The principles of (laser-driven) inertial confinement fusion Stefano Atzeni Dipartimento di Scienze di Base e Applicate per l Ingegneria (SBAI) Università di Roma La Sapienza and CNISM, Italy Three lectures at the International School of Quantum Electronics 54 th Course: Atoms and Plasmas in Super-Intense Laser Fields Erice, Italy, 21 31 July 2013 stefano.atzeni@uniroma1.it! http://gaps.ing2.uniroma1.it/atzeni! Outline! Lecture I : Inertial confinement fusion (ICF) preview!! controlled nuclear fusion and ICF!! essential ingredients of ICF!! ICF by laser-driven spherical implosion:!! illustration by simulation!! parameter estimate, issue identification!! ICF schemes (again, a preview)! Lecture II: The issues for ICF feasibility!! drive efficiency!! compression efficiency!! implosion symmetry!! Rayleigh-Taylor instability! Lecture III: Indirect-drive; alternative ignition schemes!! alternative compression scheme: indirect-drive!! advanced igntion schemes: fast ignition & shock ignition! 2 Literature!!""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, 339-491 (2004)!! "W. L. Kruer, The Physics of Laser Plasma Interactions, Westwood Press (2003)!! plan of NIF experiments: series on articles in Phys. Plasmas 18 (2011): art. 050901-3; # status of NIF experiments: D. G. Hicks et al., Phys. Plasmas 19, 122702 (2012)!! 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) 243-277.!! on fast ignition: special issue, Fusion Sci. Technol. 46 (3) 2006 (M. E. Campbell et al., eds.)!!"on shock ignition:# "R. Betti et al., Phys. Rev. Lett. 98, 155001 (2007); Ribeyre et al., Plasma Phys. Controll.! "Fusion 51, 015013 (2009); S. Atzeni et al., Plasma Phys. Controll. Fusion 53, 035010 (2011);# S. Atzeni et al., New J. Phys. 15, 045004 (2013); K. S. Anderson et al., Phys. Plasmas 20, # ""056312 (2013)# Thanks to! Acknowledgments!! A. Schiavi and A. Marocchino! Università di Roma La Sapienza and CNISM!! G. Schurtz, X. Ribeyre (CELIA, Un. Bordeaux 1)!! S. Haan (LLNL)!! HiPER project!! HiPER Work Package 9!
Summary of lecture I:! Inertial confinement fusion preview! a few fusion reactions!! Fusion reactions for energy production! the easiest!! ICF principles and basic requirements!! ICF by spherical implosion illustrated by simulations and movies!! Back-of-the envelope parameter estimates!! Issue preview:!! drive efficiency!! compression efficiency!! implosion symmetry!! implosion stability!! ICF schemes: many options (a preview)! 5 deuterium cycle! a dream! D + 3 He -->! (3.67 MeV) + p (14.7 MeV)! Fuel for controlled fusion: deuterium-tritium mixture! Why fusion energy research! D + T =>! + n + 17.6 MeV! has by far the largest cross-section (") and reactivity (<"v>)!! Primary fuel (deuterium and litium, see next vg) practically inexhaustible, well distributed on earth, at low cost!! very high specific yield: 341 TJ/kg = 8000 tep/kg!! intrinsic safety # (no criticality, modest reactor radioactive inventory)!! low environmental impact# (no greenhouse gases; much less long-lived radioactive wastes than fission)!! modest proliferation issues # (neutrons, but not fissile materials)#
Deuterium and lithium raw materials for DT fusion energy! (D + T -->! + n + 17.6 MeV)!! Deuterium from water: 37 g of D per 1000 kg of water; # cost (2009): 4000 $/kg!! Tritium bred from Lithium by DT fusion neutrons;!!lithium reserves: 12 Mt in the earth crust; 10 11 t in the oceans# (present production 40 kt/year)!!! However, 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 #, 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! Even for deuterium-tritium! the temperature must exceed 5 kev! D + T =>! + n + 17.6 MeV! has by far the largest reactivity! at 4.2 kev fusion alpha particle power! exceeds bremsstrahlung power! Confinement. An option:! 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! (mass) confinement time # = 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)! 12
