Chapter 11. Introduction to (Laser-Driven) Inertial Confinement Fusion

Transcription

1 Chapter 11 Introduction to (Laser-Driven) Inertial Confinement Fusion Stefano Atzeni Dipartimento di Scienze di Base e Applicate per l Ingegneria (SBAI) Università di Roma La Sapienza May 17, 2017 stefano.atzeni@uniroma1.it

2 Summary I. ICF principles II. III. IV. ICF by spherical implosion Main issues Direct and indirect drive V. Modelling ICF experiments VI. Lasers for fusion VII. Ignition experiments at the NIF VIII. Towards the reactor Appendix A: Ablative acceleration; rocket model Appendix B: Additional materials on Rayleigh-Taylor instability Bibliography 2

3 I. ICF principles 3

4 Controlled fusion requires the achievement of extreme conditions thermonuclear reactions (no beam-target, no beam-beam) temperature T 5 x 10 7 K ==> plasma confinement: the reacting plasma must be kept at suitable density and temperature, and its energy/mass must be confined for a sufficiently long time τ, so that in a steady reactor the released power exceeds the power spent to keep the plasma reacting in a pulsed reactor the released energy per pulse exceeds the energy spent to bring the fuel to burning conditions

5 Confinement. An option: Inertial confinement fusion (ICF) Fusion reactions from a target containing a few mg of DT fuel compressed to very high density (ρ > 1000 times solid density) and heated to very high temperature No external confinement => fuel confined by its own inertia (mass) confinement time τ = R/c s, c s : sound speed; R: linear dimension of the compressed fuel Explosive, pulsed process Energy has to be provided cyclically by a suitable driver The mass of the fuel must be limited to about 10 mg, in order to contain the explosion (1 mg of DT releases 340 MJ, equivalent to 85 kg of TNT) [Q DT = 17.6 MeV/reaction = 340 MJ/mg = 3.4 x J/kg]

6 ρr: ICF confinement parameter Φ: burn efficiency ICF is pulsed. The fuel must remain confined for a time longer than the burn time 1 reaction time: τ reaz, n = ρ/m i : ion number density n < σv > ρ: mass density confinement time: τ conf R c s, c s = T (kev) cm/s (sound speed) τ conf > τ reaz ==> ρr c sm i < σv > = => ρr > 1.2 g/cm 2 at T = kev, rhs depends weakly on T It can be shown that the fraction of burned fuel is, approximately, Φ = ρr / (ρr + 7 g/cm 2 ), and in practice the confinement requirement is ρr > (2 3) g/cm 2 6

7 ICF performance is measured by the GAIN: target gain, fuel gain G = ICF is pulsed. Each target must release an energy well in excess of the energy used to bring it to fusion conditions. We define the target gain G Fusion energy Energy delivered by the driver to the target = E Fus E driver = Φm DT Q DT E driver and the fuel energy gain G F G F = Fusion energy Energy delivered to the fuel = E Fus E F = E Fus ηe driver where η is the energy coupling efficiency, typically of 5-10% 7

8 Pulsed fusion for energy production: general requirements set by power balance and economics laser repetition rate: ν driver Close the cycle: G η d = 1/(Mη th f) Power production: P grid = ν driver E grid = ν driver [(1-f) η th GM E d ] target cost < 20% COE; (COE: cost of energy)

9 Reactor cycle: numbers for a 1 GW reactor Possible set of parameters for a 1000 MW reactor Closing the cycle: G η d = 10; e.g. G = 100; η d = 10% Power production: E d = 2.5 MJ; ν driver = 10 Hz 1 target electrical energy to grid = 100 MJ = 27.8 kwh; if COE = 0.05 /kwh, cost of target < (burnt DT in 1 target: mg; DT in 1 target 2.5 mg) 9

10 Required: target gain 100 few MJ driver Cost of target critical G η d 10 => G = 100 (or larger) Large capital costs, economy of scale; P grid 1 GW e => E d = 2 5 MJ cost of target < 20% Cost Of Energy => Y fus cost of target < 28 cent 250 MJ COE 5 cent/kwh h th 40%

