Where are we with laser fusion?

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1 Where are we with laser fusion? R. Betti Laboratory for Laser Energetics Fusion Science Center Dept. Mechanical Engineering and Physics & Astronomy University of Rochester HEDSA HEDP Summer School August 16-1, 015 San Diego, CA

2 Alpha particle heating is the mechanism leading to thermonuclear ignition of Deuterium-Tritium fuel The -particles release their energy in the plasma thus causing self-heating (or alpha heating). Deuterium + Tritium Ignition condition alpha-power> power-losses χ= alpha-power/power-losses>1 n Neutrons (14 MeV) leave without depositing its energy Alpha particles (3.5MeV) slow down in the plasma through collisions with the electrons The plasma gets hotter and produces more fusion reactions leading to a thermal runaway Thermonuclear instability Ignition

3 FSC Driving ICF targets is a very inefficient process Expanding ablated (blow-off) plasma (CH) Examples: V i Ablator NIF Indirect Drive Laser energy = 1.8MJ Shell final kinetic energy = 10-14kJ Total efficiency = % DT vapor DT ice Useful kinetic energy = 1 shell M unablated Vi V i = implosion velocity Only a small fraction of the driver energy is converted into useful kinetic energy of the implosion

4 1 The imploding shell has two functions: (a) heating of the central low-density plasma (hot spot) to ignition temperatures, (b) providing the inertial confinement FSC Useful kinetic energy shell M unablated Vi ~50% ~50% Compression and heating of the central hot spot Compression of the dense shell to provide the inertial confinement COMPRESSED CORE AT STAGNATION Dense shell Ignition takes place ~ g/cc in the hot spot Hot spot 5-10 KeV Dense shell Provides the confinement of the hot spot (and more)

5 Up to the onset of ignition, burning plasmas are confined within the hot spot FSC Hot spot ~5kJ Dense Shell ~5kJ

6 FSC The energy balance determines the time evolution of the plasma pressure Fusion Plasma (HOT SPOT) P no The DT plasma is brought to a pressure P no using only a spherical piston (the imploding shell) The alpha particles deposit their energy in the plasma while the plasma looses energy on a time scale τ Plasma volume Fusion reactivity d 3 n 3 PV dt ENERGY BALANCE PV = σv ε V 4 P nt 3.5 MeV τ Confinement time P(0) = no P

7 FSC The dimensionless form of the energy balance only depends on the no-alpha Lawson 1 parameter dp P Pτ = 1 dt τ S ( T ) S ( T) ε 4T σv Dimensionless variables and assume σ v ~ T ( ) S T = S = const dpˆ = P ˆ χ ˆ no P 1 dtˆ χ no Lawson, Proc. Phys. Soc. London (1957) P no S Pˆ τ P P no ˆ t t P ˆ(0) 1 τ No-alpha Lawson parameter Note: S has the dimensions of Pτ

8 FSC Pˆ The explosive solution defines the ignition condition determined by the no-alpha Lawson parameter = 5 χ no 1 no ˆ ( χ 1) e t IGNITION CONDITION χ no 1 P τ = S P [ τ] min no no ign Pt ˆ() ˆ 4 3 χ = 1.5 χ no = 1 1 χ no = no ˆt ignition χ no S P no [ P τ ] min no τ ign

9 FSC A neutron yield with alphas and a yield without alphas are defined Neutron yield including alpha particle heating for subignited plasmas P ˆ ˆ Vτ P no 1 τ no = χ 0 no χno 1 χno Yield V P P dt Ln Yield is measured in the experiments Neutron yield if alpha particle heating is switched off dpˆ = P ˆ χ ˆ no P 1 Pˆ dtˆ ˆ ˆ Vτ Pno Yieldno Vτ P no P dt = 0 = exp ˆ ( t) Yield no cannot be measured in DT experiments

10 FSC Yield Yield The amplification of the yield due to alpha heating is a unique function of the no-alpha Lawson parameter 1 = Ln χ no χno 1 χno no χ no P no [ P τ ] min no τ ign Yield Yield no χ no

11 FSC How can one measure the no-alpha Lawson parameter? Start from estimating the confinement time τ M R = 4π PR sh DT Newton s law of the dense shell confining the hot spot pressure DT Dense shell R Hot spot M M sh DT DT τ R M PR sh ~ ~ DT PR τ Areal density Shell mass ~ ( ρ ) R shell V ~ R 3

12 FSC A simple formula relates the Lawson parameters with and without alphas (using previous slide) Yield ~ P τv Pτ χ = S Pτ ig [ Pτ ] min χ Yield 3 ~ sh M DT ( ρ ) Yield is measured Areal density ρ is measured Mass of shell is known χ no ~ Yield 1/3 no χ 1/3 ~ Yield χ Yield = χno Yieldn 1/3 χ can be measured

13 The amplification of the yield due to alpha heating is also a unique function of the Lawson parameter with alphas FSC Yield Yield 1 = Ln χ no χno 1 χno no χ Yield = χno Yieldn 1/3 Yield amplification Yield Yield n = F ( χ ) χ 1/3 0.4Yield 16 ~ sh g / cm M DT ( mg ) ( ρr ) /3 χ can be measured

14 FSC In the best NIF shot the fusion yield increased by more than x due to alpha heating 1D-simulations D-simulations analytic 1D-simulations D-simulations analytic Ignition Best NIF shot χ no [ Pτ ] [ Pτ ] no ign no Best High-Foot NIF shot: ρr 0.7g/cm, Yield = 10 16, M DT = 0.17mg χ 0.95

15 A significant amount of alpha particle energy (relative to the pdv work) was obtained in NIF shot N14010 FSC P T 180Gbar 5keV Energy balance input E E + 0.5E 0.5E hot spot pdv rad R hot spot 34µ m input EpdV 4kJ Ehot spot 5kJ tot 0.5E.3kJ Qhot spot = input E tot Erad E E tot fusion 5.kJ 6kJ pdv 0.65

16 In a burning plasma, the alpha heating is the dominant power input to the fusion plasma. W external Fusion plasma W Wfusion Q Q W = 5W = 5 ext ext. W Burning plasmas Q >1 Super-simple steady-state (?) model of a burning plasma with external input energy model of implosion before stagnation when input power from shell convergence (piston) to the hot spot is large.

