ICF ignition and the Lawson criterion

Transcription

1 ICF ignition and the Lawson criterion Riccardo Betti Fusion Science Center Laboratory for Laser Energetics, University of Rochester Seminar Massachusetts Institute of Technology, January 0, 010, Cambridge MA

2 Collaborators University of Rochester Laboratory for Laser Energetics K. Anderson P. Chang R. Nora C. Zhou

3 Lasers can compress solid hydrogen through laser-driven ablation Rocket engine effect

4 laser Solid DT laser ICF capsules are mm-size shells with hundreds μm-thick layers of cryogenic solid DT driven to an implosion velocity of hundreds km/s laser laser R inner DT gas laser CH or Be ablator may or may not be present. laser Δ(0) laser Δ ( 0) mm ice laser Target size and initial density solid ρ DT (18 K)=0.5g/cc Rinner( 0) mm The target is driven to an implosion velocity V i of km/s by a laser or other driver 300 Vi 400 km/s

5 After the capsule reaches the maximum implosion velocity, is slowed down by the pressure building up in the center until it stagnates and ignites Laser power Max. power We are interested in the deceleration and stagnation Laser is off Neutron rate Imploding shell acceleration Deceleration time Peak implosion velocity V=V i stagnation

6 The final assembly consists of a hot spot at several kev s surrounded by a cold dense shell 7 Stagnation density and temperature Stagnation density and pressure 1400 T i (kev) T i HOT SPOT DENSE SHELL ρ Density (g/cc) P (Gbar) P HOT SPOT DENSE SHELL ρ Density (g/cc) R (μm) R (μm) Imploding shell Dense shell Stagnating core Hot spot Ignition starts in the hot spot

7 The 3.5 MeV alpha particles ( 4 He) slow down within the hot spot causing further heating and more fusion Reactions triggering the thermonuclear instability. This is hot spot ignition. Dense DT shell D + T α(3.5mev)+n(17.1mev) Δ R HOT SPOT If the hot spot is dense and large enough, the alpha particles deposit their energy in the hot spot. The condition for alpha energy deposition in the hot spot is (ρr) hot-spot >0.g cm -

8 The Lawson criterion for thermonuclear ignition requires that the alpha-particle heating of the hot spot exceeds all the energy losses 3.5MeV α-particle heating rate > energy loss rate ε α 4 n σv V > 3 P τ V Plasma pressure ion particle density Fusion reactivity Energy confinement time P = ( n T + nt ) nt e e i i

9 Fusion reactivity is highest for DT Fusion reaction rate (m 3 /s) 00,000,000 o F Temperature in millions of o F

10 Performance parameters for fusion devices based on thermonuclear ignition The product Pτ: Pτ > 4 T ε σv α The ignition parameter: χ ε σv α Pτ > 4 T 1

11 n The Lawson criterion and the ignition parameter for Magnetic Confinement Fusion (MCF). MCF requires <P>τ > 7 atm-s uniform and T T / V 0 ε σv α χ P τ > 4 T v 1 V P 15 τ >7 atm-s at 9 kev Ignition parameter = Lawson criterion σv T V V m s kev T ( kev )

12 JET (MCF) has achieved <P>τ ~ 1 atm-s and an ignition parameter χ 0.14 in DT discharges with <T> ~ 10 kev JET has achieved <T i > 14 kev, <T e > 7 kev n T i (0)τ m -3 kev s [Keilhacker Nuc. Fus (1999)] <p>τ = <p i +p e > τ 1 atm-s χ ε α 4 P τ V σv V 014. T ~10 kev Not clear how to use this criterion for T e <T i. This value (0.14) is probably an upper bound

13 The Lawson criterion and the ignition parameter for ICF hot-spot ignition P uniform in hot spot ε α σv χ Pτ > 4 T Ignition parameter = Lawson criterion 1 V σv T 10 V 3 1 m s kev 5 P τ >10 atm-s at 14keV T ( kev )

14 ICF implosions cannot achieve ~14keV temperatures through compression alone Imploding shell T ~ V i High T requires high implosion velocity V i High V i requires thin shells Thin shells break up in flight due to hydrodynamic instabilities

15 Stable ICF implosions can achieve average temperatures of ~ 4-5keV through compression. ICF requires Pτ above 0 atm-s ε α σv χ Pτ > 4 T 1 V 4 Pτ > σv εα T T = 5keV 0 atm-s

