are based on the experiments performed by Martinolli

et al1 on the LULI and Vulcan laser.

• The big uncertainty is the initial hot electron beam parameters.

Al3+ Al3+Cu2+

R

Z20μm 20μm 20μm

VACUUM

300μm

20μm

100μmHot ElectronBeam

1E. Martinolli, et al., Laser & Part. Beams 20, 171 (2002).

UCRL-PRES-204413-9

A significant “halo” surrounds the short-pulse high intensity spot

• Typical data from Nova Petawatt laser shows about 30 to 40% of the laser energy in the central spot.

• We have approximated the laser intensity pattern as two Gaussians.

0.0 40.0 80.0 120.0100

102

104

106

Displacement (m)

Ener

gy d

ensi

ty(c

ount

s/pi

xel)

Airy functionCCD image ofFocal spot

UCRL-PRES-204413-10

Determining the input electron distribution is based on experimental measurements

• The conversion efficiency into hot electrons has been measured by many experimentalists over a wide range of intensities:

= 0.000175 I(W/cm2)0.2661

UCRL-PRES-204413-11

There are two well-known scaling laws for hot electron temperature which we have used

• Pondermotive scaling:Thot(MeV)= (I2/(1019W/cm2m2))1/2

• Beg scaling:Thot(MeV)= 0.1(I2/(1017W/cm2m2))1/3

Pondermotive

Beg

UCRL-PRES-204413-12

The current density and energy distribution can now be defined in terms of laser intensity

• Using the new Python front end to LSP the injected beam energy and current density can be calculated from:– conversion efficiency; and– hot temperature scaling law.

• A thermal spread is also added.

rold = 0.0for i in range(400): r = (i+0.5)*0.00002 intensity = Gaussian(r, 1.0e-3, 1.0e20, 0.0, 1.0e12) +Gaussian(r, 1.0e-2, 1.0e17, 0.0, 1.0e12) if intensity > 0.0: thot = BegScaling( intensity ) ehot = 1.6022e-16*thot area = pi*(r**2-rold**2) lpower = intensity*area epower = lpower*conversionEfficiency(intensity) Density =1.6022e-19*epower/(area*ehot) rold = r

Pondermotive

Beg

UCRL-PRES-204413-13

The LSP code uses Spitzer conductivity, which we know is not valid at low temperatures.

• The calculated resistivity of aluminum at solid density increases with temperature.

10-8

10-7

10-6

10-5

10-1 100 101 102 103

Temperature (eV)

Res

istiv

ity (

m)

SpitzerNon-Spitzer

UCRL-PRES-204413-14

Reduced filamentation is observed when the conductivity is constant to 100eV

• Beam density at 1.6 ps

0 50 100 1500

100

200

300

Z(m)

Spitzer conductivity Constant conductivity to 100eV

0 50 100 1500

100

200

300

Z(m)

1018 7.1018 6.1019 4.1020

density(cm-3)

UCRL-PRES-204413-15

The K diagnostic gives time-integrated images of the emission generated by the hot electron beam

• The diagnostic will record both K photons generated by the forward going and backward going “refluxed” electrons.

UCRL-PRES-204413-16

K images were generated at various times throughout the simulations

• A time history displaying the birth positions of the K photons can be generated for each source.

Photons created 0.5ps 1.5ps 3.0ps

Base source case: Beg Temperature Scaling, 200keV transverse thermal energy

X (m) X (m)

R (m

icro

ns)

X (m)

Y (

m)

Y (

m)

Y (

m)

The time integrated diagnostic is a good The time integrated diagnostic is a good measure of hot electron beammeasure of hot electron beam transport. transport.

UCRL-PRES-204413-17

LSP calculations show reasonable agreement with experimental data for moderate Al thicknesses • There appears to be moderate agreement in the trend of increasing spot diameter

with Al thickness, based on the average between vertical and horizontal line-outs.

• The large asymmetry in the horizontal direction is under investigation.

Spot

Dia

met

er (

m)

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Experimental Data

LSP calculations

Al Thickness (m)

UCRL-PRES-204413-18

We can also compare these source scenarios using the K spot diameter at half-max intensity

• A significant asymmetry was detected when taking similar line-outs in the horizontal direction, resulting in the relatively large error in spot diameter for many of the data points.

140

120

100

80

60

40

20

02D Source Injection

Spot

Dia

met

er (m

icro

ns)

Thermal transverse temperature (keV)

(I2)3/2(I2)1/2 (I2)1/30 100 200 300 400 500 600

140

120

100

80

60

40

20

0

Spot

Dia

met

er (

m)

UCRL-PRES-204413-19

The LSP calculation matches the measured temperature pattern at the rear surface of the target

• 27J of hot electrons, in a 1-ps pulse, with Beg scaling and a thermal spread of 300keV injected into a 100m Al3+ plasma.

• The temperature was obtained by post-processing the LSP energy data at the rear surface with a realistic equation of state.

UCRL-PRES-204413-20

Z3 is being used to generate hot electrons from LASNEX-predicted pre-pulse plasmas

• 1-D line out of plasma formed by 10mJ prepulse on a CH target:

• (z,x) plots of electrons with energies > 12 MeV:

0.5 ps

1.0 ps

UCRL-PRES-204413-20

UCRL-PRES-204413-21

Extracting the correct electron distribution function is more complicated for oblique incidence

• A 1019 W/cm2 laser incident on a 16 nc plasma (shown by white lines) at a 30o angle of incidence.

• (z,x) phase space plot of electrons with energies > 5 MeV.

0.3 ps 0.6 psElectronsinjected at

a significantangle

We are using Python to closely We are using Python to closely couple Z3 output to LSP inputcouple Z3 output to LSP input

0.5 ps0.3 ps

UCRL-PRES-204413-22

We have recently started large scale cone calculations using LSP

• Background electron density profile of a gold cone touching a perfect conductor.

2MeV electronspromoted

along surface

UCRL-PRES-204413-23

Hot electrons start on inner edge and then diffuse into the cone

0.16 ps 1.4 ps

Transport efficiency <20% of hot electron out of cone

UCRL-PRES-204413-24

The LSP code has been used to study fast ignition relevant transport experiments

• A critical issue for Fast Ignition is understanding the transport of the ignitor electrons to the fuel.

• Experiments have shown a rapid increase in beam width followed by reasonable collimation with a 20° half angle.

• We have used the LSP code to:– generate simulated K images; – model XUV images; and– model cone focus experiments.

• The LSP code has been used to study the effect on beam transport of:– non-Spitzer conductivity; and– the initial beam divergence.

UCRL-PRES-204413-25

Collaborators:

• C. Chen, L. A. Cottrill, M. H. Key, W. L. Kruer, A. B. Langdon, B. F. Lasinski, B. C. McCandless, R. A. Snavely, C. H. Still, M. Tabak, S. C. Wilks, LLNL, Livermore, CA, USA.

• D. R. Welch, MRC, Albuquerque, NM, USA.