!R: ICF confinement parameter! $: burn efficiency!! ICF is pulsed.!! The fuel must remain confined for a time longer than the burn time! 1! reaction time: "! reaz #!, n =!/m i : ion number density! n < $v >!!!!!!: mass density!! confinement time:!! " conf! > " reaz! ==>!! #R $ c sm i < %v >!!!!!at T = 20 40 kev, rhs depends weakly on T!! = =>!R > 1.2 g/cm 2!! It can be shown that the fraction of burned fuel is, approximately,!!!!$ =!R / (!R + 7 g/cm 2 ), and in practice the confinement requirement is! " " " "!R > (2 3) g/cm 2!!!!!!! " conf # R c s, c s = 2.7 $10 7 T (kev) cm/s (sound speed) 13 ICF performance is measured by the GAIN:! target gain, fuel gain!! 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# G = Fusion energy Energy delivered by the driver to the target = E Fus E driver and the fuel energy gain G F! G F = Fusion energy Energy delivered to the fuel = E Fus E F = E Fus "E driver where % is the energy coupling efficiency, typically of 5-10%! 14 Reactor cycle: gain, rep-rate,...! Reactor cycle: numbers for a 1 GW reactor! Possible set of parameters for a 1000 MW reactor! Laser repetition rate & driver!! Close the cycle: G % d = 1/(M% th f)! Power production: P grid = & driver E grid = & driver [(1-f) % th GM E d ]! target cost < 20% COE; (COE: cost of energy) 15! Closing the cycle: G % d = 10; e.g. G = 100; % d = 10%!! Power production: E d = 2.5 MJ; & driver = 10 Hz!! 1 target electrical energy to grid = 100 MJ = 27.8 kwh;! if COE = 0.05 %/kwh, cost of target < 0.278 "! (burnt DT in 1 target: 0.733 mg; DT in 1 target & 2.5 mg)! 16
Fom the reactor cycle: high gain! required to overcome cycle inefficiencies! G % D > 10! The essential physical ingredients of ICF:! Compression! Hot spot ignition! (homogeneous sphere of DT, radius R, density!)! and, typically,! G > 100! G F > 1000!! COMPRESSION:! ' $ > 30% ==>!R > 3 g/cm 2! mass m = (4(/3)!R 3 300 < few mg ==> "! >!! m(mg) g/cm 3! HOT SPOT IGNITION! do not heat the whole fuel to 5 kev;! heat to 5 10 kev the smallest amount of fuel capable of self heating and triggering a burn wave!!!!!!!!! 17 18 Why hot spot ignition! uniform heating of the whole fuel = > unacceptably low fuel gain! Ignition: once the central fuel is heated and compressed,! competition! between heating (alpha-particles)! and cooling (electrons, bremsstrahlung, mechanical work)! Indeed:!! 1 DT reaction => 17 600 kev!! heating deuteron, triton and their electrons to 5 kev: (3/2)*5*4 = 30 kev! = => # G F = 17600 " 30 = 580 " <<1000 Hot spot ignition to save energy and allow for the needed high gain! Good estimates obtained! from simple models! assuming model configurations! as in this figure! a) standard, isobaric! b) isochoric (applies to fast ignitor,! see lecture III)! Ignition conditions can be written in the! form of Lawson-conditions (T vs )R),! see next viewgraph!
Hot spot ignition condition:! Lawson-like and n#t (or )RT) criteria! the standard approach: central ignition! imploding fuel kinetic energy converted into internal energy! and concentrated in the centre of the fuel! implosion velocity for ignition:! u imp > 250 400 km/s! depending of the fuel mass:! u imp * m -1/8! (see, e.g., S. Atzeni and J. Meyer-ter-Vehn, The Physics of Inertial Fusion, Oxford University Press, 2004.)! 22 Next viewgraphs (and movies), from 1-D and 2-D simulations (DUED code)! Hollow shell target,! irradiated by a large number of overlapping beams! Simulation of a standard direct-drive target! Irradiated by a laser pulse, with wavelength of 0.25 µm! total energy of 1.6 MJ! Target (hollow shell) Fuel mass: few mg Radius: 1 3 mm Fuel radius / thickness = 10 Achieves energy gain about 60! It can be improved to achieve gain higher than 100! Ref: S. Atzeni and J. Meyer-ter-Vehn:! The Physics of Inertial Fusion, Oxford (2004, 2009)! 23 Laser driver pulse Energy: 1 5 MJ Duration: 10 20 ns Peak power: 300 500 TW Peak intensity: 10 15 W/cm 2 Wavelength: (1/4) (1/3) µm Compressed fuel Density: 200 1000 g/cm 3 Low average entropy, but hot-spot with T = 10 kev 24
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 )! 10-4! 10-1! 10 2! temperature (K)! 10 2! 10 5! 10 8! Zoom (in space and time):! final compression, ignition, burn and explosion! Density! temperature! 3 mm! 0.15 mm! 3 mm! S. Atzeni, 1992! simulated interval = 25 ns! 25 S. Atzeni, 1992! 0,15 mm! simulated time = 0.5 ns! 26 Rayleigh-Taylor instability hinders hot spot formation and ignition! (multimode perturbation with rms amplitude at the end of the coasting stage = 1.5 µm)! Text! Ion temperature (ev) map evolution! S. Atzeni and A. Schiavi, 2004! Laser power vs time! 1-D! Flow chart! 27
Shocks driven by laser absorption! ==> shell inward acceleration (implosion) = rocket! Laser absorption ==>! ablation! high temperature plasma! very high pressure! (next lecture)! corona expands,! shocks launched in the shell! The ablative pressure! drives the implosion! of the shell! At stagnation substantial! fuel compression and! heating occur (see curves 5)! 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)!
