# Inertial-confinement fusion with lasers

## Abstract

The quest for controlled fusion energy has been ongoing for over a half century. The demonstration of ignition and energy gain from thermonuclear fuels in the laboratory has been a major goal of fusion research for decades. Thermonuclear ignition is widely considered a milestone in the development of fusion energy, as well as a major scientific achievement with important applications in national security and basic sciences. The US is arguably the world leader in the inertial confinement approach to fusion and has invested in large facilities to pursue it, with the objective of establishing the science related to the safety and reliability of the stockpile of nuclear weapons. Although significant progress has been made in recent years, major challenges still remain in the quest for thermonuclear ignition via laser fusion. Here, we review the current state of the art in inertial confinement fusion research and describe the underlying physical principles.

## Access options

from\$8.99

All prices are NET prices.

## Change history

• ### 01 June 2016

In the version of this Review Article originally published, the size of the gold hohlraum described in the section 'Laser indirect drive' was incorrect and it should have read '5.75 mm in diameter'. This has been corrected in the online versions after print 1 June 2016.

## References

1. 1

Nuckolls, J. et al. Laser compression of matter to super-high densities: thermonuclear (CTR) applications. Nature 239, 139–142 (1972).

2. 2

Atzeni, S. & Meyer-ter-vehn, J. The Physics of Inertial Fusion (Clarendon, 2004).

3. 3

Lindl, J. D. Inertial Confinement Fusion (Springer, 1998).

4. 4

Lawson, J. D. Some criteria for a power producing thermonuclear reactor. Proc. Phys. Soc. Lond. B 70, 6–10 (1957).

5. 5

Betti, R. et al. Thermonuclear ignition in inertial confinement fusion and comparison with magnetic confinement. Phys. Plasmas 17, 058102 (2010).

6. 6

Zhou, C. D. & Betti, R. Hydrodynamic relations for direct-drive fast-ignition and conventional inertial confinement fusion implosions. Phys. Plasmas 14, 072703 (2008).

7. 7

Glebov, V. Y. et al. Development of nuclear diagnostics for the National Ignition Facility. Rev. Sci. Instrum. 77, 10E715 (2006).

8. 8

Frenje, J. A. et al. Probing high areal-density cryogenic deuterium–tritium implosions using downscattered neutron spectra measured by the magnetic recoil spectrometer. Phys. Plasmas 17, 056311 (2010).

9. 9

Casey, D. T. et al. The magnetic recoil spectrometer for measurements of the absolute neutron spectrum at OMEGA and the NIF. Rev. Sci. Instrum. 84, 043506 (2013).

10. 10

Kishony, R. & Shvarts, D. Ignition condition and gain prediction for perturbed inertial confinement fusion targets. Phys. Plasmas 8, 4925–4936 (2001).

11. 11

Campbell, E. M. & Hogan, W. J. The National Ignition Facility—applications for inertial fusion energy and high-energy-density science. Plasma Phys. Control. Fusion 41, B39 (1999).

12. 12

Moses, E. I. Ignition on the National Ignition Facility. J. Phys. Conf. Ser. 112, 012003 (2008).

13. 13

Hurricane, O. A. et al. Fuel gain exceeding unity in an inertially confined fusion implosion. Nature 506, 343–348 (2014).

14. 14

Patel, P. et al. Performance of DT layered implosions on the NIF. in 55th Ann. Meet. APS Div. Plasma Phys. NO4.00001 (American Physical Society, 2013); http://meetings.aps.org/link/BAPS.2013.DPP.NO4.1

15. 15

Cerjan, C., Springer, P. T. & Sepke, S. M. Integrated diagnostic analysis of inertial confinement fusion capsule performance. Phys. Plasmas 20, 056319 (2013).

16. 16

Doeppner, T. et al. Demonstration of high performance in layered deuterium–tritium capsule implosions in uranium hohlraums at the National Ignition Facility. Phys. Rev. Lett. 115, 055001 (2015).

17. 17

Betti, R. et al. Alpha heating and burning plasmas in inertial confinement fusion. Phys. Rev. Lett. 114, 255003 (2015).

18. 18

Hurricane, O. A. et al. Inertially confined fusion plasmas dominated by alpha-particle self-heating. Nature Phys. http://dx.doi.org/10.1038/nphys3720 (2016).

