laser induced shock waves

THE COMEBACK of SHOCK WAVES in INERTIAL FUSION ENERGY

S. Eliezer and J. M. Martinez-Val Institute of Nuclear Fusion, Polytechnic University of Madrid, Spain

ICENES 2011, San Francisco, May 15-19 (2011)

Contents 1. Introduction 2. Shock waves collision 3. Fast ignition: 8 ideas 4. Instability at the critical surface 5. Fast ignition – an “old-new” approach

consequently…

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1. Introduction  Eliezer, S. “The interaction of high-power lasers with plasmas”, 







Chapters 9-10, IoP, Bristol, UK (2002). Eliezer, S., Ghatak, A., Hora H. and Teller E. , “Fundamental of equations of state”, World Scientific, Singapore (2002). This book was first published in 1986 by Cambridge Univ. Press, UK with the title “High-pressure equations of state: theory and applications”. Eliezer, S. and R. A. Ricci (eds.), “High-pressure equations of state: theory and applications”, Enrico Fermi international school of physics, 1989, North-Holland, Amsterdam (1991). Trunin, R. F., “Shock compression of condensed materials”, Cambridge Univ. Press, Cambridge (1998). Zeldovich, Y. B. and Raizer, Y. P., “Physics of shock waves and high temperature hydrodynamic phenomena”, vols. 1 and 2, Academic Press, New York (1966)

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Shock-wave generators: 1) Guns (accelerate foil to collide with target) 2) Chemical explosives, 3) Magnetic compression, 4) Nuclear explosions

5) high power lasers.  In 1974 (Garching-Germany) the first direct observation

of a laser-driven shock wave was reported : 2 Mbar.  In 1994 Livermore-USA created a pressure of ~1Gbar (Indirect drive).  In 2005 Osaka-Japan created a pressure of ~1Gbar (Direct drive). 4

Hugoniot and thermodynamic curves

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2. SHOCK WAVES COLLISION 

P

After

After

Before

Before

x Pressure profile

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x Density profile

Impendance:

Z  0 c 0

P

P 1

P2

2

P1

P1

1

1

2

P

2

1

u ( 2) 1s

u2s

P1

u1s

P3

P0

P0

u ( 2) 1R

u2s

P0

x

x

x Z1Z2

Shock wave transition profile 7

Collision of shock waves before the era of “fast ignition” S. Jackel, S. Eliezer et al., Phys Fluids (1983) 26, 3138-3147. IL

IL

~1015

~1015

~1014

~1014

A

Wall

x

B

x

(A) Αl target (B) Al target;  wall =270g/cc Compression ( / 0 )

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40

Pressure (Mbars)

40

300 8

ICF Ignition Spark ignition ICF : NIF

J. Nuckolls et al., Nature 239, 139 (1972)

Plasma formation

Fast ignition ICF

N. Basov et al., J. Soviet Laser Res., 13, 396 (1992) 9 M. Tabak et al., Phys. Plasmas 1, 1626 (1994)

3. Fast ignition: 8 ideas 1) Fast ignition by electrons (produced in fs.-laser plasma interaction) P. A. Norreys et. Al., Phys. Plasmas 7, 3721 (2000) 2) Fast ignition with clusters S. Eliezer, J. M. Martinez Val, C. Deutsch, LPB 13, 43 (1995). Energy ~ 105 J; Area ~ 1 mm2; Time ~ 100 ps; Icluster ~ 1017 W/cm2.

3) Fast ignition by plasma jets P. Velarde, S. Eliezer, et al., AIP Conf. Proc. 406, 182 (1997). J. Martinez-Val, S. Eliezer, et al., AIP Conf. Proc. 406, 208 (1997). 4) Fast ignition by protons (produced in fs.-laser plasma interaction) M. Roth et al., Phys. Rev. Lett. 86, 436 (2001). 5) Fast ignition by plasma flow. Caruso et al., 26th ECLIM Proc., 248 (SPIE, 2001). S. Yu. Gus’kov, Quantum Electronics N31, 885 (2001). 10

6) The idea of cone-stuck spherical target: R. Kodama et al., Nature 418, 933 (2002) 2.5 KJ compression pulse + 0.5 ps-PW fast heating pulse

