the most unsolved problem in plasma physics: …reaction fast neutron (14.1 mev) alpha particle (3.5...

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

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

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 driveX shot 770681.9 MJ 125 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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the most unsolved problem in plasma physics: …reaction fast neutron (14.1 mev) alpha particle (3.5...

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