11 The essential physical ingredients of ICF: Compression Hot spot ignition (homogeneous sphere of DT, radius R, density ρ) COMPRESSION: Φ > 30% ==> ρr > 3 g/cm 2 mass m DT = (4π/3)ρR 3 < few mg ==> r > HOT SPOT IGNITION do not heat the whole fuel to 5 kev; heat to 5 10 kev the smallest amount of fuel capable self heating and triggering a burn wave 300 m DT (mg) g/cm3 of 11

12 Why hot spot ignition uniform heating of the whole fuel = > unacceptably low fuel gain Indeed: 1 DT reaction => kev heating deuteron, triton and their electrons to 5 kev: (3/2)*5*4 = 30 kev = => G F = Φ 30 = 580 Φ <<1000 Hot spot ignition to save energy and allow for the needed high gain

13 Ignition: once the central fuel is heated and compressed, competition between heating (alpha-particles) and cooling (electrons, bremsstrahlung, mechanical work) Good estimates obtained from simple models assuming model configurations as in this figure a) standard, isobaric b) isochoric (applies to fast ignitor, see next lectures) Ignition conditions can be written in the form of Lawson-conditions (T vs ρr)

14 Hot spot ignition condition: Lawson-like and nτt (or ρrt) criteria

15 The ignition condition is essentially a condition on the hot spot pressure fuel at ignition pressure for ignition: [ρ c /ρ h = 5 7] p (Gbar) > 500 R h 30 µm! pr h > 15 Tbar µm S. Atzeni et al. NJP (2013); J. Lindl et al, NF (2014)

16 II. ICF by spherical implosion 16

17 the standard approach: implosion and central ignition imploding fuel kinetic energy converted into internal energy and concentrated in the centre of the fuel to achieve the ignition conditions: implosion velocity for ignition: u imp > km/s depending of the fuel mass: u imp m -1/8 17 (see, e.g., S. Atzeni and J. Meyer-ter-Vehn, The Physics of Inertial Fusion, Oxford University Press, 2004.)

18 Simulation of a standard direct-drive target Irradiated by a laser pulse, with wavelength of 0.25 µm total energy of 1.6 MJ Achieves energy gain about 60 It can be improved to achieve gain higher than 100 Next viewgraphs (and movies), from 1-D and 2-D simulations (DUED code) Ref: S. Atzeni and J. Meyer-ter-Vehn: The Physics of Inertial Fusion, Oxford (2004, 2009) 18

19 Hollow shell (*) target, irradiated by a large number of overlapping beams Target (hollow shell) Fuel mass: few mg Radius: 1 3 mm Fuel radius / thickness = 10 Laser driver pulse Energy: 1 5 MJ Duration: ns Peak power: TW Peak intensity: W/cm 2 Wavelength: (1/4) (1/3) µm (*) Shell instead of sphere to increase target surface and increase irradiation time: => reduced laser intensity, reduced laser power Compressed fuel Density: g/cm 3 Low average entropy, but hot-spot with T = 10 kev

20 Irradiation, implosion, compression, ignition & burn (shell with 1.67 mg of DT fuel, irradiated by 1.6 MJ pulse, see later) density (g/cm 3 ) temperature (K) mm 3 mm S. Atzeni, 1992 simulated interval = 25 ns 20

21 Zoom (in space and time): final compression, ignition, burn and explosion Density temperature 0.15 mm S. Atzeni, ,15 mm simulated time = 0.5 ns 21

22 Text Laser power vs time (notice the log scale) 1-D Flow chart

23 Laser absorption ==> ablation high temperature plasma very high pressure corona expands, shocks launched in the shell

24 Shocks driven by laser absorption ==> shell inward acceleration (implosion)

25 The ablative pressure drives the implosion of the shell shell inward acceleration (implosion) = rocket [see previous lectures] At stagnation substantial fuel compression and heating occur (see curves 5)

26 At the end of the implosion a hot spot is formed, which suddenly self-heats and drives a fusion burn wave (notice the time scales)