Text! Back-of-the envelope estimate of target parameters!! specific energy = > implosion velocity! fusion burn wave! propagating to the! whole fuel in less! than 100 ps!! 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 /+R 0 ):! The larger the aspect ratio the lower power and intensity,! but more critical target stability and symmetry (next lectures)! Specific internal energy (compression* and thermal) at ignition = specific kinetic energy of the imploding fuel = u i2 /2! => implosion velocity u imp = 300-350 km/s! Back-of-the-envelope estimates of target parameters! 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)(4(/3) R 0 3#!<p> & (12/7) ) DT u imp 2 (+R 0 /R 0 ) (**)! Peak pressure & 2.5 <p> (see next lecture)!,! for R 0 /+R 0 = 10, peak pressure = 80-100 Mbar! Pressure generation and coupling efficiency: next lecture# Optimal use of coupled energy to compress: next lecture#!!) ) DT : density of solid DT (need for solid => next lecture)! *) Partial degeneracy important!
time! =======>! Implosion concentrates energy in space, multiplies pressure,! but! four key issues! 1.! couple efficiently driver energy to the target, to achieve adequate imposion velocity! 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)! implosion symmetry:! long scale shape of compressed fuel depend! on driving pressure non uniformity! "R R ="u imp = "p u imp p # 2 "I 3 I we want hot spot relative deformation -R h /R h << 1! but R h is typically 1/30 of the initial radius R 0! ==> -I/I << 1/20; ==> we request -I/I < 1%! 37 (the larger the ignition margin, the larger tolerable -I/I (eg, Atzeni, Eurphys. Lett. 1990)! Rayleigh-Taylor instability# unavoidable in inertial fusion A variety of inertial fusion schemes! have been proposed!! drivers:! o! lasers! o! ion beams! o! pulsed power sources!! compression-driving irradiation schemes:! o! direct! o! indirect! deceleration-phase instability at the hot spot boundary! (2D simulation)! 39 Atzeni & Schiavi, PPCF 2004!! ignition schemes:! o! conventional central ignition! o! fast ignition! o! shock ignition! 40
direct drive and indirect drive! Fast ignition! the hot spot is generated by an ultra-intense laser pulse! (see lecture III)! In indirect drive, the fuel containing capsule is irradiated by thermal X-rays (200-300 ev), generated and confined in a cavity (a hohlraum).! Indirect drive: see lecture III! 41! 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)! 42 Shock ignition (*)# the hot spot is generated by # a properly timed, laser-driven strong shock# (see lecture III)! --- standard implosion (moderate velocity)! a)! b)! c)! d)! pulse generates imploding shock! imploding shock amplified as it converges! imploding shock pregresses, while shock bounces from center! the two shocks collide, and launch new shocks; the imploding shock heats the hot spot! (*) R. Betti et al., Phys. Rev. Lett., 98, 155001 (2007).! Fast ignition vs shock ignition pulses! intense laser pulse towards the end of the imposion to generate a strong converging shock which increases hot spot pressure! pulse for the HiPER target (Ribeyre et al., PPCF 2009, SA et al., PPCF 2011)!
ICF involves a variety of physics processes! and of space- and time-scales! Appendices to Lecture I! 1)! Space- and time scales and modelling needs!! 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! 2)! Large lasers for fusion!! Mass density: 10-6 "10 3 g/cm 3!! Temperature: 10 3 x 10 9 K! Time scales:!! Implosion: few 30 ns!! Ignition: few 100 ps!! Fluid instabilities: 0.1 1 ns!! Plasma instabilities: < 1 ps to ns! Space scales:!! Target size: few mm!! Compressed fuel: 0.1 mm!! Density scale-lengths: down to 1 µm!! Fluid modes: down to µm! 46! Plasma instabillities: Debye length, skin depth,..! ICF involves extreme values of! temperature, density and pressure! ICF simulation codes inlcude a lot of physics! and must resolve small scales! 47! 48
The largest 1980 s laser fusion facility: NOVA! Titolo! NIF: a 1.8 MJ laser for fusion ignition demonstration! (Lawrence Livermore National Laboratory)! pulses with up to 50 kj! in a few ns! (from LLNL website) 49! 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 2009! 51 50
Summary of lecture II:! The Four Issues for ICF!! gain formula => issues!! issue 1: generate pressure and accelerate efficiently!! collisional laser absorption & absorption efficiency!! ablation pressure!! ablative drive: rocket model (efficiency, in-flight-tickness)!! issue 2: compress efficiently => keep entropy low!! issue 3: drive a symmetric implosion!! issue 4: control Rayleigh-Taylor instability! 53 Issues 1 and 2 apparent from a simple gain factorisation! E G = Fus = m DTQ DT " m = # E driver E a # DT Q DT " h DT E DT m # DT : DT fuel mass! Q DT = 340 MJ/mg: DT yield! $!=!R / (!R + 7 g/cm 2 ): burn fraction! E DT = E c + E hs : DT fuel energy = cold dense fuel energy + hot spot energy! %! = % a % h : coupling efficiency! % a : laser absorption efficiency! % h : hydrodynamic efficiency (energy to fuel/absorbed energy)! E c &!m DT * degenerate matter energy =!m DT C d ) 2/3 ; C d = 2.3 10 12 (erg/g)(cm 3 /g) 2/3!!: isentrope parameter of imploded fuel! = = >! G = " a " h # $R /($R + 7 g cm 2 ) % $ 2 / 3 1+ E ( hs ' * & ) E c Q DT C d E hs /E c from ignition model (see, eg, ch. 5 of book by SA & Meyer-ter-Vehn)! 54 An operating window (large enough gain, not too large target)! identified from a simple gain model (previous page + ignition model))! 1st issue: coupling laser light! -! use short laser wavelength (e.g.. = 0.35 µm)! -! limit intensity I to 10 15 W/cm 2!!=>!use hollow shell target, instead of sphere! Required:! low preheating! (! < 3)! specific energy:! 50 kj/mg! => u imp = 320 km/s! good assorption in the collisional regime, at short wavelength p * (I/.) 2/3 @ I = 10 15 Wcm 2. = 0.35 µm = => pressure p = 80 Mbar Garban-Labaune et al, PRL (1982) 55
Laser absorption ==>! ablation! high temperature plasma! very high pressure! corona expands,! shocks launched in the shell! Collisional and non collisional & relativistic regimes of! Laser - plasma interaction!
