Three-Dimensional Modeling of Cross-Beam Energy Transfer ...
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D. H. EdgellUniversity of RochesterLaboratory for Laser Energetics
Three-Dimensional Modeling of Cross-Beam Energy Transfer and Its Mitigation in Symmetric Implosions on OMEGA
1
1.40
1.42
1.44
1.46
1.44 TW/sr!0.16% 0.76 TW/sr!2.0%
0.72
0.74
0.76
0.78
No CBET TW/sr CBET TW/sr
47th Annual AnomalousAbsorption Conference
Florence, OR11–16 June 2017
Cross-beam energy transfer (CBET) modeling suggests that 3-D effects may be important for symmetric direct drive
Summary
E26181
2
• CBET between beams at angles of 40° to 110° are most significant
• Non-axially symmetric details of the absorption profile can increase the absorption rms (root mean square) over the target surface by an order of magnitude
• The total absorption and rms asymmetry can be greatly improved over a standard symmetric implosion by wavelength separating
the three OMEGA beam legs
D. H. Edgell et al., “Mitigation of Cross-Beam Energy Transfer in Symmetric Implosions on OMEGA Using Wavelength Detuning,” to be published in Physics of Plasmas.
Collaborators
R. K. Follett, I. V. Igumenshev, J. F. Myatt, J. G. Shaw, and D. H. Froula
University of RochesterLaboratory for Laser Energetics
3
Three-dimensional modeling uses a geometric optics ray-based model using the coronal plasma taken from hydrodynamic code
E25950
4
–500
x (nm)
–1000
–500
0
500
1000
y (n
m)
0 500
0.6
0.8
1.0
0.4
0.2
0.0
6810
s (nm)
u (n
m)
–500–1000
–10001000
1000
0
0
0 500
×1013
420
ne /nc
ShadowCaustic
rmin
Turningpoint
Turningpoint
CBET is calculated in each beamlet cell for crossings with all other beamlets
E25951
• Both intrabeam and interbeam crossings
• Beamlet intensities at crossings are determined using
– inverse bremsstrahlung absorption
– intensity law of geometric optics
– CBET at crossings using a 3-D extension of Randall’s quasi-slab model fluid model*
5
~IAW = ~1 – ~2
kIAW = k1 – k2< < <
IAW: ion-acoustic wave*C. J. Randall, J. R. Albritton, and J. J. Thomson, Phys. Fluids 24, 1474 (1981).
The model is in good agreement with LPSE* calculations of CBET in a simple geometry
E25952
6
×10
14 W
/cm
2Inte
nsi
ty o
ut
Po
lari
zati
on
co
sin
e
Beam 1
0
2
4
6
8
0
2
4
6
8
–30 –20 –10 0
Beam profile (nm) Beam profile (nm)
0.4
0.5
0.6
0.7
0.8
10 20 30
–40 –20 0
OES
y (nm)
x (n
m)
–40
–20
0
20
40
400
1
2
3
4
5
6
20
Bea
m 1
Beam 2
Beam 2
–30 –20 –10 0 10 20 30
LPSEBEAMER
*R. K. Follett et al., ThP-2, this conference.J. F. Myatt et al., Phys. Plasmas 24, 056308 (2017).
u (n
m)
×108
–400
v (nm)
0
Nearest neighbor
400
3
2
1
0
–400
0
400
TW/sr
Absorptionwith CBET
0.78
0.76
0.74
0.72
–s
+srnc /4
rMach 1
TargetplasmaTargetplasma
Impactparameter
Turning points = 0
Turning points = 0
rmin
rmin
To display 3-D calculations on 2-D slides we use integrated images and surface maps
E25955
7
dEabss/
Two-beam modeling shows that CBET exchange is strongest for beams that are at angles between 40-110°
E25954
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Angle between beams (°)
84
88
92
90
86
94
Las
er a
bso
rpti
on
(%)
0 6030 90 150120
Beams at anglesgreater than 150°are essentiallydecoupled
180
Two-beam CBETOne-beam self-CBETNo CBET
CBET adds non-axisymmetric features to the beams’ absorption profile that depend on their 3-D orientation
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0 400
0
No CBET ×108
Beams at 90°
v (nm)
u (n
m)
–400
–400
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 400
×108
v (nm)–400
–1.0
–0.5
0.0
0.5
1.0
0 400
CBET ×108
v (nm)–400
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5400
dEabss/ dECBET
s/ dEabs
s/
For the OMEGA symmetric geometry, profile features are the sum of interactions between 60 beams
E25956
10
–400
v (nm)
–400
0
400
u (n
m)
0 400
2
1
–1
0
–2
–400
v (nm)
0 400
16
12
8
4
0
×108 ×107
dECBETs/ dEabs
s/
CBET can increase the absorption nonuniformity of a symmetric implosion by an order of magnitude
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The nonuniformity is not simply caused by 1-D CBET from inside to outside of beam profile.
, , dE r rabs i {^ h#
dEabss/
No CBET
Absorptionsurface maps
Absorptionprofiles
×108
0.51.01.52.02.53.03.5
1.40
1.42
1.44
1.46
CBET ×107
2
6
10
14
18 18
0.72
0.74
0.76
0.78
CBET(axiSym averaged) ×107
2
6
10
14
0.73
0.75
0.77
0.79
1.44 TW/sr!0.16% TW/sr 0.76 TW/sr!2.0% TW/sr 0.76 TW/sr!0.13% TW/sr
–400
v (nm)
–400
0
400
u (n
m)
0 400 –400
v (nm)
0 400 –400
v (nm)
0 400
The nonuniformity originates from the subtle non-axially symmetric details of the absorption profile
E26183
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TW/sr
0.72
0.74
0.76
0.78
No CBET CBET
Single-beam pattern
Wavelength shifting a single OMEGA beam provides insight into multicolor CBET mitigation
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13
–30 –20 –10 0
Ab
sorb
ed p
ow
er (
TW)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Dm (Å)
10 20 30
Shifted beamUnshifted beamsSelf-CBET limit
Breaking cadence: Wavelength shifting the three OMEGA beamline legs to mitigate CBET
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14
There is a “sweet spot” around Dm = 10 Å, where the absorbed power is maximum and the nonuniformity is near minimum.
Dm (Å)
0.0
0.1
0.2
0.3
0.4
Ab
sorb
ed p
ow
er (
TW)
0 20 10
Dm (Å)
00
2
4
6
8
Ab
sorp
tio
n r
ms (%
)
3020
Leg 1Leg 2Leg 3AverageSelf-CBET limit
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Summary/Conclusions
Cross-beam energy transfer (CBET) modeling suggests that 3-D effects may be important for symmetric direct drive
• CBET between beams at angles of 40° to 110° are most significant
• Non-axially symmetric details of the absorption profile can increase the absorption rms (root mean square) over the target surface by an order of magnitude
• The total absorption and rms asymmetry can be greatly improved over a standard symmetric implosion by wavelength separating
the three OMEGA beam legs
D. H. Edgell et al., “Mitigation of Cross-Beam Energy Transfer in Symmetric Implosions on OMEGA Using Wavelength Detuning,” to be published in Physics of Plasmas.
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