27 Text fusion burn wave propagating to the whole fuel in less than 100 ps

28 Back-of-the envelope parameter estimate specific energy = > implosion velocity implosion velocity & target size => driving pressure size and velocity => implosion time and pulse time target mass and specific energy => fuel energy coupling efficiency (next lecture) & fuel energy => driver energy driver energy, pulse time, target size => driver power and intensity A key parameter is the shell aspect ratio (radius to thickness, R 0 /ΔR 0 ): The larger the aspect ratio the lower power and intensity, but more critical target stability and symmetry (next lectures)

29 Specific internal energy (compression* and thermal) at ignition = specific kinetic energy of the imploding fuel = u i2 /2 => implosion velocity u imp = km/s Average pressure: assume constant pressure applied at thin hollow shell, as the radius shrinks by 50%: => (1/2) m f u imp 2 <p> (7/8)(4π/3) R 0 3 <p> (12/7) ρ DT u imp 2 (ΔR 0 /R 0 ) (**) Peak pressure 2.5 <p> for R 0 /ΔR 0 = 10, peak pressure = Mbar 100 Mbar pressure (***) required to implode at u imp = 350 km/s *) Partial degeneracy important **) ρ DT : density of solid DT ***) 100 Mbar = 100 millions atmospheres = 10 TPa

30 Back-of-the-envelope estimates of target parameters

31 III. Main issues 31

32 Implosion concentrates energy in space, multiplies pressure, but four key issues 1. couple efficiently driver energy to the target, to achieve adequate imposion velocity (discussed in detail in the next lectures) 2. use efficiently the coupled energy to compress the fuel 3. mantain nearly spherical symmetry (small, central hot spot to be created) 4. limit dangerous effects of Rayleigh-Taylor instabilities (RTI) (discussed in detail in the next lectures) 32

33 1st issue: coupling laser light - short laser wavelength (e.g. λ = 0.35 µm; next lectures) - limit intensity I to W/cm 2 (next lectures) => use hollow shell target, instead of sphere good assorption in the collisional regime, at short wavelength p (I/λ) I = Wcm 2 λ = 0.35 µm = => pressure p = 80 Mbar Garban-Labaune et al, PRL (1982) (see next page) 33

34 Ablation pressure vs absorbed laser intensity 34

35 2nd issue: compress efficiently do not heat before compressing => - no preheating by fast particles, hard X-rays - tune the pulse, to reach high pressure gradually laser power vs time Pulse shaping Laser power carefully tuned, to launch a sequence of properly timed shocks, that approximate adiabatic compression 1-D Flow chart we want α = p(ρ,t)/p Fermi (ρ) as small as possible 35

36 3rd issue: symmetry: irradiate as uniformly as possible long scale shape of compressed fuel depends on driving pressure non uniformity δr R =δu imp = δp u imp p 2 δi 3 I we want hot spot relative deformation δr h /R h << 1 but R h is typically 1/30 of the initial radius R 0 ==> δi/i << 1/20; ==> we request δi/i < 1% (the larger the ignition margin, the larger tolerable δi/i (eg, Atzeni, Europhys. Lett. 1990)

37 3rd issue: symmetry: operate with safety margins 37

38 3rd issue: symmetry: operate with safety margins (S. Atzeni, Europhys. Lett. 1990) 38

39 3rd issue: symmetry another aspect: accurate target positioning required Shock-ignition: sensitive to mispositioning S. Atzeni, A. Schiavi, A. Marocchino, Plasma Phys. Controll. Fusion µm displacement Gain = 95% of 1D gain 20 µm displacement Gain = 1% of 1D gain

40 time =======> 4 th issue: Rayleigh-Taylor instability unavoidable in inertial fusion deceleration-phase instability at the hot spot boundary (2D simulation) Atzeni & Schiavi, PPCF

41 RTI hinders hot spot formation Here simulations assuming initial multimode spectrum on the inner surface of the shell moderate initial amplitude (1.5 µm rms) at the end of the implosion coasting stage: deformed hot spot; ignition still occurs large initial amplitude (6 µm rms): hot spot NOT formed Ion temperature (ev) map evolution movies by S. Atzeni and A. Schiavi, 2004

