Physics of Fast Ignition

Transcription

1 (some aspects of the) Physics of Fast Ignition and target studies for the HiPER project Stefano Atzeni Dipartimento di Energetica, Università di Roma La Sapienza and CNISM,Italy IOP Plasma Physics Group Annual Meeting Institute of Physics, London, 1 4 April 2008

2 Collaborators: - A. Schiavi (Univ. Roma La Sapienza) - C. Bellei (Univ. Roma La Sapienza and Imperial College) + HiPER Target study group: - J. Honrubia (U. P. Madrid), - X. Ribeyre, G. Schurtz, M. Olazabal-Loumé, P. Nicolai (U. Bordeaux), - R. Evans (Imperial College) - J. Davies (IST, Lisbon) Thanks to - R. Betti (U. Rochester) for discussions on target simulations - M. Tabak (Livermore) for discussions on gain models - S. Baton (LULI) for materials on electron generation

3 Summary Inertial confinement fusion central ignition vs fast ignition Fast ignition basic requirements possible schemes issues HiPER The project target studies

4 Inertial confinement fusion (ICF) Fusion reactions from a target containing a few mg of DT fuel compressed to very high density (1000 times solid density) and heated to very high temperature No external confinement => fuel confined by its own inertia (t = R/c s where c s is the sound speed) Pulsed process: for energy production burn targets at 1-10 Hz (Target gain) * (efficiency) %

5 The essential physical ingredients of ICF COMPRESSION, to increase burn during confinement phase density > 200 g/cm 3 confinement: density * radius > 2 g/cm 2 HOT SPOT IGNITION, to use input energy efficiently 10 kev over a small hot spot

6 the standard approach: central ignition imploding fuel kinetic energy converted into internal energy and concentrated in the centre of the fuel

7 Central ignition ICF Pros: Energy concentration in space (from target surface to hot spot) in time (from 10 ns laser pulse to 100 ps hot fuel confinement time) Cons: high implosion velocity ==> Rayleigh-Taylor instability (RTI) at outer surface central hot spot ==> symmetry, inner surface RTI

8 a key issue for central ignition: Rayleigh-Taylor instability time =======> deceleration-phase instability at the hot spot boundary (2D simulation)

9 Rayleigh-Taylor instability hinders hot spot formation and ignition (multimode perturbation with rms amplitude at the end of the coasting stage = 1.5 µm) Ion temperature (ev) map evolution

10 A too large initial corrugation (rms amplitude 6 µm), amplified by RTI, makes hot spot formation impossible Ion temperature (ev) map evolution

11 The NIF & LMJ original approach Risk reduction ==> large driver ==> low gain (*) (*) Presently: also direct-drive seriously considered; room for substantial improvements in indirect drive, too.

12 Alternative ICF scheme - the fast ignitor Scheme: M. Tabak et al., Phys. Plasmas 1, 1626 (1994). Ignition mechanism: S. Atzeni, Jpn. J. Appl. Phys. 34, 1980 (1995) Ignition requirements: S. Atzeni, Phys. Plasmas 6, 3316 (1999); S. Atzeni and M. Tabak, Plasma Phys. Controll. Fusion 47, B769 (2005)

13 No need for central hot spot: Fast ignition insensitive to compressed fuel geometry Movies by S. A. & M.L. Ciampi, 1996 (Pisa Easter Meeting, April 1996) M. Temporal, S. A. & J. Honrubia, PoP 2002,

14 No central hot spot ==> relaxed implosion symmetry and stability requirements Lower density ==> relaxed stability requirements ==> higher energy gain ==> lower laser energy ignition threshold

15 isochoric rather than isobaric ignition configuration: fast ignition allows for - higher gain then central ignition at given driver energy - (much) lower driver energy to achieve a given gain isochoric vs isobaric, ideal (SA, 1995, 1999) Fast ignition vs central ignition

16 The advantages of fast ignition paid by the need for an ultra-intense (& efficiently coupled) driver optimal parameters for density ρ = 300 g/cm 3 delivered energy 18 kj spot radius 20 µm pulse duration 20 ps delivered pulse power 0.9 PW delivered pulse intensity 7.2 x W/cm 2 beam energy delivered to the compressed fuel igniting laser beam energy = " ig