17 Steady state plasmas: energy balance External input n 4 σ ε v V ~ C n T V ~ C p V Alpha heating Energy losses 3 p W ext + C pv= V τ Energy confinement time

18 In the presence of alpha heating, the plasma pressure depends on Q W Q W = CpV ext W ext Energy balance with alphas 3 p 3 p W + ext C pv V Wext ( 1 Q) V 0 τ = + τ = Pressure with alphas τ C p τ 0.5 p = W ext ( 1+ Q ) C 3V τ 3

19 The yield amplification due to alpha heating depends exclusively on Q W ext Energy balance and pressure without alphas = 3 p τ no no V τ no C p τ 0.5 no p no = W extcτ 3V 3 Yield amplification vs Q Y Y no p = = + p 4 ( 1 Q ) 3 no

20 Indirect drive implosions on NIF have achieved significant alpha heating (1). Access to the burning plasma regime requires doubling the neutron yield () FSC -heating model (ICF) hydro-sim (ICF) 30kJ-MJ 10kJ Steady state (for τ P -1/ ) 6kJ 50kJ Applies to current ID implosions

21 How was the alpha heating result achieved at LLNL? Hurricane et al, Nature, March 014 Parks et al, Phys. Rev. Lett. 014

22 6kJ O. Hurricane, APS DPP meeting (013)

23 The best NIF implosions used the High-Foot laser pulse that drives stronger shocks in the foot O. Hurricane, APS DPP meeting (013) High foot Low foot The high foot pulse set the imploding shell on a higher isentrope (nothing to do with alpha particles) because it launches stronger shocks in the foot of the pulse when the shell density is low Stronger picket Drop this precompession

24 High-foot growth-factor calculations and simulations are consistent with the expectation of less instability O. Hurricane, APS DPP meeting (013)

25 The current path to indirect drive ignition includes: increasing the velocity, looking for ways to reduce the Rayleigh-Taylor instability, trying new ablators and new hohlraums FSC Near Vacuum Hohlraums have the potential of eliminating the Laser-Plasma- Instabilities problem leading to better control of the implosion symmetry and greater x-ray energy HDC (diamond) Ablator has higher density and requires shorter laser pulses allowing the use of vacuum hohlraums (with less energy losses due to laser-plasma instabilities) Beryllium Ablator has greater hydrodynamic efficiency allowing a more massive (and more stable) shell to be imploded

26 Direct-Drive Laser Fusion

27 Hydrodynamic equivalence provides a tool to scale the performance of OMEGA implosions to NIF energies FSC Hydro-equivalent scaled-down experiments are carried out on OMEGA

28 FSC OMEGA implosions continue to improve towards the goal of demonstrating hydro-equivalent ignition at 1.8MJ of laser energy Ignition on NIF likely no OMEGA OMEGA (015) Ignition on NIF possible but unlikely Threshold depends on the level of nonuniformities OMEGA R. Nora et al, Phys. Plasmas (014)

29 The performance of direct drive capsules is currently degraded by Cross-Beam-Energy-Transfer FSC

30 Techniques to mitigate Cross-Beam Energy Transfer include zooming phase plates and two-color split FSC Zooming Phase Plates 1 Picket are NOT zoomed Main pulse is zoomed 1 D. Froula et al, submitted to Phys. Plasmas (013) I. Igumenshchev et al, Phys. Plasmas 19, (01)

31 FSC Shock ignition is an alterative ignition scheme to achieve higher pressures than conventional ignition R. Betti et al, Phys. Rev. Lett., 98, (007) D. Batani et al, Review, Nuclear Fusion (014) S. Atzeni et al, Review, Nuclear Fusion (014)

32 FSC Experimentally inferred ablation pressures above 300Mbar exceed the requirements for shock ignition R. Nora et al, Phys. Rev. Lett. 114, (015) Planar experiments achieved 35-70Mbar S. Baton et al, Phys. Rev. Lett. (01) M. Hohemberger et al, Phys. Plasmas (014)

33 conclusions The recent results from the NIF are exciting and give hope of achieving burning plasma conditions FSC Significant alpha heating of a DT plasma has been demonstrated at NIF. Estimates indicate that heating from the alphas has more than double the number of fusion reactions This is only fusion physics and reaching any conclusion about fusion energy is premature The possibility of producing a burning plasma is real and the indirect drive approach seems to be on the right path The path to ignition and gain is still uncertain Direct-drive offers a promising alternative path to ignition and initial experiments on NIF are under way

34 FSC Despite the exciting results, the path to ignition is uncertain with current indirect-drive targets imp no kin 3/5 F χ ~E YOC Best shot to date E kin = kinetic energy YOC is V χ no 0.65 YOC = Yield-Over-Clean = Yield(3D)/Yield(1D) 50% in NIF High Foot V imp = Implosion Velocity F = Adiabat (entropy) no- ignition parameter in terms of in-flight properties Needed for ignition χno 1 Direct-drive High Velocity (40km/s) Easiest options to approach ignition: Increase V imp and/or reduce the Adiabat (this is the current path of the HF campaign) but stability may eventually become an issue again (YOC drops)

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