42 Rayleigh instability of superposed fluids Taylor instability of accelerated fluid Rayleigh instability of interface in hydrostatic equilibrium Taylor instability of accelerated interface; equivalent to Rayleigh instability if analysed in a frame moving with the interface 42

43 43

44 Rayleigh instability, single mode and multimode, nonlinear evolution 44

45 RTI in ICF: instability at ablation front & instability at stagnation (Lindl et al, 2004) perturbation fed from outer to inner surface of the shell 45

46 Simulation by the NRL group; Bates et al., HEDP 2010; Schmitt et al., PoP

47 Inner surface RTI in ICF 47 (Atzeni & Schiavi, PPCF 2004)

48 IV. Direct- and indirect-drive 48

49 drivers: o lasers o ion beams o pulsed power sources A variety of inertial fusion schemes have been proposed compression-driving irradiation schemes: o direct o indirect ignition schemes: o conventional central ignition o fast ignition o shock ignition 49

50 direct drive and indirect drive In indirect drive, the fuel containing capsule is irradiated by thermal X-rays ( ev), generated and confined in a cavity (a hohlraum). 50

51 Why indirect-drive? Pros: long scale irradiation uniformity weakly dependent on beam disposition smooth radiation field on short scales RTI less violent then in direct drive, due to much higher ablation velocity (linear growth rate γ = (ak) 1/2 - k u abl, with a: acceleration, k mode number, u abl ablation velocity = areal mass ablation rate/ density) Con: lower coupling efficiency [& much more complex modelling] (laser => X-rays => capsule, with loss to generate the radiating plasma, loss from the hole, loss of X in the hohlraum wall) 51

52 V. Modelling ICF experiments 52

53 ICF: a variety of basic physics processes and of space- and time-scales Laser matter (plasma) [or particle-beam plasma] interaction Plasma physics (including non-ideal plasma, partially degenerate plasma, partial ionization, etc.) Phase transitions (from cryogenic matter to hot plasma) Transport processes Radiative transfer Fusion reactions and product (charged products and neutrons) transport Mass density: g/cm 3 Temperature: 10 K 3 x 10 9 K Time-scales Implosion: few 30 ns Ignition: few 100 ps Fluid instabilities: ns Plasma instabilities: < 1 ps to ns Space-scales Target size: few mm Compressed fuel: 0.1 mm Density scale-lengths: down to 0.1 µm Fluid modes: down to µm Plasma instabillities: Debye length, skin depth,..

54 ICF involves extreme values of temperature, density and pressure NIF expts,

55 ICF target simulation codes inlcude a lot of physics and must resolve small scales 55

56 VI. Lasers for fusion 56

57 The largest 1980 s laser fusion facility: NOVA pulses with up to 50 kj in a few ns 57

58 Titolo NIF: a 1.8 MJ laser for fusion ignition demonstration (Lawrence Livermore National Laboratory) (from LLNL website) 58

59 NIF: a 1.8 MJ laser for fusion ignition demonstration (Lawrence Livermore National Laboratory) movie taken during NIF construction (downloaded from LLNL site). NIF was completed in

60 NIF: How does it work? movie from LLNL site:

61

62 Camera di reazione

63 VII. Ignition experiments at the NIF 63

64 Laser fusion early history 1950 s: driver power levels, times scales for manageable release of fusion energy(< 1 GJ; few mg DT fuel) computed; no appropriate driver available : laser + Q-switch lasers fusion concept (R. Kidder, J. Nuckolls, A. Sakharov, N. Basov,...) lasers for fusion: o wavelength: ¼ ½ µm o few 100 TW; 1-to-few MJ; few ns pulses o High rep. rate, high efficiency (for reactor)

