R. BettiUniversity of RochesterLaboratory for Laser Energetics
Solved and Unsolved Problems in Plasma Physics
Princeton, NJ28–30 March 2016
The Most Unsolved Problem in Plasma Physics: Demonstrating a Burning Plasma in the Laboratory
FSC
00
2
4
6
8
10
1 2 3 4 5
Ya
Y
no
a
Indirect driveN140520 " 25 kJ
Burning-plasma regime
Qa = a heating
PdV
Direct driveX " tR = 0.260 Y = 7 # 1013
NIF (1.8 MJ) " 520 kJ
Direct driveX " tR = 0.220 Y = 6 # 1013
NIF (1.8 MJ) " 230 kJ
hs
Direct driveX shot 77068NIF " 130 kJ
Y = yield
1
0.5 - 0.6
Collaborators
A. R. Christopherson,* A. Bose,* K. M. Woo,* and J. Howard*
K. S. Anderson, E. M. Campbell, J. A. Delettrez, V. N. Goncharov, F. J. Marshall, R. L. McCrory, S. P. Regan, T. C. Sangster, C. Stoeckl, and W. Theobald
University of RochesterLaboratory for Laser Energetics
*also Fusion Science Center
M. J. Edwards, R. Nora, and B. K. Spears
Lawrence Livermore National Laboratory
J. Sanz
Escuela Técnica Superior de Ingenieros Aeronáuticos Universidad Politécnica de Madrid
Madrid, Spain
3
FSC
The simplest a-heating model assumes that fusion reactions start after the plasma stagnates
TC12266a
6
The plasma is brought to a pressure Pno a using only a spherical piston (the imploding shell).
DT fusion plasma (hot spot)P(0) = Pno a
FSC
Time-dependent energy balance
–ddt P
n P P P23
4 23 0 no
2vo f x= =a ab ^l h
Fusion reactivity
Confinement time
3.5 MeVP á 2nT
+
++
+
+
Fusionreaction
Fast neutron(14.1 MeV)
Alpha particle(3.5 MeV)
Triton Deuteron
+
+
The dimensionless form of the energy balancedepends only on the no-a Lawson* parameter
TC12268a
7
FSC
• Assume T2+vo Set P PPno
/a
t t t/ xt P 0 1/t ^ h
*J. D. Lawson, Proc. Phys. Soc. Lond. B 70, 6 (1957).
S T P24 no ignmin
2/
f vox=a
aa^ h
SP
nono/|
xaa
a
No-a Lawson parameter
–ddtP P P 1no|= attt t_ i Without a heating$ –
ddtP P=tt
t
Note: Sa has the dimensions of Px
The amplification of the yield caused by alpha heating is a unique function of the no-a Lawson parameter
TC12271
8
FSC
0.0
6
3
5
2
0.2 0.80.4 0.6 1.0
7
4
1
|no a
– –YY
nlP
P21
1no no no
no nono ign
nomin2 /| |
| |x
x=
a
a
a aa a
a
ac ^m h= GYY
noa
a
Generalized in 3-D in P.-Y. Chang et al., Phys. Rev. Lett. 104, 135002 (2010).
The scaling of the no-a Lawson parameter follows that of the ignition threshold factor* (ITFx)
TC12272a
9
FSC
–M R PR4DTsh 2r=p
Newton’s law of the dense shellconfining the hot-spot pressure**
M R PRMPRDT
sh DTsh
22(+ +
xx
M RDT shell 2+ t D^ h
DT dense shell
R
Hot spotD
Shell mass
Approximate total areal density tR
Y P V2+ x
YM
RDTsh
3 2+| t^ h
Same as LLNL ITFx, with tR replaced by the down-scatter
ratio (DSR)*
*B. K. Spears et al., Phys. Plasmas 19, 056316 (2012).**R. Betti et al., Phys. Plasmas 17, 058102 (2010).
The amplification of the yield caused by a heating is also a unique function of the Lawson parameter with a
TC12282a
10
FSC
– –YY
nl2 11
no no nono2| |
|=a
a
a aac m= G
. YM
R0 24 /
//
DT mgsh g cm
161 3
2 32+| ta
a
_^
ih
> H
YY
Fno
|=a
aa^ h
Y /no no1 3+| a a
|a can be measured
Y /1 3+|a a
|no a cannot be measured
YY /
nono
1 3| |=a a
a
ae o
#|a valid in 3-D,* although the definition of tR is difficult; use DSR**
*P.-Y. Chang et al., Phys. Rev. Lett. 104, 135002 (2010).**B. K. Spears et al., Phys. Plasmas 22, 056317 (2012).
In high-foot implosions, the fusion yield increasedby about 2.5× because of a heating
TC12283a
11
FSC
0.0 0.5 1.0|a
1.5 2.0 2.50.0
6
10
4
2
00.2 0.4
|no a
0.6 1.0 1.20.8
8
N140520
1-D simulations2-D simulationsAnalytic
Ignition
YYn
oa
a
.0 95.|a
High-foot N140520:tR á 0.8 g/cm2,
Y = 9 # 1015, MDT = 0.18 mg
O. A. Hurricane et al., Phys. Rev. Lett. 115,
055001 (2015).