In the collisional regime, at intensity 10 14 10 15 W/cm 2, (#) scaling from simple (rough) model (eg., Manheimer et al., Phys Fluids 1982; Lindl, Phys. Plasmas 1995)! Ablation pressure! Assume light absorbed at critical density! Assume critical density = sonic point! Shocks driven by laser absorption! ==> shell inward acceleration (implosion) = rocket! I = p u ex & p u sound & ) c v th 2 v th *. -2 v th 3 (u ex : expansion velocity)! p a & ) c v 2 th * (I/.) 2/3 ; for DT ablator p a = 38 (I 15 /. µ ) 2/3 Mbar (*)! [I 15 : I/10 15 W/cm 2 ;. µ : laser wavelength in µm]! = => use sub-micron light, intensity about 10 15 W/cm 2! Ablation rate (mass per unit time per unit surface)! dµ/dt & ) c u ex & ) c v th * (I/. 4 ) 1/3! for plastic: dµ/dt & 3 x 10 5 (I 15 /. µ4 ) 1/3 g/(s cm 2 )! (*) coefficients for plastic: see Lindl, Phys. Plasmas 1995! (#) at lower intensity: Caruso & Gratton Plasma Phys. 1968; Atzeni et al, New J. Phys. 2013! A simple spherical rocket model (*)! dm dµ = " 4#R 2 dt dt M du dt = "4#R 2 p a = = >! u imp = p a dµ / dt ln M imp M 0 = u ex ln 1 x but shell in-flight-aspect ratio grows with velocity! (the faster the implosion, the thinner the shell)! = => problem with RTI! A very simple estimate (for more accurate results, see cited refs by Lindl and SA-MtV)! x = M imp /M 0 = fraction of imploding mass (typically 50% in direct-drive laser fusion)! For DT, u ex = 1200 I 15 1/3. µ 2/3 "km/s = => required 350 km/s can be attained! Hydrodynamic efficiency! ==> u imp = u ex ln 1 x " h = (1/ 2)M 2 impu imp = 1 ( dµ / dt )u ex E driver " a 2 I " a ( ln x ) 2 x = 0.24( ln x ) 2 x 1# x 1# x (above front coefficient for DT) typically, x = 0.5, and % h = 5 10%! (*) Lindl, Phys. Plasmas 1995; SA et al., Phys. Plasmas 2007; Betti & Zhou, Phys. Plasmas 2005!
Energy of compressed DT:! E c &! m DT C d ) 2/3 ; # C d = 2.3 10 12 (erg/g)(cm 3 /g) 2/3! the isentrope parameter! of imploded fuel must be kept small (close to 1)! 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! 3rd issue: symmetry:! irradiate as uniformly as possible! long scale shape of compressed fuel depends! on driving pressure non uniformity! "R R ="u imp = "p u imp p # 2 "I 3 I 3rd issue: symmetry:! operate with safety margins! we want hot spot relative deformation -R h /R h << 1! but R h is typically 1/30 of the initial radius R 0! ==> -I/I << 1/20; ==> we request -I/I < 1%! 67 (the larger the ignition margin, the larger tolerable -I/I (eg, Atzeni, Europhys. Lett. 1990)! 68
time! =======>! 3rd issue: symmetry! another aspect: accurate target positioning required! 3rd issue: symmetry:! operate with safety margins! Shock-ignition: sensitive to mispositioning! (S. Atzeni, Europhys. Lett. 1990)! 69 S. Atzeni, A. Schiavi, A. Marocchino,! Plasma Phys. Controll. Fusion 2011! 10 µm displacement! Gain = 95% of 1D gain! 20 µm displacement! 70 Gain = 1% of 1D gain! 4th issue: Rayleigh-Taylor instability# unavoidable in inertial fusion 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! deceleration-phase instability at the hot spot boundary! (2D simulation)! 71! Atzeni & Schiavi, PPCF 2004! 72
73 Rayleigh instability, single mode and multimode, nonlinear evolution! 74 RTI in ICF:! instability at ablation front & instability at stagnation! (Lindl et al, 2004) perturbation fed from outer to inner surface of the shell 75 76
Experiment on single mode RTI of radiation driven foil! (Lindl et al, 2004)! Inner surface RTI in ICF! 77 78 (Atzeni & Schiavi, PPCF 2004)! RTI limits the size of the hot spot! Below: density maps at the same time (290 ps) for cases with different perturbation amplitude:! The size of the hot spot [see the 10 kev (red) and 5 kev (orange) contours] is reduced by the penetration of the RTI spikes.! 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! S. Atzeni and A. Schiavi, 2004! 79 (Atzeni & Schiavi, PPCF 2004)! 80
A too large initial corrugation (rms amplitude 6 µm),! amplified by RTI, makes hot spot formation impossible! Ion temperature (ev) map evolution! S. Atzeni and A. Schiavi, 2004! 81 animation by A. Schiavi, 2009! 82 As the amplitude of the perturbation (at the end of the coasting stage) increases!! Gain decreases (same trends for different spectra)!! Ignition is delayed! Classical Rayleigh instability of superposed fluids Linear theory (see Appendix A):! Sinusoidal perturbations of the interface between incompressible, ideal fluids, with wavelength. (i.e. wave number k = 2 (/.) ' and small initial amplitude A 0, ' grow exponentially in time! A = A 0 exp(/t)! with growth rate! " = " cl = Agk A = " 2 # " 1, Atwood number " 2 + " 1 83 84