65 The effort to demonstrate ignition 1995: experimental, theoretical, computational data base, supporting design of ignition experiments (Lindl, PoP 1995) Indirect drive: weaker RTI, low sensitivity to beam non-uniformities Laser: 1.8 MJ 400 TW; vuv (0.35 µm), accurate pulse shaping fuel mass m DT = 0.17 mg implosion velocity u = 370 km/s adiabat α = 1.5 objective: Y > 15 MJ (G 10) fuel parameters at ignition: hot spot pressure > 350 Gbar; <ρr> = 1.5 g/cm 2 ; peak density = 1000 g/cm 3

66 Experiments at the NIF (National Ignition Facility) aim at achieving ignition using indirect drive. NIF laser (Lawrence Livermore Laboratory, CA, USA): laser a vetro:nd, con triplicazione di frequenza energia totale per impulso: 1.8 MJ (λ = 0.35 µm) potenza di picco: 500 TW 192 fasci, focalizzabili con errore < 50 µm potenza (di ciascun bundle di fasci) programmabile nel tempo (range dinamico 1:100); funziona meglio delle specifiche di progetto! costruita fra il 1998 e il 2009; opera a piena potenza dal 2011 costo: 4 G$; finanziata dal Defence Program del DoE (ora dalla NNSA del DoE) 66

67 NIF hohlraum target coupling & symmetry symmetry control: beam orientation beam pointing hohlraum aspect ratio hohlraum fill beam coupling: choice of materials entropy control: cryogenic fuel, pulse shaping (courtesy of LLNL) preheat limitation: ablator doping

68 National ignition campaign, NIC, ( ) demonstrated strong compression, but did not achieve ignition implosion velocity smaller than expected (see later) pressure (much) smaller than expected Note that NIF laser outperforms design specs D. Hicks et al., Phys. Plasmas 19, (2012); N. B. Meezan et al., Phys. Plasmas 20, (2013); O. L. Landen et al., Plasma Phys. Controll. Fusion 54, (2012) J. D. Lindl et al., Phys. Plasmas 21, (2014)

69 NIF baseline ignition experiments (NIC campaign) vs simulations NIC campaign: general qualitative agreement, strong compression, but 15% laser light backscattered from the hohlraum (vs few % expected) (laser-plasma instabilities, LPI s) Implosion velocity 10% smaller than expected (for given absorbed energy) Low-mode asymmetries poorly controlled once the required implosion velocity was approached (by increasing laser power and/or reducing shell thickness) fuel contaminated as a consequence of instabilities outstanding (and unique) diagnostics essential for understanding above results

70 2014 (high-foot) experiments (Hurricane et al, Nature 2014): higher foot power: entropy increased to - reduce RTI growth - make imploding shell thicker shorter pulse => less LPI s implosion velocity 320 km/s; α 2.5 Understading key issues separately: try to get 1D implosion, at the expense of compression = => record yield => fusion yield nearly as predicted by 1D sims fuel gain > 1 yield multiplication by self-heating M y = 2 but compression insufficient for ignition

71 : Further progress: for the first time 1) fusion energy larger than fuel energy at burn time 2) about 50% of the reactions due to self-heating O. Hurricane et al., Nature 506, 343 (2014) Nov Spring increased temperature - improved symmetry - reduced instabilityinduced mixing - lower compression (higher entropy) for a detailed discussion see Rosen, APS-DPP 2014, LLNL-PRES

72 NIF National Ignition Campaign ( ) high resolution radiography, showing implosion, stagnation, bounce [D. Hicks et al., Phys. Plasmas 19, (2012)] 72

73 X-ray and neutron imaging of the hot spot O. Hurricane et al., Nature 506, 343 (2014) 73

74 How far from ignition? Yield in high foot experiments ~ 30 kj, while ignition yield Y > 1 MJ Really so far from ignition? Is yield the right metric? A better metric (*) : generalized Lawson parameter χ = (pτ)/(pτ) ignition [τ: confinement t] Yield multiplication by self-heating M y is a unique function of χ: M y =M y (χ) In terms of measurable quantities: χ = const (ρr) 0.61 (Y/m DT ) 0.24 Low foot experiments: χ 0.3 (M y 1.3) High foot experiments: χ = 0.6 (M y = 2) For ignition: χ 1 (M y > 100): progress by a factor 2 needed (*) R. Betti et al., Phys. Plasmas 17, (2010)