19. 19

Neiuport, J. et al. Design, optical characterization, and operation of large transmission gratings for the laser integration line and laser megajoule facilities. Appl. Opt. 44, 3143–3152 (2005).

20. 20

Boehly, T. R. et al. Initial performance results of the OMEGA laser system. Opt. Commun. 133, 495–506 (1997).

21. 21

Obenschain, S. P. et al. The Nike KrF laser facility: Performance and initial target experiments. Phys. Plasmas 3, 2098–2107 (1996).

22. 22

Gardner, J. H. & Bodner, S. E. Wavelength scaling for reactor-size laser-fusion targets. Phys. Rev. Lett. 47, 1137–1140 (1981).

23. 23

Bodner, E. S. et al. Direct-drive laser fusion: status and prospects. Phys. Plasmas 5, 1901–1918 (1998).

24. 24

Goncharov, V. N. et al. A model of laser imprinting. Phys. Plasmas 7, 2062–2068 (2000).

25. 25

Kruer, W. L. in The Physics of Laser–Plasma Interactions, Frontiers in Physics Vol. 73 (ed. Pines, D.) Ch. 6–8 (Addison-Wesley, 1988).

26. 26

Kidder, R. E. Hot-electron preheat of laser-driven targets. Nucl. Fusion 21, 145–151 (1981).

27. 27

Regan, S. P. et al. Demonstration of 55 ± 7-Gbar hot-spot pressure in direct-drive layered DT cryogenic implosions on OMEGA. in 57th Ann. Meet. Div. Plasma Phys. CI3.00005 (American Physical Society, 2015).

28. 28

Bose, A. et al. Effects of long- and intermediate-wavelength nonuniformities on hot-spot energetics of hydrodynamic equivalent targets. in 57th Ann. Meet. Div. Plasma Phys. GO5.00004 (American Physical Society, 2015).

29. 29

Tabak, M. et al. Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 1626–1634 (1994).

30. 30

Betti, R. et al. Shock ignition of thermonuclear fuel with high areal density. Phys. Rev. Lett. 98, 155001 (2007).

31. 31

Theobald, W. et al. Initial cone-in-shell fast-ignition experiments on OMEGA. Phys. Plasmas 18, 056305 (2011).

32. 32

Azechi, H. et al. Present status of fast ignition realization experiment and inertial fusion energy development. Nucl. Fusion 53, 104021 (2013).

33. 33

Nora, R. et al. Gigabar spherical shock generation on the OMEGA laser. Phys. Rev. Lett. 114, 045001 (2015).

34. 34

Gotchev, O. V. et al. Laser-driven magnetic-flux compression in high-energy-density plasmas. Phys. Rev. Lett. 103, 215004 (2009).

35. 35

Slutz, S. A. et al. Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field. Phys. Plasmas 17, 56303 (2010).

36. 36

Gomez, M. R. et al. Experimental demonstration of fusion-relevant conditions in magnetized liner inertial fusion. Phys. Rev. Lett. 113, 155003 (2014).

37. 37

Lindl, J. D. et al. The Physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. Plasmas 11, 339–491 (2004).

38. 38

Haan, S. W. et al. Point design targets, specifications, and requirements for the 2010 ignition campaign on the National Ignition Facility. Phys. Plasmas 18, 051001 (2011).

39. 39

Lindl, J. et al. Review of the National Ignition Campaign 2009–2012. Phys. Plasmas 21, 020501 (2014); erratum 21, 129902 (2014).

40. 40

Clark, D. S. et al. Radiation hydrodynamics modeling of the highest compression inertial confinement fusion ignition experiment from the National Ignition Campaign. Phys. Plasmas 22, 022703 (2015).

41. 41

Stadermann, M. et al. Improvements to Formvar tent fabrication using the meniscus coater. Fusion Sci. Tech. 59, 58–62 (2011).

42. 42

Haan, S. W. et al. Instability growth seeded by oxygen in CH shells on the National Ignition Facility. Phys. Plasmas 22, 032708 (2015).

43. 43

Regan, S. P. et al. Hot-spot mix in ignition-scale implosions on the NIF. Phys. Plasmas 19, 056307 (2012).

44. 44

Jones, O. S. et al. A high-resolution integrated model of the National Ignition Campaign cryogenic layered experiments. Phys. Plasmas 19, 056315 (2012).