If RTI growth at ablation front were classical,! ICF would not be feasible! Linear growth a perturbation of initial amplitude 0 0 and wavelength.:! ' t * "(#,t ) = " 0 exp ) & $(#, t %) d t %, = " 0 exp[ -(#,t )] ( 0 + Assume!!!" = Aak # 2$a / % ( 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 +R:! # = $+R (for shorter wavelengths linear growth saturation)! = => for the worst mode, at the end of acceleration stage! 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)! " # 2R 0 $R = 2R 0 R R $R >11, i.e. % > 60 000 % 0 clearly unacceptable! (here we have assumed R = R 0 /2, and R/+R > 30 (see Lecture I)! 85 86 More on RTI in Appendix A.! Here and in the Appendix A, linear model for RTI,! but a number of detailed studies include!! linear growth saturation!! second order effects!! mode coupling!! feed through!! 3 D effects!! turbulent mixing!! interplay between Richtmyer-Meshkov instability (occurring when a shock crosses an interface) and RTI!...! 87 Conclusion on the 4th issue:! limit Rayleigh-Taylor instability! RTI unavoidable, but growth can be limited! To reduce effects!! limit seeds:!! target defects,!! short-scale irradiation non-uniformity!! choose less unstable regime (increase ablation velocity)!! limit implosion velocity (trade-off with ignition energy)! 88
Rayleigh instability of superposed fluids growth rate derivation from a simple energy principle! (H. J. Kull, Laser Part. Beams 1986)! Appendix to Lecture II:! more on linear RTI results! 89 90 = = > the classical RTI growth rate (Lord Rayleigh, 1883)! " = " cl = Agk A = " 2 # " 1 " 2 + " 1, Atwood number 91 92
If RTI growth at ablation front were classical,! ICF would not be feasible! Linear growth a perturbation of initial amplitude 0 0 and wavelength.:! ' t * "(#,t ) = " 0 exp ) & $(#, t %) d t %, = " 0 exp[ -(#,t )] ( 0 + Assume!!!" = Aak # 2$a / % ( 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 +R:! # = $+R (for shorter wavelengths linear growth saturation)! = => for the worst mode, at the end of acceleration stage! RTI, classical vs ICF! ablation reduces growth, stabilises short wavelengths! classical RTI:! uniform density, sharp interface, no fluxes, incompressible fluids! in ICF, ablative RTI:! continous density; mass, momentum & energy fluxes (ablation),! [+ compressible fluids, + spherical geometry +...]! ablative RTI:! - growth rate reduced! -!short wavelengths stable! " # 2R 0 $R = 2R 0 R R $R >11, i.e. % > 60 000 % 0 clearly unacceptable! (here we have assumed R = R 0 /2, and R/+R > 30 (see Lecture I)! 93 94 RTI, classical vs ICF! ablation reduces growth, stabilises short wavelengths! Ablative stabilisation:! theory, simulations, experiments! 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)! " = # RT ak 1+ kl min $% RT ku a where! RT = 0.9 1 and 1 RT = 1 3 are coefficients depending on laser intensity, light wavelength and material,! dm / dt u a = is the ablation velocity, with! " pa ) pa peak density ahead of the ablation front! (*) For detailed treatment and bibliography see Ch. 8 of Atzeni & Meyer-ter-Vehn, 2004.! 95 Theory vs experiment! (Budil et al. 1996)! Takabe-like formula vs simulation (Tabak et al. 1990)! 96
Ablative RTI allows for significant reduction of! the growth factor 2 ' Ablative RTI allows for significant reduction of! the growth factor 2 ' from ablative RTI linear growth rate and rocket implosion model! (Lindl et al 2004)! 2! for indirect drive! from ablative RTI linear growth rate and rocket implosion model! (Lindl et al 2004)! for direct drive:! " max = 8.5 % u ( imp 2 / 5 I ' * 1/15 3 $10 7 cm/s 15 & ) # if 1.4 reduction with respect to classical case, but still insufficient,! unless in-flight isentrope factor! if is raised to 3 5! Indirect drive:! high implosion velocity: strong stabilisation, 2 acceptable! 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!! 97 98 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)! Ablative stabilisation also affects! deceleration-phase Rayleigh-Taylor instability!! in ICF, dense shell ablated by heat flux and fusion!-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! adiabat shaping RX2 technique! (Anderson & Betti, 2004)! 99 100 Atzeni, Schiavi, Temporal, PPCF 2004!