Used in J. Lindl et al., Phys. Plasmas 21, 020501 (2014); 21, 129902(E) (2014).
TC12284a
13
In a burning plasma, the a heating is the dominant power input to the fusion plasmaFSC
Fusionplasma
Wexternal
Wa
•
•
QWW
ext/a
ao
o
Burning plasmasQa > 1
W C V VP P23
ext2
x+ =aoExternal
inputEnergylosses
foralpha heating vW T2+v=ao
Steady-state energy balance with power input
TC12286a
14
The yield amplification caused by a heating depends exclusively on QaFSC
QWW
ext/a
ao
o
Yield amplification is a unique function of Qa
From the power balance: pressure with a
PC
.ICF 0 5.xa
xV W Q CP 32 1
/
ext
2 3= +a a xo ^ h: D
YY
QPP
1 /no no
2
24 3= = +
a
a
a
aa^ h
V W CP 32 /
no ext
2 3=a xo: D
From the power balance: pressure without a
0.6
TC12300
19
Hydrodynamic equivalence provides a tool to scale the performance of OMEGA direct-drive implosions to NIF energies for symmetric illuminationFSC
Hydrodynamic scaling
Direct driveNIF 1.8 MJ
Direct driveNIF 1.8 MJ
3.6 mm
0.86 mm
OMEGA 30 kJ
OMEGA NIF
Scale 1:60in energy
Scale 1:4in size
Hydrodynamic scaling does NOT account for differences in laser–plasma interactions between OMEGA and the NIF.
3-D theory for R. Nora et al., Phys. Plasmas 21, 056316 (2014).
The hydrodynamic scaling holds in three dimensions
TC10975b
• In-flight scaling: R E /L1 3+ P E /LL
2 3+ E /Lpulse1 3+x
constVimp + onstc+a RT growth factors const+
• Stagnation scaling: constP + T R .0 2+ V Rhs 3+
Rburn +x R Rtot +t
20
r (nm)r (nm)
z (n
m)
150
50
100
00 50 100 150
40
10
00 10 20 30 40
30
20
YOCNIF = 60% YOCX = 61%t (g/cm2)
425
0
142
283NIFNIF OMEGAOMEGA
A. Bose et al., Phys. Plasmas 22, 072702 (2015); R. Nora et al., Phys. Plasmas 21, 056316 (2014).
FSC
5
TC12302c
Access to the burning-plasma regime requires about 50 kJ of HF targets in indirect drive and about 200 kJ of fusion energy for direct drive
27
Both direct and indirect drive must double the yield amplificationto access the burning-plasma regime.
00
2
4
6
8
10
1 2 3 4 5
Ya
Y
no
a
Qa hs
Qa tot
0 1
Burning-plasma regime
Direct driveX shot 77068
F " 130 kJ
Direct drive (1.9 MJ) " 210 kJIndirect drive (HF) " 50 kJ
Direct drive (1.9 MJ) " 210 kJIndirect drive (HF) " 50 kJ
Direct driveX shot 770681.9 MJ 125 kJ
Direct drive (1.9 MJ) " 500 kJIndirect drive (HF) " 120 kJ
Direct drive (1.9 MJ) " 500 kJIndirect drive (HF) " 120 kJ
Indirect driveN140120 " 26 kJ
Indirect driveN140120 " 26 kJ
0.5 - 0.6
TC12303
25
Despite the exciting results, the path to ignition is uncertain with current direct- and indirect-drive targetsFSC
No-a ignition parameter in terms of in-flight properties
YOC YOC IFAREV
E P. . /. . /
no kF
impk abl
0 37 0 43 5
20 37 0 4 2 5+ +|
aa
Best shot to date " |no a á 0.65Ek = kinetic energy
YOC = yield-over-clean = D DY Y3 1- -^ ^h hYOC is $50% in NIF high foot
Vimp = implosion velocity
aF = adiabat (entropy)
Needed for ignition " |no a á 1
7.5t (g/cm3)
3.5
0.5
–5000
200
400
600
800
1000
–250 0z (nm)
r (n
m)
250 500
Increasing the IFAR* while preserving the YOC is a challenge.
*In-flight aspect ratio
Only half of the a energy can be counted whendetermining Qa for ICF
TC12288
15
FSC
90
4
6
2
3
0
1
95 100 115 120110105
Hot spot Qa
5
Rhs
–PdV < 0–PdV > 0
Only positivePdV work beforestagnation Neutron rate a heating
Ho
t-sp
ot
rad
ius,
neu
tro
n r
ate
(arb
itra
ry u
nit
s)
Time (arbitrary units)
–/
Q dVE
P1 2hs
hs=a
a
Two burning-plasma regimes are identified: a heating exceeds PdV work to the hot spot a heating exceeds PdV to hot spot + shell
TC12289a
16
FSC
QdV
E
P21
hs
hs=a
a
Hot spot Qa
QPdV PdV
E21
tot
hs sh=
+aa
Total Qa
• First burning-plasma regime
Q 1hs $a Q 1tot $a
• Second burning-plasma regime
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