75 Towards the reactor? A very long path After ignition demonstration, we have to increase driver efficiency x 10 driver rep rate x target gain x 5 10 However, potential solutions exists and are being studied (Diode pumped solid-state lasers)

76 VIII. Towards the reactor 76

77 Inertial fusion reactor conceptual design

78 Conclusions on Inertial Fusion I presented a brief, personal, incomplete and unavoidably biased, perspective on laser fusion A few final remarks impressive progress in lasers impressive progress in physics understanding and modelling crucial role of diagnostics (often, laser-based: backlighters, proton imaging,...) a number of ingenious schemes proposed synergy with other laser-driven physics Ignition not faraway, the path to reactor anyhow (very) long = => a lot of exciting opportunities (and demanding work) for young scientists and engineers!

79 Appendix A Ablative acceleration of a plane target Rocket model of ablation 79

80 Irradiation of a tick disk, plasma formation SA, 1985;

81 Ablative acceleration of a thin disk SA, 1985;

82 Laser acceleration = acceleration of a rocket (of mass m(t) No exerternal forces: momentum is conserved dq ex + dq rocket = 0 dm d(mv ) +[ dm(u ex + v )] = 0 => dv = u ex m v(t) = u ex ln m (t) m 0 82

83 rocket efficiency (in laser fusion hydrodynamic efficiency) η h ideal = E payload E payload +E exhaust = 1 2 mv2 1 2 (m m)u 2 0 ex = xln x2 1 x η h = For laser drive, after some algebra: 1 2 mv2 E laser-absorbed = 1 2 d(m/s ) d t 2 u ex xln x 2 I abs 1 x = h xln x2 1 x, h 0.25 for low - Z materials

84 Appendix B Additional materials on Rayleigh-Taylor instability 84

85 Rayleigh instability of superposed fluids Taylor instability of accelerated fluid Rayleigh instability of interface in hydrostatic equilibrium Taylor instability of accelerated interface; equivalent to Rayleigh instability if analysed in a frame moving with the interface 85

86 86

87 Rayleigh instability, single mode and multimode, nonlinear evolution 87

88 88

89 Classical Rayleigh instability of superposed fluids Linear theory: Sinusoidal perturbations of the interface between incompressible, ideal fluids, with wavelength λ (i.e. wave number k = 2 π/λ) and small initial amplitude ξ 0, grow exponentially in time ξ = ξ 0 exp(γt) [for ξ λ/10] with growth rate g = g cl = Agk and A = (ρ 2 ρ 1 )/(ρ 2 + ρ 1 ) 89

90 Rayleigh instability of superposed fluids growth rate derivation from a simple energy principle (H. J. Kull, Laser Part. Beams 1986) 90

91 91

92 = = > the classical RTI growth rate (Lord Rayleigh, 1883) γ = γ cl = Agk A = ρ 2 ρ 1 ρ 2 + ρ 1, Atwood number RTI of a layer of finite thickness: G. I. Taylor (1950) General stability condition (energy principle): Chandrasekhar s book Hydrodynamic and hydromagnetic stability, Oxford (1961) 92

93 If RTI growth at ablation front were classical, ICF would not be feasible Linear growth a perturbation of initial amplitude ξ 0 and wavelength λ: ξ(λ,t ) = ξ 0 exp t 0 γ(λ, t ʹ ) dt ʹ = ξ 0 exp Γ(λ,t ) [ ] Assume γ = Aak 2πa / λ ( A 1 at ablation front) constant acceleration between r = R 0 and r = (1/2) R 0 = > at 2 = R 0 worst (=most dangerous) mode for a layer of thickness ΔR: λ = πδr (for shorter wavelengths linear growth saturation) = => for the worst mode, at the end of acceleration stage Γ 2R 0 ΔR = 2R 0 R R ΔR >11, i.e. ξ > ξ 0 clearly unacceptable (here we have assumed R = R 0 /2, and R/ΔR > 30 93