45. 45

Edwards, M. J. et al. Progress towards ignition on the National Ignition Facility. Phys. Plasmas 20, 070501 (2013).

46. 46

Ma, T. et al. Onset of hydrodynamic mix in high-velocity, highly compressed inertial confinement fusion implosions. Phys. Rev. Lett. 111, 085004 (2013).

47. 47

Town, R. P. J. et al. Dynamic symmetry of indirectly driven inertial confinement fusion capsules on the National Ignition Facility. Phys. Plasmas 21, 056313 (2014).

48. 48

Moody, J. D. et al. Early time implosion symmetry from two-axis shock-timing measurements on indirect drive NIF experiments. Phys. Plasmas 21, 092702 (2014).

49. 49

Moody, J. D. et al. Progress in hohlraum physics for the National Ignition Facility. Phys. Plasmas 21, 056317 (2014).

50. 50

MacLaren, S. A. et al. Novel characterization of capsule X-ray drive at the National Ignition Facility. Phys. Rev. Lett. 112, 105003 (2014).

51. 51

Callahan, D. et al. Higher velocity, high-foot implosions on the National Ignition Facility laser. Phys. Plasmas 22, 056314 (2015).

52. 52

MacPhee, A. et al. Stabilization of high-compression indirect-drive inertial confinement fusion implosions using a 4-shock adiabat-shaped drive. Phys. Plasmas 22, 080702 (2015).

53. 53

Raman, K. S. et al. An in-flight radiography platform to measure hydrodynamic instability growth in inertial confinement fusion capsules at the National Ignition Facility. Phys. Plasmas 21, 072710 (2014).

54. 54

Peterson, J. L. et al. Validating hydrodynamic growth in National Ignition Facility implosions. Phys. Plasmas 22, 056309 (2015).

55. 55

Smalyuk, V. A. et al. Hydrodynamic instability growth of three-dimensional, “native-roughness” modulations in X-ray driven, spherical implosions at the National Ignition Facility. Phys. Plasmas 22, 072704 (2015).

56. 56

Casey, D. T. et al. Reduced instability growth with high-adiabat high-foot implosions at the National Ignition Facility. Phys. Rev. E 90, 011102(R) (2014).

57. 57

Dittrich, T. R. et al. Design of a high-foot/high-adiabat ICF capsule for the National Ignition Facility. Phys. Rev. Lett. 112, 055002 (2014).

58. 58

Peterson, J. L. et al. Differential ablator-fuel adiabat tuning in indirect-drive implosions. Phys. Rev. E 91, 031101(R) (2015).

59. 59

Park, H.-S. et al. High-adiabat, high-foot, inertial confinement fusion implosion experiments on the National Ignition Facility. Phys. Rev. Lett. 112, 055001 (2014).

60. 60

Hurricane, O. A. et al. The high-foot implosion campaign on the National Ignition Facility. Phys. Plasmas 21, 056314 (2014).

61. 61

Casey, D. et al. Improved performance of high areal density indirect drive implosions at the National Ignition Facility using a four-shock adiabat shaped drive. Phys. Rev. Lett. 115, 105001 (2015).

62. 62

Smalyuk, V. et al. First results of radiation-driven, layered deuterium–tritium implosions with a 3-shock adiabat-shaped drive at the National Ignition Facility. Phys. Plasmas 22, 080703 (2015).

63. 63

Mackinnon, A. J. et al. High-density carbon ablator experiments on the National Ignition Facility. Phys. Plasmas 21, 056318 (2014).

64. 64

Berzak Hopkins, L. F. et al. First high-convergence cryogenic implosion in a near-vacuum hohlraum. Phys. Rev. Lett. 114, 175001 (2015).

65. 65

Meezan, N. B. et al. Cryogenic tritium–hydrogen–deuterium and deuterium–tritium layer implosions with high density carbon ablators in near-vacuum hohlraums. Phys. Plasmas 22, 062703 (2015).

66. 66

Ross, J. S. et al. High-density carbon capsule experiments on the National Ignition Facility. Phys. Rev. E 91, 021101(R) (2015).

67. 67

Ma, T. et al. Thin-shell high-velocity ICF implosions on the National Ignition Facility. Phys. Rev. Lett. 114, 145004 (2015).