17 Nonlinear, relativistic plasma physics involved Ultraintense laser ==> hot electrons (few MeV) ==> hot-spot creation Hot electron generation efficiency interaction (at critical density) transport ( 1 GA current) deposition (in compressed plasma)????? see later So far, no reliable scalings for hot-e generation and transport ==> We take the coupling efficiency η ig as a parameter (with reference value of 25%)

18 Fast ignition with beam channeling (hole boring) (M. Tabak et al., 1994)

19 Cone-guiding: a possible solution to shorten the path from critical surface to compressed fuel It seems to work! (can be scaled? see Hatchett et al. FST, 2006)

20 laser accelerated protons (instead of hot electrons) as ignitors: Fast ignition by laser accelerated proton beams Petawatt- beams (5ps 6kJ) Conical shaped target Proton beams Hohlraum Target shield Pellet Primary driver Converter Radiation shields (Roth et al, PRL 2001)

21 Beam requirements for Fast Ignition

22 Ignition requirements (delivered energy, power, intensity) crucially depend on fuel density ρ optimal parameters (SA, PoP 1999) E ig =18 # % $ " 300 g/cm 3 & ( ' )1.85 kj beam radius: $ # ' r b " 20 & % 300 g/cm 3 ) ( *0.97 µm $ # ' W ig = 0.9 "10 15 & % 300 g/cm 3 ) ( $ # ' I ig = 7.2 "10 19 & % 300 g/cm 3 ) ( *1 W 0.95 W/cm 2 pulse duration: t " 20 $ & % # 300 g/cm 3 ' ) ( *0.85 ps (for particles with penetration depth 1.2 g/cm 2 )

23 ignition requirements depend on fuel density, and on spot radius and particle penetration depth (R) for non-optimal parameters (Tabak et al. 2005, from SA s D simulations): E ig (kj) =18 # % $ " 300 g/cm 3 & ( ' )1.85 # " & I ig (W/cm 2 ) = 7.2 *10 19 % $ 300 g/cm 3 ( ' # R & * max% 1, $ 1.2 g/cm 2 ( * f (spot radius) ' 0.95 R R # R & * max% 1, $ 1.2 g/cm 2 ( * g(spot radius) ' penetration depth R hot-electrons: depends on hot-e temperature ==> laser I protons: depends on p-temperature & on plasma temperature

24 Hot-electron temperature and range: large uncertainties (thanks to Sophie Baton) where Standard scalings & I$ 2 ) T hot"el # ( ' 1.2 % * 1/2 I = I ig /η ig f R : range multiplier Tabak: f R = 1 [Deutsch et al.: f R = 0.5] MeV R hot"el R # f R 0.6T hot"el g/cm 2

25 η ig = 0.25 ignition laser energy below 100 kj: ρ > 300 g/cm 3 and either range smaller than classical or/and short wavelength ignition laser solid curves: ignition energy at given f R λ dashed: ignition energy assuming no dependence on range, but limitation to beam radius dot-dashed: no dependence on range; no limitation to beam radius But 2ω or 3ω is expensive and transfers risk to the laser builders

26 Fast ignition by laser-produced protons: to keep power at needed level, source must be very close to the compressed fuel velocity dispersion --> power spread for T p = 5 MeV, and source - fuel distance 1 d < 4 mm ignition beam energy grows dramatically with distance source-to-target E ig *! 90 # % $ 0.7 d mm " 100 g/cm 3 & ( ' 1.3 kj S.A., M. Temporal, S. Honrubia, Nuclear Fusion, 2002, L1 For d = 3 mm and ρ = 400 g/cm 3 ; ==> E ig > 35 kj Cone Targets?

27 1993: fast ignition proposal 2001: successful integrated heating experiments at ILE Osaka (few kj compression; 100 s J heating) : Omega EP: 30 kj compression, 2.6 kj heating 2010: FIREX: 10 kj compression, 10 kj heating Next?

