Fuel–Shell Mix Measurements Based on X-Ray Continuum Emission

from Isobaric Implosion Cores on OMEGA

R. EpsteinUniversity of RochesterLaboratory for Laser Energetics

56th Annual Meeting of theAmerican Physical SocietyDivision of Plasma Physics

New Orleans, LA27–31 October 2014

Experiment

Mix

36

4

2

0

2

1

01.5 2.0 2.5 3.0 3.5N

orm

aliz

ed e

mis

sio

n/Y

0.5

7n

Sh

ell m

ix f

ract

ion

fC

H (

%)

Shell adiabat

Simulation

The x-ray emission of imploded cryogenic hot spots provides a diagnostic of fuel–shell mix*,**

Summary

• The photon-yield scaling with neutron yield is a consequence of the isentropic compression of isobaric hot spots

• The excess hot-spot x-ray emission relative to the scaled neutron emission serves as a fuel–shell mix diagnostic**

• The photon–neutron yield scaling and the appropriate x-ray yield normalization for the mix diagnostic is determined by the x-ray detector spectral response

TC11508

* S. P. Regan et al., Phys. Rev. Lett. 111, 045001 (2013). ** T. Ma et al., Phys. Rev. Lett. 111, 085004 (2013).

Collaborators

F. J. Marshall and V. N. Goncharov

University of RochesterLaboratory for Laser Energetics

R. Betti, R. Nora, and A. R. Christopherson

University of RochesterFusion Science Center and Laboratory for Laser Energetics

Core x-ray emission exhibits simple scaling with neutron yield in cryogenic implosion simulations*

TC10254c

160

120

80

40

00.0 0.5

1-D calculations Experiment

Mix

1.0

X-r

ay c

ore

em

issi

on

(ho

0 =

5.3

keV

, arb

itra

ry u

nit

s)

Neutron yield (×1014)

3

2

1

01.5 2.0 2.5 3.0 3.5N

orm

aliz

ed e

mis

sio

n/Y

0.57

nShell adiabat

Simulation

Fit: Y 0.57n

• Measured yields are consistent with Y Y .n0 57?o scaling

for higher adiabats

• Excess x-ray emission for low adiabats suggests ablator mix in the hot spot

**T. C. Sangster et al., Phys. Plasmas 20, 056317 (2013).

The neutron-yield scaling of the photon yield is a property of isentropically compressed isobaric hot spots

TC10951a

• Neutron yield from the Bosch–Hale* reaction rate T4?vo f+ :

Y P T Vtn2 2? f+

• Photon yield using Kulsrud** Gaunt factor ? P TFF 2foh

Y P T Vt20?o

h near kTh 20 .o

– postulate a hot-spot adiabat P V– /5 3HS?a

– the inertial force of shell deceleration balanced by the core stagnation pressure† /M R t R P4Sh

2 2r= gives the Vt product

• Obtain scaling Y Ynq?o , where .q 9 2

5 20 56.f

h= +

+ for f = 0 and h = 0

* H.-S. Bosch and G. M. Hale, Nucl. Fusion 32, 611 (1992). ** R. M. Kulsrud, Astrophys. J. 119, 386 (1954). † R. Betti et al., Phys. Plasmas 17, 058102 (2010).

0.8

0.7

0.6

0.5

0.57

0.41.5 2.0 3.5

kT (keV)

Yie

ld-s

calin

g in

dex

q2.5 3.0

q

GkTHn ± vkT

The full photon–neutron yield scaling expression includes stagnation parameter dependence

TC11510

• The scaling .q 0 57= is obtained for . keVkT 2 21= , which is marginally representative of hot-spot temperatures in the LILAC simulation ensemble

/ .–

p 1 2 9 1 01 2

.ff h

= ++ ^ h

YM M

Y/

/ /

HS

S HSn

hp

q4 9

2 9 10 9

0?

ao > H

. .at keVq kT9 25 2

0 57 2 1.fh

= ++

=

The yield-scaling index value obtained using the Zhou–Betti* hot-spot mass agrees with the LILAC result

0.8

0.7

0.6

0.5

0.41.5 2.0 3.5

kT (keV)

Yie

ld-s

calin

g in

dex

q2.5 3.0

q

kT = ho0/2

GkTHn ± vkT

TC11595

• The scaling .q 0 57= is consistent with the range of neutron-averaged temperatures in the LILAC simulation ensemble

• Zhou–Betti* M M P R/ / /HS Sh

1 7 4 7 16 7?

from inner-shell mass ablation

• Alternative scaling

./–

p 1 01 21

112.f

f h= +

+ ^ h

Y M Y/Sh np q4 11

0?o

. atq 11 27 2

0 57.fh

= ++

*C. D. Zhou and R. Betti, Phys. Plasmas 14, 072703 (2007).

kT = 3.0 keV

TC11511

• Free-free ?Y n n Z Vt,FF

i eZ2

o plus free-bound ?Y n n Z kT Vt,F

iHB

Z e4 |

o b l x-ray “yield” for each atomic fraction fZ*

*Gaunt factors gZ,FF and gZ,FB from W. J. Karzas and R. Latter, Astrophys. J. Suppl. Ser. 6, 167 (1961).