68. 68

Michel, P. et al. Tuning the implosion symmetry of ICF targets via controlled crossed-beam energy transfer. Phys. Rev. Lett. 102, 025004 (2009).

69. 69

Michel, P. et al. Symmetry tuning via controlled crossed-beam energy transfer on the National Ignition Facility. Phys. Plasmas 17, 056305 (2010).

70. 70

Moody, J. D. et al. Multistep redirection by cross-beam power transfer of ultrahigh-power lasers in a plasma. Nature Phys. 8, 344–349 (2012).

71. 71

Callahan, D. A. et al. The velocity campaign for ignition on NIF. Phys. Plasmas 19, 056305 (2012).

72. 72

Kritcher, A. et al. Integrated modeling of cryogenic layered high-foot experiments at the NIF. Phys. Plasmas (submitted, 2016).

73. 73

Clark, D. S. et al. Three-dimensional simulations of low foot and high foot implosion experiments on the National Ignition Facility. Phys. Plasmas 23, 056302 (2016).

74. 74

Nagel, S. R. et al. Effect of the mounting membrane on shape in inertial confinement fusion implosions. Phys. Plasmas 22, 022704 (2015).

75. 75

Tommasini, R. et al. Tent-induced perturbations on areal density of implosions at the National Ignition Facility. Phys. Plasmas 22, 056315 (2015).

76. 76

Regan, S. P. et al. Suprathermal electrons generated by the two-plasmon-decay instability in gas-filled hohlraums. Phys. Plasmas 17, 020703 (2010).

77. 77

Kritcher, A. L. et al. Metrics for long wavelength asymmetries in inertial confinement fusion implosions on the National Ignition Facility. Phys. Plasmas 21, 042708 (2014).

78. 78

Spears, B. K. et al. Three-dimensional simulations of National Ignition Facility implosions: insight into experimental observables. Phys. Plasmas 22, 056317 (2015).

79. 79

Zylstra, A. B. et al. In-flight observations of low-mode ρR asymmetries in NIF implosions. Phys. Plasmas 22, 056301 (2015).

80. 80

Pak, A. et al. Laser absorbtion, power transfer, and radiation symmetry during the first shock of inertial confinement fusion gas-filled hohlraum experiments. Phys. Plasmas 22, 122701 (2015).

81. 81

Simakov, A. et al. Optimized beryllium target design for indirectly driven inertial confinement fusion experiments on the National Ignition Facility. Phys. Plasmas 21, 022701 (2014).

82. 82

Yi, S. A. et al. Hydrodynamic instabilities in beryllium targets for the National Ignition Facility. Phys. Plasmas 21, 092701 (2014).

83. 83

Clark, D. S. et al. A survey of pulse shape options for a revised plastic ablator ignition design. Phys. Plasmas 21, 112705 (2014).

84. 84

Baker, K. et al. Adiabat-shaping in indirect drive inertial confinement fusion. Phys. Plasmas 22, 052702 (2015).

85. 85

Milovich, J. et al. Design of indirectly driven, high-compression Inertial Confinement Fusion Implosions with improved hydrodynamic stability using a 4-shock adiabat-shaped drive. Phys. Plasmas 22, 122702 (2015).

86. 86

Robey, H. et al. Performance of indirectly driven capsule implosions on NIF using adiabat-shaping. Phys. Plasmas 23, 056303 (2016).

87. 87

Hinkel, D. E. et al. Improved hohlraums for high foot implosions. in 57th Ann. Meet. APS Div. Plasma Phys. BO4.00004 (American Physical Society, 2015); http://meetings.aps.org/link/BAPS.2015.DPP.BO4.4

88. 88

Leidinger, J.-P. et al. NIF Rugby High Foot Campaign from the design side.  in Proc. 9th Int. Conf. Inertial Fusion Sci. Appl. J. Phys. Conf. Ser. Paper 174 (in the press).

89. 89

Hohenberger, M. et al. Polar-direct-drive experiments on the National Ignition Facility. Phys. Plasmas 22, 056308 (2015).

90. 90

Radha, P. B. et al. Polar direct drive—simulations and results from OMEGA and the National Ignition Facility. in 57th Ann. Meet. Div. Plasma Phys. CI3.00004 (American Physical Society, 2015).