Neutron yield (full scale 108 n)

Heating laser power (PW) (full scale = 1PW)

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7) Fast ignition by impact collision of laser-accelerated spherical shell (ECLIM 2004 &Nucl. Fusion 46, 99 (2006)) M. Murakami, H. Nagatomo, H. Azechi, K. Nishihara, F. Ogando, P. Velarde, M. Perlado and S. Eliezer

2 orders of magnitude increase in neutron yield H. Azechi et al (2009), PRL 102, 235002

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8) Fast ignition by shock wave (2007): R. Betti, C. D. Zhou et al PRL, 98, 155001 (2007) IL

(1983) S. Jackel, D. Salzmann, A.Krumbein and S. Eliezer, Phys. Plasma 26, 3138

~1015

IL

~1014 s.w.

t ~1015 ~1014

t

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4. Instability at the critical surface RT + RM hydrodynamic instabilities + ……Instability at critical surface

at critical surface

 1v1   0 v 0  2 2 P   v    P   v 1 1 0 0 0  1  I    L (1  R ); R=50% c   IL 16 2   5Mbar for I L  10 W / cm ; c

 0 1

xc

x

 /  0  1  M 0  (v 0 / C0 )  1    /  0  1  M 0  (v 0 / C0 )  1  

S. Eliezer, J. M. Martinez-Val, C. Deutsch, LPB, 13, 43 (1995).

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5. Fast ignition an “old-new” approach Fast ignition with shock wave induced by impact S. Eliezer & J. M. Martinez Val, LPB 29 (2011)

Wire Foil

Compiled data of the flight distance vs. time. (1.5 kJ,400TW/cm2, 0.35mm) H. Azechi,….,S. Eliezer, …PRL 102,235002 (2009).

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THE HOT SPOT

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Ideal gas EOS estimation 2   1   1   1 2 2   4; P2    v ; k T  m v B 2  1 2   i 2 1   1 2 4     3    2.5; 2   1 

P4   4    ; P3   3  (  , P, T)1  (  , P, T) 2  (  , P, T)3  (  , P, T) 4 

P3 3  1   6; P2   1

T3 3  1   2.4 T2 

 1

T4   4    T3   3 

 0.2g / cm , 10bar, 0.025eV   0.8g / cm , 1.1Mbar, 1`70eV   2g / cm , 6.7Mbar, 415eV  130g / cm , 3.4Gbar, 5keV  3

3

3

3

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Laser energy for foil acceleration 

s ELs 

  4 x4 S  1 2  x S v  3    k BT4 f f  f 2  mi 

 20 g / cm x f [ m m]  18   f 

3

2

 vf    4 x 4   k BT4       8 2    3  10 cm / s   0.3g / cm   5keV 

Foil 100m m  100m m  20m m  Foil kinetic energy  20 kJ (simulation for the foil (impactor) with same volume: 10 kJ, H. Azechi et al., PRL 102, 235002 (2009).

s  0.2  E Ls  100 kJ 18

 F  Fermi Energy 





e

8 me 2

 2.25  1011  C

3

[cgs, for DT]

P fuel 5T Themain   [  3 is a reasonable number] C

C

Pdeg

C

F

[C is expected to be as small as possible (isentropic compression) ] ELC  laser energy directed into the main fuel

C  efficiency from laser to thermal energy The burn fraction   

HC HC  H0 1

 3 C 2 M C  3 H C   C RC    ,  4 

H 0  7 [ g / cm 2 ]

ENERGY CONSERVATION:

C ELC

 MC  2 12  3 k BTC   3.3  10 C  C 3 M C    2.5  m p   

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Fusion gain C ( g / cm 3 )  300  S ( g / cm 3 )  100 C ( EOS )  3

Total Driver Energy  Ed  ELC  ELS

C 

1.5 1015  2 1  2    3 S S Ed  C  C  6

Efusion 10 GAIN  G   Ed

[cgs ]

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consequently… It seems that Fast ignition needs less laser energy (~100 kJ) than other schemes. (remember the 10 Hz repetition rate!)

Therefore Fast ignition has the potential to be the best route to achieve nuclear fusion as an energy source

However Much more work, new ideas with a little bit of LUCK is needed to reach

“the desired energy”

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THANK YOU

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