Optical Properties of Compressed LiF

D. E. FratanduonoUniversity of RochesterLaboratory for Laser Energetics

Omega Laser Facility Users’ Group Workshop

Rochester, NY29 April – 1 May 2009

Compression strain

0.50

0.48

0.46

n–1

0.44

0.42

0.40

0.38

0.360.0 0.1 0.2 0.3 0.4

Lorentz–LorenzGladstone–DaleDrudeModified Gladstone–DaleWise and Chhabildas

Goal is to measure refractive index of compressed LiF

E17784

• AccuracyofshockcompressedandisentropicallycompressedLiFrefractive index to pressures above ~1 Mbar has not been validated

– important for the accuracy of VISAR measurements

• Newtechniquestoexaminetherefractiveindexunder

– shock compression

– ramp compression

• Proof-of-principleexperimentsusingtheJanusLaserFacility havebeenconductedandcorrelatedwithexistingdata

• Shotshavebeenallocatedforfutureexperiments

Summary

VISARvelocitycorrectionsforLiFwindows

E17785

• Dopplershiftofreflectedlight is manifested as a fringe shift in VISAR

• Fringephaseisproportionalto the optical path

• Undercompression(tc) refractive index can change

• Thiscorrectionmaynot be constant

* ,V tdtd n x t dx

x t

xr-= l l] ^]

g hg

< F#

Forlinearwindowmaterials

*

n a b

V t aV t a V t1 FS-

t= +

=+

]] ] ]

gg g g

LiF

Reflectingsurface

Freesurface

Dia

mo

nd

tc t0

VISAR

Measurements of the LiF index are extrapolated to higher velocities

E17786

• ShockedLiFhasbeenstudied up to ~1.0 Mbar

(4.2 g/cm3)

• VISARexperimentsuseLiFwindowsforpressures up to 5 Mbar

• Linearextrapolationisusedfor higher pressures and density

LiF refractive index asa function of density

Ref

ract

ive

ind

ex (

n)

Density (g/cm3)

1.48

1.46

1.44

1.42

1.40

3.0 3.4 3.8 4.2 4.6

Wise and ChhabildasLinear fit

Methods to study the LiF refractive index

E16851a *K.T.Lorenzet al., High Energy Density Phys. 2, 113 (2006).

Pressure (Mbar)

*Compression t/t0

Tem

per

atu

re (

100

0 K

)

00

81.1 1.3 1.5 1.7 1.9 2.1 2.3

6

1 2 3 4

4

2

Hugoniot

Multiple shock

Aluminum

fcc

Isentrope

hcp bcc

• Twomethodsofstudy

– shock compression

– ramp compression

• Eachmethodmakesit possible to study different regions of phase space

Proof-of-principleexperimentswereconductedtomeasuretherefractiveindexofshock-compressedLiF†

E17787

Theapparent particle velocity (Up*) measured by VISAR is not an accurate measurement of the particle velocity caused by the LiF refractive index (n).

†Experiments were performed by J. Eggert and R. Smith at the Janus Laser Facility.

VISAR record

Vel

oci

ty (

km/s

)

Flyer platevelocity (Uf)

Time (ns)

0 10

5

4

3

2

1

020 30 40 50

Polyimide Al

Ramploading Flyer

Uf

LiF

~300 J, 4 ns1-mm spot VISAR

Polyimide

Ramp loading

LiF

~300 J, 4 ns1-mm spot VISAR

Up*

Apparent particle

velocity (Up*)

LiF collision analysis to recover the absolute particle velocity (Up)

E17788

• Absoluteparticlevelocitydeducedfromflyerplatevelocity and EOS of materials

• Comparisonoftheabsolute and apparent particle velocity determines the refractive index correction

Collision analysis in the P, U plane

Pre

ssu

re (

Mb

ar)

Velocity (km/s)

Flyer platevelocity (Uf)

00.0

1 2 3 4 5 6

1.0

0.8

0.6

0.4

0.2

LiF particle velocity (Up)

LiF HugoniotAl Hugoniot

*

U

U1

p

p

0ooD= +

Correction factor:

Refractive index†:

U UU

U U

Un n 1

s p

s

s p

p0 0-

--o

oD= +d n

†D.R.Hardesty,J.Appl.Phys.47, 1994 (1976).

Comparisonofproof-of-principleexperiments withWiseandChhabildasgas-gundata

E17789

• Correlationbetween Janusexperiments and gas gun

• Extendtheseshockexperiments to higher pressures

• Expecttherefractiveindexof shocked and ramp compressed LiF to differ

• Developtechniques to study ramp compressed LiF

Ref

ract

ive

ind

ex (

n)

1.60

1.55

1.50

1.45

1.40

1.35

1.303.0 3.4 3.8 4.64.2

Wise and ChhabildasLinear fitExperimental data

LiF refractive index asa function of density

Density (g/cm3)

Isentropic compression is a gentle continuous compression of material

E16856a

• Soundspeedinamaterialincreaseswithcompression

• Subsequentcompressionwavesto travel faster than predecessors

• Thesewavescancoalesce,forming a shock

• Designalaserdrivethatmaximizestheappliedpressurewithoutformingshock

*R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Corr. 5th print, Applied Mathematical Sciences, v. 21 (Springer-Verlag,NewYork,1999).

x

tPiston

C+

C+: x = c0 t0

Gas at rest

Characteristics of piston/gas*

CCdt

dPx d

dP< L

L0

2 :CC

t x t0

00= ++

LiF ramp compression target design

E17790

• Diamondablatorallowsrampcompression to reach high pressure (~5 Mbar) in a short period of time (~10 ns)

• Targetdesignmakesitpossible to measure both the apparent particle velocity and the free surface velocity simultaneously

• Adirectcomparisonofthefree surface velocity and the apparent particle velocity cannot be made

• Backwardintegrationtotheloading surface enables the determination of the LiF refractive index

Free surface velocity

Apparent particle velocity

VISAR

Diamond

OMEGA EP

LiF

BackwardintegrationtorecovertheLiFrefractiveindex

E17791

• VISARrecordcontainsthe velocity “boundary conditions”

• UsingtheEOSofLiFanddiamondcanbackwardintegrate to the loading surface

• Comparisonofthebackward-integrated free surface velocity and apparent particle velocity makes it possible to recover the refractive index of LiF

• Experimentsareplannedfortheweekof22June2009

Diamond/LiF characteristics

Distance (nm)

Tim

e (n

s)

00

2

4

6

8

10

12

14

25 50 75 100 125

Diamond LiF

Boundaryconditions

Free surface PDiamond = 0

Interface PDiamond = PLiFUp Diamond = Up LiF

E17784

Summary/Conclusions

Goal is to measure refractive index of compressed LiF

• AccuracyofshockcompressedandisentropicallycompressedLiFrefractive index to pressures above ~1 Mbar has not been validated

– important for the accuracy of VISAR measurements

• Newtechniquestoexaminetherefractiveindexunder

– shock compression

– ramp compression

• Proof-of-principleexperimentsusingtheJanusLaserFacility havebeenconductedandcorrelatedwithexistingdata

• Shotshavebeenallocatedforfutureexperiments