91. 91

Rosenberg, M. J. et al. Planar two-plasmon–decay experiments at polar-direct-drive ignition-relevant scale lengths at the National Ignition Facility. in 57th Ann. Meet. Div. Plasma Phys. NO5.00006 (American Physical Society, 2015).

92. 92

Stoeckl, C. et al. First results from cryogenic target implosions on OMEGA. Phys. Plasmas 9, 2195–2201 (2002).

93. 93

Sangster, T. C. et al. Improving cryogenic deuterium–tritium implosion performance on OMEGA. Phys. Plasmas 20, 056317 (2013).

94. 94

Goncharov, V. N. et al. Improved performance of direct-drive inertial confinement fusion target designs with adiabat shaping using an intensity picket. Phys. Plasmas 10, 1906–1918 (2003).

95. 95

Anderson, K. et al. Laser-induced adiabat shaping by relaxation in inertial fusion implosions. Phys. Plasmas 11, 5–8 (2004).

96. 96

Goncharov, V. N. et al. Demonstration of the highest deuterium–tritium areal density using multiple-picket cryogenic designs on omega. Phys. Rev. Lett. 104, 165001 (2010).

97. 97

Takabe, H. et al. Selfconsistent growth rate of the Rayleigh–Taylor instability in an ablatively accelerating plasma. Phys. Fluids 28, 3676–3682 (1985).

98. 98

Nora, R. et al. Theory of hydro-equivalent ignition for inertial fusion and its applications to OMEGA and the National Ignition Facility. Phys. Plasmas 21, 056316 (2014).

99. 99

Stoeckl, C. et al. Ten-inch manipulator-based neutron temporal diagnostic for cryogenic experiments on OMEGA. Rev. Sci. Instrum. 74, 1713–1716 (2003).

100. 100

Seka, W. et al. Two-plasmon-decay instability in direct-drive inertial confinement fusion experiments. Phys. Plasmas 16, 052701 (2009).

101. 101

Simon, A. et al. On the inhomogeneous two-plasmon instability. Phys. Fluids 26, 3107–3118 (1983).

102. 102

Skupsky, S. et al. Improved laser-beam uniformity using the angular dispersion of frequency-modulated light. J. Appl. Phys. 66, 3456–3462 (1989).

103. 103

Lehmberg, R. H. & Obenschain, S. P. Use of induced spatial incoherence for uniform illumination of laser fusion targets. Opt. Commun. 46, 27–31 (1983).

104. 104

Regan, S. P. et al. Performance of 1-THz-bandwidth, two-dimensional smoothing by spectral dispersion and polarization smoothing of high-power, solid-state laser beams. J. Opt. Soc. Am. B 22, 998–1002 (2005).

105. 105

Collins, T. J. B. et al. A polar-drive ignition design for the National Ignition Facility. Phys. Plasmas 19, 056308 (2012).

106. 106

Igumenshchev, I. V. et al. Crossed-beam energy transfer in implosion experiments on OMEGA. Phys. Plasmas 17, 122708 (2010).

107. 107

Igumenshchev, I. V. et al. Crossed-beam energy transfer in direct-drive implosions. Phys. Plasmas 19, 056314 (2012).

108. 108

Goncharov, V. et al. Improving the hot-spot pressure and demonstrating ignition hydrodynamic equivalence in cryogenic deuterium–tritium implosions on OMEGA. Phys. Plasmas 21, 056315 (2014).

109. 109

Froula, D. H. et al. Mitigation of cross-beam energy transfer: implication of two-state focal zooming on OMEGA. Phys. Plasmas 20, 082704 (2013).

110. 110

Hu, S. et al. Mitigating laser imprint in direct-drive inertial confinement fusion implosions with high-z dopants. Phys. Rev. Lett. 108, 195003 (2012).

111. 111

Karasik, M. et al. Suppression of laser nonuniformity imprinting using a thin high-z coating. Phys. Rev. Lett. 114, 085001 (2015).

112. 112

Smalyuk, V. A. et al. Role of hot-electron preheating in the compression of direct-drive imploding targets with cryogenic D2 ablators. Phys. Rev. Lett. 100, 185005 (2008).

113. 113

Sangster, T. C. et al. High-areal-density fuel assembly in direct-drive cryogenic implosions. Phys. Rev. Lett. 100, 185006 (2008).