94 RTI, classical vs ICF ablation reduces growth, stabilises short wavelengths classical RTI: uniform density, sharp interface, no fluxes, incompress. fluids in ICF, ablative RTI: continous density; mass, momentum & energy fluxes (ablation), [+ compressible fluids, + spherical geometry +...] ablative RTI: growth rate reduced, short wavelengths stable Theory vs experiment (Budil et al. 1996) theory vs simulation (Tabak et al. 1990) 94

95 RTI, classical vs ICF ablation reduces growth, stabilises short wavelengths The major differences with classical RTI are caused by (*) - finite density gradient (with minimum density scale-length L min ) - ablation (with surface rate dµ/dt) Theory (Sanz 1994, Betti et al 1996, 1998) is involved. However results are fitted well by (Betti et al. 1998, generalising Takabe et al. 1985) γ = α RT ak 1+ kl min β RT ku a where α RT = and β RT = 1 3 are coefficients depending on laser intensity, light wavelength and material, u a = dm / dt ρ pa is the ablation velocity, with ρ pa peak density ahead of the ablation front (*) For detailed treatment and bibliography see Ch. 8 of Atzeni & Meyer-ter-Vehn, 2004.

96 Ablative stabilisation: theory, simulations, experiments Theory vs experiment (Budil et al. 1996) Takabe-like formula vs simulation (Tabak et al. 1990) 96

97 Ablative RTI allows for significant reduction of the growth factor Γ from ablative RTI linear growth rate and rocket implosion model (Lindl et al 2004) for indirect drive Γ Indirect drive: high implosion velocity: strong stabilisation, Γ acceptable 97

98 Ablative RTI allows for significant reduction of the growth factor Γ from ablative RTI linear growth rate and rocket implosion model (Lindl et al 2004) for direct drive: Γ max = α if 8.5 u imp 2 / 5 I 1/ cm/s reduction with respect to classical case, but still insufficient, unless in-flight isentrope factor α if is raised to 3 5 Solution: increase isentrope factor at the outer surface of the shell, without affecting inner layers: ADIABAT SHAPING (several different scheme, by all major labs. They work! 98

99 Example of adiabat shaping (for a shock ignition target): large RTI growth reduction Atzeni, Schiavi, Bellei 2007, confirmed by Olazabal et al (2011), and Atzeni et al (2011) adiabat shaping RX2 technique (Anderson & Betti, 2004) 99

100 Ablative stabilisation also affects deceleration-phase Rayleigh-Taylor instability in ICF, dense shell ablated by heat flux and fusion α-particles from the hot spot (Guskov and Rozanov 1976, Atzeni and Caruso 1981; 1984) Lobatchev and Betti [PRL, 85 (2000)]: ablation stabilizes dp-rti, just in the same way as at a radiation/laser-driven front Atzeni, Schiavi, Temporal, PPCF

101 Experiment on single mode RTI of radiation driven foil (Lindl et al, 2004) 101

102 RTI in ICF: instability at ablation front & instability at stagnation (Lindl et al, 2004) perturbation fed from outer to inner surface of the shell 102

103 Bibliography S. Atzeni and J. Meyer-ter-Vehn, The Physics of Inertial Fusion, Oxford University Press, Oxford (2004, 2009) J. D. Lindl, Inertial Confinement Fusion, Springer, New York (1998) J. D. Lindl et al., The Physics Basis for Ignition using Indirect Drive on the NIF, Phys. Plasmas 11, (2004) W. L. Kruer, The Physics of Laser Plasma Interactions, Westwood Press (2003) NIF experiments; status and perspective of research: see next page A short perspective: S. Atzeni, EPL 109 (2015) lectures on advanced ignition schemes: S. Atzeni: Inertial Fusion with advanced ignition schemes: Fast ignition and shock ignition, in Laser Plasma Interactions and Applications, (P. McKenna et al., Eds.), Springer (2013) on shock ignition: S. Atzeni et al., Nucl. Fusion 54, (2014); D. Batani et al., Nucl. Fusion 54, (2014);

104 Bibliography status of research [Nature Physics 12 (May 2016)]