28 A new project for fast ignition: HiPER (#) (#) M. Dunne, Nature Phys. 2, 2 (2006); HiPER technical design report:

29 Another big laser for fusion? two very large lasers (NIF, Livermore; LMJ, Bordeaux), designed in the early 1990 s, buing built to achieve ICF ignition. Ignition experiments planned in but: large, too expensive for energy production [NIF: 192 beams, 1.5 MJ pulses; cost > 3 G$] low-gain targets (indirect-drive) funded by defence programmes ==> limited access Can one do better? potentially more efficient scheme: fast ignition ===> HiPER reduced military interest: direct-drive

30 HiPER: High Power Laser for Energy Research goal: demonstrate laser-driven inertial fusion fast ignition tentative main parameters: compression pulse: 250 kj, few ns, λ c = 0.35 µm, 60 beams ignition pulse (CPA): 70 kj, 15 ps, λ ig = 0.53 µm (preferred) scheme: direct-drive compression, with cone-guided ignition beam construction cost: 900 M status: in the ESFRI 2006 Roadmap; Project admitted to negotiation for EU - FP7 funds for Infrastructure Preparatory Phase (a few M )

31 70kJ, 10psec, 1ω, 2ω or 3ω c) a) artist s view kJ, 5nsec, 3ω

32 Target studies for the HiPER project (*) S. Atzeni, A. Schiavi, Università di Roma La Sapienza J. Honrubia, UPM-GIFI Madrid C. Bellei, Imperial College, London X. Ribeyre, G. Schurtz, P. Nicolai and M. Olazabal-Loume, CELIA, Bordeaux R. G. Evans, Imperial College, London and RAL J. R. C. Davies, IST, Lisbon (*) S. Atzeni, A. Schiavi and C. Bellei, Phys. Plasmas, 14, (2007) S. Atzeni et al., Phys. Plasmas, 15, May 2008 issue.

33 (INITIAL) TARGET STUDIES FOR HiPER or What are the requirements for moderate size fast-ignition demonstrator? Can we ignite a target with above assumed HiPER parameters? What else is needed? What assumptions do we have to rely on? What are the critical physics issues? Next: first target overview, then rationale for design

34 reference target concept driven by 130 kj compression laser compression laser pulse wavelength = 0.35 µm focussing optics f/18 energy = 132 kj absorbed energy = 90 kj ref: S. Atzeni, A. Schiavi and C. Bellei, Phys. Plasmas, 15, (2007)

35 1. Laser driven implosion (1-D simulation) absorbed energy = 95 kj imploding mass = 0.29 mg implosion velocity = 2.4 x 10 7 cm/s hydrodynamic efficiency = 10.5% overall coupling eff. = 7.2% in-flight-isentrope (inner surf.) = 1.0 IFAR at (R=0.75R 0 ) = 36 (only one of six mesh point drawn here)

36 2. Assembly with high density (ρ peak = 500 g/cm 3 ) and confinement (ρr peak = 1.58 g/cm 2 ) produced central hole ; density can be increased by high-z doping dense fuel shell

37 The compressed fuel assembly can be produced by a cone-guided target By properly tuning the driving pulse (10% P1 drive asymmetry) same peak density and ρ R as in 1-D simulation, central void expelled (as seen by Hatchett et al., 2001, 2006) (SARA code simulation) J. Honrubia, UPM-Madrid IFSA 2007

38 But POLLUX simulations show significant shear => material mixing? density temperature velocity materials (R. G. Evans, 2007)

39 3. Fast ignition induced by a beam of particles with range = 1.2 g/cm 2, delivering 20 kj, in 16 ps, onto a spot of radius = 20 µm. Fusion yield: 13 MJ.