114. 114

Seka, W. et al. Nonuniformly driven two-plasmon-decay instability in direct-drive implosions. Phys. Rev. Lett. 112, 145001 (2014).

115. 115

Follett, R. K. Direct observation of the two-plasmon-decay common plasma wave using ultraviolet Thomson scattering. Phys. Rev. E 91, 031104(R) (2015).

116. 116

Michel, D. T. et al. Experimental validation of the two-plasmon-decay common-wave process. Phys. Rev. Lett. 109, 155007 (2012).

117. 117

Froula, D. H. et al. Saturation of the two-plasmon decay instability in long-scale-length plasmas relevant to direct-drive inertial confinement fusion. Phys. Rev. Lett. 108, 165003 (2012).

118. 118

Yan, R. et al. Generating energetic electrons through staged acceleration in the two-plasmon-decay instability in inertial confinement fusion. Phys. Rev. Lett. 108, 175002 (2012).

119. 119

Zhang, J. et al. Multiple beam two-plasmon decay: linear threshold to nonlinear saturation in three dimensions. Phys. Rev. Lett. 113, 105001 (2014).

120. 120

Myatt, J. F. et al. Mitigation of two-plasmon decay in direct-drive inertial confinement fusion through the manipulation of ion-acoustic and Langmuir wave damping. Phys. Plasmas 20, 052705 (2013).

121. 121

Smalyuk, V. et al. Implosion experiments using glass ablators for direct-drive inertial confinement fusion. Phys. Rev. Lett. 104, 165002 (2010).

122. 122

Froula, D. H. et al. Laser–plasma interactions in direct-drive ignition plasmas. Plasma Phys. Control. Fusion 54, 124016 (2012).

123. 123

Lafon, M. et al. Direct-drive ignition designs with mid-Z ablators. Phys. Plasmas 22, 032703 (2015).

124. 124

Betti, R. & Zhou, C. D. High-density and high-ρR fuel assembly for fast-ignition inertial confinement fusion. Phys. Plasmas 12, 110702 (2005).

125. 125

Key, M. H. Status of and prospects for the fast ignition inertial fusion concept. Phys. Plasmas 14, 055502 (2007).

126. 126

Craxton, R. S. et al. Direct-drive inertial confinement fusion: a review. Phys. Plasmas 22, 110501 (2015).

127. 127

Kodama, R. et al. Nuclear fusion: fast heating scalable to laser fusion ignition. Nature 418, 933–934 (2002).

128. 128

Roth, M. et al. Fast ignition by intense laser-accelerated proton beams. Phys. Rev. Lett. 86, 436–439 (2001).

129. 129

Atzeni, S. Inertial fusion fast ignitor: igniting pulse parameter window vs the penetration depth of the heating particles and the density of the precompressed fuel. Phys. Plasmas 6, 3316–3326 (1999).

130. 130

Stoeckl, C. et al. Hydrodynamics studies of direct-drive cone-in-shell, fast-ignitor targets on OMEGA. Phys. Plasmas 14, 112702 (2007).

131. 131

Green, J. S. et al. Effect of laser intensity on fast-electron-beam divergence in solid-density plasmas. Phys. Rev. Lett. 100, 015003 (2008).

132. 132

Jarrott, L. C. et al. Visualizing fast electron energy transport into laser-compressed high-density fast-ignition targets. Nature Phys. http://dx.doi.org/10.1038/nphys3614 (2016).

133. 133

Strozzi, D. et al. Fast-ignition transport studies: realistic electron source, integrated particle-in-cell and hydrodynamic modeling, imposed magnetic fields. Phys. Plasmas 19, 072711 (2012).

134. 134

Robinson, A. et al. Focusing of relativistic electrons in dense plasma using a resistivity-gradient-generated magnetic switchyard. Phys. Rev. Lett. 108, 125004 (2012).

135. 135

Bellei, C. et al. Fast ignition: dependence of the ignition energy on source and target parameters for particle-in-cell-modelled energy and angular distributions of the fast electrons. Phys. Plasmas 20, 052704 (2013).

136. 136

Shcherbakov, V. A. Ignition of a laser-fusion target by a focusing shock wave. Sov. J. Plasma Phys. 9, 240–241 (1983).

137. 137

Atzeni, S. et al. Shock ignition of thermonuclear fuel: principles and modelling. Nucl. Fusion 54, 054008 (2014).

