Fuel–Shell Mix Measurements Based on X-Ray Continuum Emission from Isobaric Implosion Cores on OMEGA R. Epstein University of Rochester Laboratory for Laser Energetics 56th Annual Meeting of the American Physical Society Division of Plasma Physics New Orleans, LA 27–31 October 2014 Experiment Mix 3 6 4 2 0 2 1 0 1.5 2.0 2.5 3.0 3.5 Normalized emission/Y 0.57 n Shell mix fraction f CH (%) Shell adiabat Simulation
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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).