40 Gain model and first simulations indicate potential for high gain assuming good coupling of igniting beam to the fuel f R λ ig = 0.4 µm

41 The rationale behind the design maximize energy multiplication ( Gain ), while at the same time keeping risks small (?) ==> minimize compression energy (keep entropy low) ignite at minimum energy at the same time make sure RTI growth is small keep LPI small try to leave safety margins S. Atzeni, A. Schiavi and C. Bellei, Phys. Plasmas, 15, (2007)

42 Ignition requirements (density, ρr) and isentrope parameter determine compression energy and implosion velocity From Betti and Zhou (PoP, 2005), for direct-drive targets: " bulk # 0.6" peak # 500 $ if I 15 & ) ( ' 3% cm/s* ( ) 0.13 u imp 0.96 g/cm 3,"R- max # 1.46 $ if 0.55 & laser E c 100 kj. ) ( a+ ' * 0.33 g/cm 2 ρ bulk > 300 g/cm 3 α if 1 ===> u imp > 2 x 10 7 cm/s ρr > 1.2 g/cm 2 compression laser energy 100 kj

43 An integrated model produces our REFERENCE GAIN CURVE: significant gain at laser energy of kj Notice: adiabat shaping to reduce RTI growth second harmonic ignition laser or anomalous stopping 25% ignition beam coupling efficiency assumed

44 3 ω laser needed for compression (if 2 ω > 150 kj required for the ignition beam) 2 ω (λ ig = 0.53 µm) ignition laser required [if 1 ω (λ ig = 1.06 µm): ignition threshold at 400 kj] flat adiabat : ignition threshold at 250 kj (with 200 kj for the ignition beam!)

45 Simulations by CELIA(1) (CHIC code) and UPM (2) (SARA code) confirm basic aspect of design Details differ due to different models & assumptions Same peak ρ, peak <ρr> as in previous study obtained by increasing the total energy to about 180 kj (1) X. Ribeyre et al., IFSA 2007; X. Ribeyre et al., PPCF 2008 (2) J. Honrubia et al., IFSA 2007

46 RTI growth made acceptable by adiabat shaping (Anderson-Betti s (2004) adiabat shaping by relaxation ): Γ reduced by a factor of 1.8 two without compression degradation by integrating Takabe dispersion relation, with 1-D flow data, over entire implosion standard by PERLE perturbation code, planar, over interval of larger acceleration (*) adiabat shaped adiabat shaped (*) X. Ribeyre et al., IFSA 2007, X. Ribeyre et al., PPCF 2008

47 The reference target is easily scaled (mass E c ; length E c 1/3, time E c 1/3, power E c 2/3 ; pulse shape needs minor tuning only) scaling of density and confinement in agreement with Betti-Zhou (2005) red and green curves refer to simulations with different electron conductivity flux-limiter and different bremsshtralung model

48 Hot-electron driven ignition (I) A large set of 2-D model-simulations (DUED code) assuming spherically symmetric initial profiles generated by 1-D IMPLO simulations, at a time close to maximum <ρr> cylindrical beam of igniting particles with assigned range, straight path & uniform stopping power; flat intensity profile in space and time

49 density Reference target, irradiated by a beam of particles with range = 1.2 g/cm 2, focal spot radius = 20 µm, delivering 20 kj, in 16 ps. Fusion yield = 13 MJ. Ion temperature

50 TARGET GAIN - (optimistically) ignition at (90+80) kj - high gain at ( ) kj (critical assumptions: ignition laser coupling & hot-e coupling) Reference target Compression driver energy (kj) Imploded fuel mass (mg) peak density(g/cm 3 ) peak R(g/cm 2 ) Ignition driver energy (kj), assuming ig=0.25 and optimal range, focus, etc Fusion yield(mj) GAIN

51 Ignition is an on/off process: steep energy threshold Particle range must fall in an appropriate window reference target, different ranges ignition energy vs range for the three targets

52 Ignition beam to be synchronized to peak compression within less than 100 ps (50 ps for the small target, 125 ps for the large one)

53 Hot-electron driven ignition (II) Same as in I, but including electron stopping and scattering (3D Monte Carlo) electron energy distribution

54 Coulomb interaction: stopping, straggling, scattering

55 Monocromatic vs Maxwellian, no scattering (analogous to Solodov et al., PoP 2007)

56 Maxwellian, with scattering Diffused heating (the more diffused, the larger d 0 )

57 velocity distribution, scattering distance d 0 between e-source and compressed fuel raise the e-beam ignition energy Optimal <E> = MeV (this demands 2ω or 3ω) (2D DUED simulations for the reference target) (similar results by Solodov et al., PoP 2007)