Summary of lecture III:! Indirect-drive; advanced ignition schemes!! Indirect drive: why & how!! pros & cons!! indirect drive ignition experiments at NIF!! Advanced ignition schemes!! fast ignition!! shock ignition!! Literature! some information on! indirect-drive inertial fusion! and ignition experiments on! the National Ignition Facility! 101 102 direct drive and indirect drive! Why indirect-drive?! In indirect drive, the fuel containing capsule is irradiated by thermal X-rays (200-300 ev), generated and confined in a cavity (a hohlraum).! 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 / = (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)! 103! 104!
about year 2000! ready to test ignition (at the NIF)! (for reviews: Lindl, PoP 1995; Lindl et al, PoP 2004! - understanding and ability to control all four above issues demonstrated# (expts at NOVA, OMEGA)! -! required drive temperature, pressure demonstrated! -! simulations predict experiments (when RTI mix is included)! [still some uncertainties from laser-plasma interactions, RTI mix]! -! diagnostics suitable for nuclear environment, large )R developed! -! design based not only on extrapolation, but also on interpolation# (@low energy: data from lasers; @ large energy: from explosions)! -! cryogenic targets developed! 105 NIF main goal (*) :! demonstrating ignition, propagating burn and gain > 10!!indirect drive!!point design [see S. Haan et al., PoP 12, 056316 (2005); S. Haan et al. PoP 18, 051001 (2011)]! pulse energy: 1.13 MJ! radiation temperature: 285 ev! implosion velocity: 380 km/s! isentrope parameter! = 1.46! yield: 15 MJ! Next: hohlraum, capsule, pulse: design vs four main issues discussed in Lectures I and II (*) " J. D. Lindl and E. I. Moses, Phys. Plasmas 18, 050901 (2011); S. Haan et al., Phys. Plasmas 18, 051001# """ "(2011); Landen O. L. et al., Phys. Plasmas 18, 051002 (2011)! (#) S. Haan et al.,, Phys. Plasmas 12, 056316 (2005); S. Haan et al., Phys. Plasmas 18, 051001 (2011)! 106 National Ignition Facility, NIF! (LLNL, USA)!!laser a vetro:nd, con triplicazione di frequenza!!energia totale per impulso: 1.8 MJ (. = 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!!costo: 4 G$; finanziata dal Defence Program del DoE (ora dalla NNSA del DoE)! NIF hohlraum! coupling & symmetry! symmetry control:!! beam orientation!! beam pointing!! hohlraum aspect ratio!! hohlraum fill! beam coupling: choice of materials! entropy control: cryogenic fuel! courtesy of LLNL!
NIF capsule & pulse! efficiency, entropy control, stability! 3D simulation of a NIF ignition experiment! S. Haan et al., Nucl. Fusion 44, S171 (2004), courtesy of LLNL! S. Haan et al., PoP 12, 056316 (2005)! pulse shaping to:# achieve p > 100 Mbar,# keeping entropy low! Be ablator: efficient absorber! Cu graded doping: to avoid preheat! to decrease instability! 110! ultra-smooth surfaces: to minimize RTI seeds! 3D simulation of a NIF ignition experiment! Reaction chamber, a few diagnostics and a target! S. Haan et al., Nucl. Fusion 44, S171 (2004), courtesy of LLNL! 60 g/cm3 surfaces! 140 ps before ignition 400 g/cm3 surfaces! at ignition 111! 112!
NIF National Ignition Campaign (2010-12)! very large improvement with respect to previous experiments, but! ignition not yet achieved! O. L. Landen et al.,! Plasma Phys. Controll. Fusion 54, 124026 (2012)! NIF National Ignition Campaign (2010-12)! data up to July 2012;! some more improvement! since then!! implosion velocity smaller than expected (hohlraum coupling?)!! pressure smaller than expected (asymmetry?)! 113 D. Hicks et al., Phys. Plasmas 19, 122702 (2012);! N. B. Meezan et al., Phys. Plasmas 20, 056311 (2013);! O. L. Landen et al., Plasma Phys. Controll. Fusion 54, 124026 (2012)! 114 NIF National Ignition Campaign (2010-12)! high resolution radiography, showing implosion, stagnation, bounce! [D. Hicks et al., Phys. Plasmas 19, 122702 (2012)]! Advanced ignition schemes! 115 116
Higher gain (than expected on NIF)?! Ignition at smaller laser energy?! Simpler targets?! Advanced ignition schemes:! separate compression and hot spot creation! NIF-LMJ designed 15 years ago; since then!! laser progress:! o! smooth beams! o! ultraintense lasers! o! pulse shaping!! new ignition schemes (fast ignition, shock ignition)!! improved understanding of RTI! ==>!! New options for direct-drive (already discussed here)! and/or!! Alternate approaches to ignition! 117 First compress, then heat! m G = DT "Q $ 2 DT u = "Q i DT + E ' d-ig & ) E d-compr + E d-ig % 2# a # h m DT ( Lower implosion velocity now required (compression only)! Higher gain can be achieved if ignition driver energy! (much) smaller than compression driver energy! *1 118 Advanced ignition (fast & shock ign.)! allow for high gain at MJ laser energy! Ignition: once the central fuel is heated and compressed,! competition! between heating (alpha-particles)! and cooling (electrons, bremsstrahlung, mechanical work)! improved hohlraum coupling efficiency With current NIF hohlraum coupling efficiency Good estimates obtained! from simple models! assuming model configurations! as in this figure! a) standard, isobaric! b) isochoric (applies to fast ignitor,)! Ignition conditions can be written in the! form of Lawson-conditions (T vs )R),! see next viewgraph! 119 120