138. 138

Batani, D. et al. Physics issues for shock ignition. Nucl. Fusion 54, 054009 (2014).

139. 139

Perkins, L. J. et al. Shock Ignition: a new approach to high gain inertial confinement fusion on the National Ignition Facility. Phys. Rev. Lett. 103, 045004 (2009).

140. 140

Schmitt, A. J. et al. Shock ignition target design for inertial fusion energy. Phys. Plasmas 17, 042701 (2010).

141. 141

Ribeyre, X. et al. Shock ignition: an alternative scheme for HiPER. Plasma Phys. Control. Fusion 51, 015013 (2009).

142. 142

Lafon, M. et al. Gain curves and hydrodynamic modeling for shock ignition. Phys. Plasmas 17, 052704 (2010).

143. 143

Atzeni, S. et al. Energy and wavelength scaling of shock-ignited inertial fusion targets. New J. Phys. 15, 045004 (2013).

144. 144

Ribeyre, X. et al. Shock ignition: modelling and target design robustness. Plasma Phys. Control. Fusion 51, 124030 (2009).

145. 145

Theobald, W. et al. Initial experiments on the shock-ignition inertial confinement fusion concept. Phys. Plasmas 15, 056306 (2008).

146. 146

Baton, S. D. et al. Experiment in planar geometry for shock ignition studies. Phys. Rev. Lett. 108, 195002 (2012).

147. 147

Hohenberger, M. et al. Shock-ignition relevant experiments with planar targets on OMEGA. Phys. Plasmas 21, 022702 (2014).

148. 148

Batani, D. et al. Generation of high pressure shocks relevant to the shock-ignition intensity regime. Phys. Plasmas 21, 032710 (2014).

149. 149

Theobald, W. et al. Spherical strong-shock generation for shock-ignition inertial fusion. Phys. Plasmas 22, 056310 (2015).

150. 150

Theobald, W. et al. Spherical shock-ignition experiments with the 40 + 20-beam configuration on OMEGA. Phys. Plasmas 19, 102706 (2012).

151. 151

Betti, R. et al. Shock ignition of thermonuclear fuel with high areal densities. J. Phys. Conf. Ser. 112, 022024 (2008).

152. 152

Piriz, A. R. et al. Ablation driven by hot electrons generated during the ignitor laser pulse in shock ignition. Phys. Plasmas 19, 122705 (2012).

153. 153

Gus’kov, S. et al. Ablation pressure driven by an energetic electron beam in a dense plasma. Phys. Rev. Lett. 109, 255004 (2012).

154. 154

Klimo, O., Weber, S., Tikhonchuk, V. T. & Limpouch, J. Particle-in-cell simulations of laser-plasma interaction for the shock ignition scenario. Plasma Phys. Control. Fusion 52, 055013 (2010).

155. 155

Yan, R. et al. Intermittent laser–plasma interactions and hot electron generation in shock ignition. Phys. Plasmas 21, 062705 (2014).

156. 156

Klimo, O. et al. Laser plasma interaction studies in the context of shock ignition—transition from collisional to collisionless absorption. Phys. Plasmas 18, 082709 (2011).

157. 157

Weber, S. et al. Fast saturation of the two-plasmon-decay instability for shock-ignition conditions. Phys. Rev. E 85, 016403 (2012).

158. 158

Nicolai, Ph. et al. Deleterious effects of nonthermal electrons in shock ignition concept. Phys. Rev. E 89, 033107 (2014).

159. 159

Tikhonchuck, V. et al. Multiscale models of laser–plasma interaction for the shock ignition scheme. in 9th Inertial Fusion Sic. Appl. Conf. (2015).

160. 160

Gotchev, O. V. et al. Seeding magnetic fields for laser-driven flux compression in high-energy-density plasmas. Rev. Sci. Instrum. 80, 043504 (2009); Fiksel, G. et al. Note: experimental platform for magnetized high-energy-density plasma studies at the OMEGA laser facility. Rev. Sci. Instrum. 86 016105 (2015).

161. 161

Chang, P. Y. et al. Fusion yield enhancement in magnetized laser-driven implosions. Phys. Rev. Lett. 107, 035006 (2011).

162. 162

Hohenberger, M. et al. Inertial confinement fusion implosions with imposed magnetic field compression using the OMEGA laser. Phys. Plasmas 19, 056306 (2012).