58 Hot-electron driven ignition (III) simulation with a hybrid code, taking self-generated fields into account Initial configuration Model problem: Gaussian laser pulse generates hot-e at distance d 0 from blob centre, with assigned efficiency η hot-el = 40% Electrons have 1D relativistic Maxwellian spectrum, with average energy as per ponderomotive scaling, and assigned divergence Θ J. Honrubia, UPM-GIFI, Madrid

59 The e-beam energy required for ignition increases with source-blob distance and beam divergence Self-generated fields collimate the beam

60 Conclusions - Key issues for moderate-energy fast ignition demonstration identified; gain curves computed and sensitivity analysed - Ignition and gain with HiPER beams requires: -efficient intense laser-hot electron coupling -efficient hot electron transport -adiabat shaping to reduce RTI growth - Reference design performed, for kj driver energy - Target easily scaled in mass and energy - Sensitivity to range, ignition beam energy, synchronization preliminarly studied - warning: just an initial study: complementary, but non selfconsistent models; hot electron generation and transport in low density plasma non included; cone poorly modeled,...

61 Additional materials

62 Two (main) routes to ignition: merits & issues Hot spot creation Ignition configuration central ignition hydrodynamic isobaric Fast ignition Direct heating isochoric intensity ==========> symmetry <=========== issues: RTinstability intensity

63 Ignition requirements (delivered energy, power, intensity) crucially depend on fuel density ρ from detailed two-dimensional numerical simulations ignition windows (S. A., PoP 1999) energy - power energy - intensity For particles with penetration depth 1.2 g/cm 2

64 Beam filamentation in the low density halo and in the ramp [Honrubia & Meyer-ter-Vehn, Nucl. Fusion 46, L25 (2006)]. Strong ohmic heating by return currents in the halo. Electron temperatures are lower and resistivities higher in the density ramp, leading to a B field of 1 kt and enhanced filament growth. Filaments carry about 10 MA each, which is almost completely compensated by the plasma return current. Heating of the dense core is almost exclusively by Coulomb energy deposition. Self-generated fields are very important for core heating indirectly by beam filamentation and collimation.

65 Ignition simulation d = 100 µm, θ = 22º, E = 2 MeV, e-beam energy = 27 kj 100 density ion temperature radius (µm) z (µm) z (µm)

66 Ignition simulation d = 100 µm, θ = 22º, E = 2 MeV, e-beam energy = 27 kj 100 density ion temperature radius (µm) z (µm) z (µm)

67 Ignition energy can be reduced by placing the proton source very close to the compressed fuel: ==> Conically guided target for proton beam induced fast ignition? crucial issues: implosion symmetry, edge effects, protection of the proton source; proton generation efficiency

68

69 Efficient burn requires ρr 1.2 g/cm 2 (From 2-D simulations of fast-ignited precompressed uniform DT spheres)

70 At 250 kj, gain 80 at A if 40 (IFAR 30) and compression laser intensity 3-5 x W/cm 2 (for f R λ ig = 0.4 µm, and r beam 20 µm) RTI Γ max contours our design point

71 Energy gain ingredients Gain = G = m DT = fuel mass Q DT = 341 MJ/mg Fusion energy Driver(s) energy = m DT Q DT " E d -compression + E d -ignition " = burn fraction E d-ignition = E ig " ig = E d -compression = E c " c = " : isentrope parameter (at ignition) [ ] C d = 0.31 (kj/mg)(g/cm 3 ) #2 / 3 gain at low driver energy: fuel ignition energy coupling efficiency of the ignition driver m DT #C d $ 2 / 3 coupling efficiency of the compression driver free parameter of the model implosion - small ignition driver energy - low in-flight-isentrope - burn propagation (Φ 0.15)

72 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 Compressed fuel Density: g/cm 3 Low average entropy, but hot-spot with T = 10 kev