Accessing the ignition domain! The pros of advanced ignition schemes! Standard central ignition! (a single step process)! Vs! Advanced ignition! (two-step processes):! Fast ignition! Require lower implosion velocity ="=>" Less susceptible to RTI! Fast ignition does not require a central hot spot! Shock ignition robust to stagnation phase RTI (see later)! Allow for direct-drive, with proper ablator design and pulse shaping! Allow for higher gain! lower velocity = lower specific energy,!!! direct-drive: efficient energy coupling)! Shock ignition! 121 122 Fast ignition driven of a precompressed fuel assembly,! by a 27 kj, 20 ps, 20 micron radius pulse! of particles with range of 1.5 g/cm 2! M. Tabak, S. Atzeni! No central hot spot! ==> relaxed implosion symmetry # and stability requirements! Lower density! ==> relaxed stability requirements! ==> higher energy gain! 123 124
Fuel burn and disassembling! first estimate of beam parameters (not so bad)! S. Atzeni, C. Bellei, A. Schiavi, 2006! we have to create a hot spot with [SA, Jpn. J. Appl. Phys. (1995)]!! <)r> h = 0.5 g/cm 2!! T h = 12 kev! delivering a pulsed beam!! onto a spot of radius r b = <)r> h / ),!! in a time t shorter than the hot spot confinement time r b /c(t h ),! 125!hence:! E ig * m h T h * (<)r> h ) 3 T h / ) 2 * ) -2! the higher the density,! W ig * E ig /t * ) -1! I ig * W/r 2 the smaller the energy,! b * )'!but! 126 the higher the intensity! Fast ignition requires an ultra-intense! (& efficiently coupled) driver [see also App. B]! optimal parameters for density ) = 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 10 19 W/cm 2! CPA lasers could meet such requirements! 127 SA, Phys. Plasmas 6, 3316 (1999)! I! Standard fast ignition:! how is energy transported to the fuel?! Nonlinear, relativistic plasma physics involved! we have to rely on large extrapolations! Ultraintense laser ==> hot electrons (few MeV) ==> hot-spot creation! interaction # (at critical density)! transport# ( 1 GA current)! deposition# (in compressed plasma)! other issue: matching hot electron range energy with hot spot;! a lot of current debate! 128!
Cone-guiding a possible solution to shorten the path from critical surface to compressed fuel works at small energy (Kodama et al, Nature 2001, 2002)! can be scaled?! pointing?! compatible with strong compression?! materials mixing? 129 FAST IGNITION has! a high gain/high risk profile!! Advantages!! Relatively immune to RTI!! Achievable at low implosion velocity!! Ignition energy independent of target scale! = = > Very high gains achievable!! Downsides!! Specific fast ignition physics hardly scalable!! Cone in a shell target!! No existing facility for demonstration!! No existing integrated modelling (despite great progress, see later)! = = > Target and laser # Specs difficult to establish! 130 next:! shock ignition! Laser pulse: Shock ignition vs fast ignition Laser wavelength = 0.35 µm intense laser pulse towards the end of the imposion generates a strong converging shock! 131 HiPER Target: S. Atzeni, A. Schiavi and C. Bellei, PoP, 15, 14052702 (2007) Pulses: X. Ribeyre et al, PPCF 51, 015013 (2009); S. Atzeni, A. Schiavi, A. Marocchino, PPCF 53, 035010 (2011) 132
The ICF hot spot ignition condition is essentially! a condition on the hot spot pressure! S. Atzeni and J. Meyer-er-Vehn,! The Physics of Inertial Fusion, Oxford (2004)! Pressure at stagnation is! 3! a strong function of the implosion velocity ( p ~ uimp )! fuel at ignition! )c/)h = 5-7! pressure for ignition:! p (Gbar) > 500 " Rh % $ ' # 30 µm &! lower implosion velocity = > lower pressure but stagnation pressure can be amplified by a properly tuned shock a)! pulse generates imploding shock! b)! imploding shock amplified as it converges! 133 134! Shock-ignition (HiPER target)! Target: HiPER baseline target Laser wavelength = 0.35 µm! Compression energy: 180 kj! Focal spot: 0.64 mm (compression)! 0.4 mm (SI)! c)! imploding shock pregresses, while shock bounces from center! d)! the two shocks collide, and launch new shocks; the imploding shock heats the hot spot! Target: S. Atzeni, A. Schiavi and C. Bellei, PoP, 15, 14052702 (2007) 136 Pulses: X. Ribeyre et al, PPCF 51, 015013 (2009); + SA et al (2011,12,13)