163. 163

Davies, J. C., Betti, R., Chang, P. Y. & Fiksel, G. The importance of electrothermal terms in Ohm’s law for magnetized spherical implosions. Phys. Plasmas 22, 112703 (2015).

164. 164

Perkins, L. J., Logan, B. G., Zimmerman, G. B. & Werner, C. J. Two-dimensional simulations of thermonuclear burn in ignition-scale inertial confinement fusion targets under compressed axial magnetic fields. Phys. Plasmas 20, 072708 (2013).

165. 165

Montgomery, D. S. et al. Use of external magnetic fields in hohlraum plasmas to improve laser-coupling. Phys. Plasmas 22, 010703 (2015); erratum 22, 079901 (2015).

166. 166

Basko, M. M., Kemp, A. J. & Meyer-ter-Vehn, J. Ignition conditions for magnetized target fusion in cylindrical geometry. Nucl. Fusion 40, 59–68 (2000).

167. 167

Sefkow, A. B. et al. Design of magnetized liner inertial fusion experiments using the Z facility. Phys. Plasmas 21, 072711 (2014).

168. 168

Slutz, S. A. & Vesey, R. A. High-gain magnetized inertial fusion. Phys. Rev. Lett. 108, 025003 (2012).

## Acknowledgements

The authors would like to thank the US and the international ICF community for their continuing efforts to make inertial fusion in the laboratory a reality. Special thanks to J. R. Davies of LLE for his input on the Magneto-Inertial Fusion section of this manuscript. The authors are grateful to M. E. Campbell, S. P. Regan, T. C. Sangster and W. Theobald of LLE, F. Beg of UCSD, D. Sinar of SNL and to D. Clark, M. J. Edwards, L. F. Berzak-Hopkins, A. Kritcher and T. Ma of LLNL for reviewing this manuscript. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344, by the University of Rochester Laboratory for Laser Energetics under Cooperative Agreements DE-NA0001944 (NNSA) and DE-FC02-04ER54789 (OFES), and with the support of the New York State Energy Research Development Authority.

## Author information

Authors

### Corresponding author

Correspondence to R. Betti.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Rights and permissions

Reprints and Permissions

Betti, R., Hurricane, O. Inertial-confinement fusion with lasers. Nature Phys 12, 435–448 (2016). https://doi.org/10.1038/nphys3736

• Accepted:

• Published:

• Issue Date:

• ### Equation of state measurements of dense krypton up to the insulator-metal transition regime: Evaluating the exchange-correlation functionals

• Zhao-Qi Wang
• , Yun-Jun Gu
• , Qi-Feng Chen
• , Zhi-Guo Li
• , Lei Liu
• , Guo-Jun Li
• , Yang-Shun Lan
•  & Xiang-Rong Chen

Physical Review B (2021)

• ### Direct-drive heavy ion beam inertial confinement fusion: a review, toward our future energy source

• Shigeo Kawata

• ### TJ cm−3 high energy density plasma formation from intense laser-irradiated foam targets composed of disordered carbon nanowires

• K Jiang
• , A Pukhov
•  & C T Zhou

Plasma Physics and Controlled Fusion (2021)

• ### Optimization of a laser plasma-based x-ray source according to WDM absorption spectroscopy requirements

• A. S. Martynenko
• , S. A. Pikuz
• , I. Yu. Skobelev
• , S. N. Ryazantsev
• , C. D. Baird
• , N. Booth
• , L. N. K. Döhl
• , P. Durey
• , A. Ya. Faenov
• , D. Farley
• , R. Kodama
• , K. Lancaster
• , P. McKenna
• , C. D. Murphy
• , C. Spindloe
• , T. A. Pikuz
•  & N. Woolsey

Matter and Radiation at Extremes (2021)

• ### Whole-beam self-focusing in fusion-relevant plasma

• B. T. Spiers
• , M. P. Hill
• , C. Brown
• , L. Ceurvorst
• , N. Ratan
• , A. F. Savin
• , P. Allan
• , E. Floyd
• , J. Fyrth
• , L. Hobbs
• , S. James
• , J. Luis
• , M. Ramsay
• , N. Sircombe
• , J. Skidmore
• , R. Aboushelbaya
• , M. W. Mayr