0.4

0.5

0.6

0.7

0.8

0.9

3

2

GkTHn±vkT

1

01 43

kT (keV)

X-r

ay e

nh

ance

men

t fa

cto

r

2

Yo ~

Yn

sca

ling

ind

ex q

fCH = 0%

fCH = 2.4%

q(fCH = 2.4%)

q(fCH = 0)

Small CH atomic fractions account for the observed excess hot-spot x-ray emission at low adiabats

• X-ray enhancement and scaling index q resulting from fCH ≈ 2.4% hot-spot contamination are plotted

• A CH atomic fraction fCH ≈ 2.4% would double the hot-spot x-ray emission

• Adding FB emission lowers the yield-scaling index slightly; q(fCH = 2.4%) á 0.54

Excess x-ray emission, relative to the scaled neutron yield in cryogenic implosions, provides a mix-mass estimate*

TC11515

• Mix fraction fCH ≈ 2.4% doubles the hot-spot emission

• For GMHSH ≈ 2.1-ng hot spots, fCH ≈ 2.4% represents DMCH ≈ 125 ng

* T. Ma et al., Phys. Rev. Lett. 111, 085004 (2013).

Experiment

Mix

4

6

2

0

1.5 2.0 2.5 3.0 3.5

Sh

ell-

mix

fra

ctio

n f

CH (

%)

3

2

1

0 No

rmal

ized

em

issi

on

/Y 0.

57n

Shell adiabat

Simulation

fCH á 2.4%

TC11508

Summary/Conclusions

The x-ray emission of imploded cryogenic hot spots provides a diagnostic of fuel–shell mix*,**

• The photon-yield scaling with neutron yield is a consequence of the isentropic compression of isobaric hot spots

• The excess hot-spot x-ray emission relative to the scaled neutron emission serves as a fuel–shell mix diagnostic**

• The photon–neutron yield scaling and the appropriate x-ray yield normalization for the mix diagnostic is determined by the x-ray detector spectral response

* S. P. Regan et al., Phys. Rev. Lett. 111, 045001 (2013). ** T. Ma et al., Phys. Rev. Lett. 111, 085004 (2013).

0.9

0.8

0.7

0.6

0.5

0.41.0 1.5 3.0

kT (keV)

q = 0.57Y

ield

-sca

ling

ind

ex q

2.0 2.5

qphf

–0.5

0.0

0.5

1.0

1.5

2.0

p, h

, f

TC11510a

• The scaling . .q 0 57 0 06!= is obtained for . . keVkT 2 21 0 43!= and is to be compared with .q 0 57= from LILAC results

The photon–neutron yield scaling obtained from scaling arguments agrees with 1-D LILAC results over a broad temperature range

/ .–

p 1 2 9 1 01 2

.ff h

= ++ ^ h

YM M

Y/

/ /

HS

S HSn

hp

q4 9

2 9 10 9

0?

ao > H

.q 9 25 2

0 57.fh

= ++

• Free-free (FF) plus bound-free (BF) x-ray “yield”

• The composition is DT nD = nT, with a trace fZ = nZ/(nD + nT + nZ) of a contaminant, e.g., C (Z = 6)

• Using and the neutron yield:

• Obtain

• The shell-mix fraction x is obtained1 from /Y Yno ratio measurements and emissivity jZ, jDT values from optical parametric chirped-pulse amplification (OPAL)2 and detailed-configuration accounting (DCA)3 tables

Excess hot-spot x-ray emission above the expected clean DT level gives the mix fraction of shell C in the hot spot1

TC10715a

|Y n n Z kT Z e kT e Vt2/

//

/e

H HI I I

kT h kT21 2

43 2

–Z?| |

+oob bl l; E

Y n n Vtn D T. vo

1T. Ma et al., Phys. Rev. Lett. 111, 085004 (2013).2F. J. Rogers, F. J. Swenson, and C. A. Iglesias, Astrophys. J. 456, 902 (1996).3H. A. Scott and S. B. Hansen, High Energy Density Phys. 6, 39 (2010).

Y Y f T f Z f j j1 1n DTZ zZ. + +o ^ ^ _h h i

n n n f Z1e D T Z= + +^ ^h h n Z n n f Z1D TIn

Zn= + +^ ^h h

The level of mix is inferred from the ratio of x-ray yield to neutron yield*

TC11513

• Bands represent 1.7 < kT < 3.9 keV and ho0 á 10.85 keV

• Measurements made near /h kT 4o = , which is ideal for

* T. Ma et al., Phys. Rev. Lett. 111, 085004 (2013).

?YY

P T Vt

PT

e Vt

Te

– /

– /

n

h kT

h kT

2 2

22

4=o

o

oc m

NIF cryogenic Si-doped CH shells through 2012*

00

250

500

750

1000

1250

0% at CH

2 4

Neutron yield (×1014 DT)

X-r

ay y

ield

[so

uth

-po

le b

ang

tim

e (S

PB

T)]

(m

J/ke

V/s

r)

6 8 10

Mix level<150 ng150 to 400 ng

400 to 750 ng>750 ng

5% at CH 2% at CH 1% at CH