Shock ignition: reduced hot spot-rti growth Shock ignition can be tested At moderate energy levels HiPER target Compression pulse! Energy! Flat-top power! Focal spot width wc Ignition pulse! Energy! Power! Focal spot width ws! Synchronization 180 kj 42 TW 0.65 mm! 80 kj! 150 TW 0.4 mm 120 ps (@ 170 TW) 250 ps (@ 270 TW) CELIA-NIF target 250 kj 80 TW 0.68 mm No SI spike with the CELIA radiation spectrum! 70 kj! 150 TW 0.345 mm Shock ignition Fusion yield 1D Gain " 24 MJ! 80 " 33 MJ! 100 Convergence ratio 35 42 30 42 0.1 0.25 mg/cm3 0.3-0.1 mg/cm3 137 vapor density S. Atzeni, A. Schiavi, A. Marocchino, PPCF 2011.; see also Ribeyre et al. PPCF 2009 We are studying shock ignition scenarii on LMJ & NIF using the indirect drive laser ports and focusing hardware : Polar Drive is required Shock-ignition! tolerates very large spike asymmetry! (warning: artifact of flux-limited SH elec. conduction?)! Beam position (Aitoff)! Reference irradiation pattern 10.4 µm displacement Symmetric ignition spike 138 33.2! 49.0! 59.5! Reference irradiation pattern 10.4 µm displacement ignition spike with l = 2, C2 = 80% asymmetry West! South! Est! North! 1 LMJ Quad formed from 4 40x40 (cm) beams! 78.0! 120.5! 131.0! 146.8! May be split! and repointed on! a sphere for! optimal illumination! 40 quads pattern : - uses quad splitting, defocusing and repointing (Polar Drive)!!80 beams for compression + spike (PDD) 3.8 kj, 1.5 TW/beam! 80 beams for spike only (DD, tight focus) 0.75 kj, 1.5 TW/beam! 139 140 courtesy of G. Schurtz, CELIA, U. Bordeaux-1
Shock ignition physics issues! some conclusions on shock ignition!! Demostrate 300 Mbar pressure and good absorption efficiency!! How does RTI at stagnation interact with the shock?!! What are the symmetry requirements for the spike?!! Intensities in spike are high: what about parametric instabilities?!! electron transport in shock ignition regime: probably non local, magnetized!! Validating polar direct drive designs!! implosion less critical than standard central ignition!! robust & classical (hydro) ignition process!! does not require two different lasers!! simple targets!! issue: laser-plasma instabilities during ignition spike!! principle tested at OMEGA (Theobald et al, 2008)!! amenable to scaled experiments (e.g. at OMEGA)!! can be tested at full scale at NIF, LMJ!! realistic target specifications and robustness studies in progress! 141 142 Towards the reactor?! A very long path! After ignition demonstration, we have to increase!! driver efficiency x 10!! driver rep rate x 10000!! target gain x 5 10! However, potential solutions exists and are being studied! (Diode pumped solid-state lasers)! Appendix to Lecture III:! More on beam requirements for fast ignition! 143 144
beam parameters for fast ignition! first estimate (scaling & OK, front factors small)! we have to create a hot spot with [SA, Jpn. J. Appl. Phys. (1995)]!! <)r> h = 0.5 g/cm 2!! T h = 12 kev! delivering a pulsed beam!! onto a spot of radius r b = <)r> h / ),!! in a time t shorter than the hot spot confinement time r b /c(t h ),!!"hence:! E ig * m h T h * (<)r> h ) 3 T h / ) 2 * ) -2! the higher the density,! W ig * E ig /t * ) -1! I ig * W/r 2 the smaller the energy,! b * )'!but! 145 the higher the intensity! (Delivered) beam parameters! from a parametric 2-D model study, assuming! straight propagation, cyl. beam,! constant stopping power! ignition windows (S. A., 1999)! energy - power energy intensity! optimal parameters! (corners of windows)! # " & E ig =18 % ( $ 300 g/cm 3 ' )1.85 kj *1 $ # ' W ig = 0.9 "10 15 & ) W % 300 g/cm 3 ( $ # ' I ig = 7.2 "10 19 & ) % 300 g/cm 3 (! For particle penetration depth $ 1.2 g/cm 2 ; longer range: more energy! 146 0.95 W/cm 2 Fast ignition requires an ultra-intense! (& efficiently coupled) driver! optimal parameters for density ) = 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 10 19 W/cm 2! CPA lasers could meet such requirements! But range and focal spot are not necessarily as desired! # " & E ig (kj) =18 % ( $ 300 g/cm 3 ' )1.85 # " & I ig (W/cm 2 ) = 7.2 *10 19 % ( $ 300 g/cm 3 ' Still not included!! Energy spectrum!! divergence! # R & * max% 1, ( * f (spot radius) $ 1.2 g/cm 2 ' 0.95 SA and M. Tabak, PPCF 2005! M. Tabak et al, FST 2006! # R & * max% 1, ( * g (spot radius) $ 1.2 g/cm 2 ' I! 147 148! SA, Phys. Plasmas 6, 3316 (1999)!
Literature!!""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, 339-491 (2004)!! "W. L. Kruer, The Physics of Laser Plasma Interactions, Westwood Press (2003)!! plan of NIF experiments: series on articles in Phys. Plasmas 18 (2011): art. 050901-3; # status of NIF experiments: D. G. Hicks et al., Phys. Plasmas 19, 122702 (2012)!! 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) 243-277.!! on fast ignition: special issue, Fusion Sci. Technol. 46 (3) 2006 (M. E. Campbell et al., eds.)!!"on shock ignition:# "R. Betti et al., Phys. Rev. Lett. 98, 155001 (2007); Ribeyre et al., Plasma Phys. Controll.! "Fusion 51, 015013 (2009); S. Atzeni et al., Plasma Phys. Controll. Fusion 53, 035010 (2011);# S. Atzeni et al., New J. Phys. 15, 045004 (2013); K. S. Anderson et al., Phys. Plasmas 20, # ""056312 (2013)# 149 The end! 150