16 How do we assess the performance of ICF implosions if we can t measure P, τ and χ?

17 Ion temperatures, areal densities and neutron yields are the only parameters of the fuel assembly that can be measured with existing (nuclear) diagnostics Neutron yields and neutron rates Ion Temperature (neutron averaged) Nneutron T i neutron dnneutron dt Total areal density (neutron averaged) ρr neutron 0 ρdr neutron 0 ( ) ρr ρdr ρδ Total ρr Shell ρδ shell stagnation Hot spot shell Δ

18 Areal densities are measured with nuclear diagnostics: secondary proton spectra, downscattered neutrons and others

19 Neutron-time-of-flight detectors are used to measure neutron yields, neutron rates and ion temperatures

20 The energy confinement in ICF

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22 The heat lost by the hot spot is deposited on the shell inner surface driving an ablative mass flow into the hot spot. The pressure is unchanged. enthalpy flux T mass ablation ρ 5 Pv a = κ(t) T heat flux hot spot shell The heat lost by the hot spot is recycled into the hot spot by mass ablation R r Heat losses lower T but raise n keeping P~nT constant

23 The hot-spot pressure confinement time is determined by the shell inertia Thin shell: Δ<<R R Hot spot P shell M s Δ MR=4πPR s R τ ~ ~ R M s 4πPR

24 The hot spot energy (pressure) comes from the shell kinetic energy. The confinement time is inversely proportional to the implosion velocity V i V i Imploding shell Dense shell Stagnating core Hot spot 4π 3 1 R P M V 3 3 s i MV s PR~ 4 i πr τ R R M s ~ ~ ~ 4πPR R V i

25 The product Pτ can be rewritten in terms of areal density and implosion velocity PR MV Pτ ~ V 4 πr i s i ~ use MV s PR~ 4 i πr Ms 4 πr ( ρδ) Thin shell mass Pτ ~( ρδ) V ~ ( ρr) V i i Implosion velocity cannot be measured Areal density can be measured ( ρr) ρdr 0

26 Temperature and implosion velocity are related Pτ can be measured T kev i ρr 0. gcm V (km/s) - Measurable Pτ for uniform (spherically symmetric 1D) implosions 0.8 P τ (1D)~8 (ρr) -T gcm kev atm-s

27 The ignition parameter ( Lawson criterion) can be measured (in 1D implosions) ε α σv χ Pτ > 1 - gcm 4 T S(T) V S(T) S(4.5) 0.8 P τ (1D)~8 (ρr) T kev atm-s ( ) 08. T kev 1D R > 1 gcm χ ρ T (kev)/4.5

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29 The performance parameters for ICF can be extended to three-dimensions P τ (3D)~8 (ρr) -T gcm kev YOC atm-s χ 3D T kev ( ρr) - gcm YOC>1 Easy fix: replace <σv> with <σv>yoc P τ (3D)~8 (ρr) -T gcm kev YOC atm-s χ 1.6 T ρr YOC >1 4.7 ( ) 0.8 kev 0.5 3D - gcm Better theory + simulations

30 The performance parameter χ predicts ignition with a ± 10% error simulation database χ 3D T χ3d ( ρr) kev 05. YOC gcm

31 Cryogenic implosions on OMEGA have achieved Pτ 1. atm-s and χ 0.0 OMEGA implosions: ρr 0. g/cm, T kev, YOC P τ (3D) 8 (ρr) -T gcm kev YOC 1. atm-s 0.8 T kev 0.5 χ( 3D) ( ρr) - YOC 0. 0 gcm JET DT discharges: Pτ 1 atm-s, χ 0.14

32 The Pτ - T plot shows progress in fusion research OMEGA implosions ρr 0. g cm - Yield neutrons YOC 0.1 <T> kev Pτ 1 atm-s χ 0.0 Gain ~ 10-3 NIF ignition targets ρr 1.8 g cm - YOC 0.4 <T> 4.7 kev Pτ 5 atm-s χ 1 Gain ~ 0

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34 Hydro-equivalent curves show how current OMEGA implosions would perform when scaled up to the NIF

35 Hydro-equivalent ignition in the Pτ -T plane Hydro-equivalent ignition on OMEGA: ρr 0.3 g cm - Yield neutrons YOC 0.15 <T> 3.4 kev Pτ 3 atm-s χ 0.08

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