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Gain Issues for Fast Ignition

This work explores the gain issues for fast ignition heavy ion fusion, including ignition power, intensity, energy, hydrodynamic efficiency, and more. The results and calculations provide insight into optimizing the performance of fast ignition systems.

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Gain Issues for Fast Ignition

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  1. Gain Issues for Fast Ignition Heavy Ion Fusion Symposium Princeton,NJ Max Tabak and Debra Callahan Lawrence Livermore National Laboratory 7 June,2004 This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

  2. We constructed a Fast Ignitor gain model based on a few ingredients • Atzeni ignition power,intensity,energy model • Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket equation using degenerate gas DT EOS(summarized in Lindl’s book) • Ponderomotive EK scaling model • “Adjusted” version of Meyer-ter-Vehn, Kemp imploding shell self-similar stagnation model • Found dependence of gain on IFAR, total laser energy, drive intensity, ignition laser energy, ignition spot size, laser wavelength, short pulse coupling efficiency, short pulse laser cost, compression laser coupling efficiency for laser direct drive targets • Fast Ignition gain curves driven by distributed radiator HIF target given • Detailed calculations are required to validate these optima

  3. The burn efficiency depends on the fuel adiabat and is one factor in Fast Ignition gain For uniform sphere • It was thought that the adiabat was entirely set by careful pulseshaping during the implosion • Modest increases in shock pressure and proper timing • Wrong! • Significant jump in adiabat during stagnation • For implosions with uniform M,g=5/3 a jumps by M1/2 • M-t-V and Schalk, Kemp and M-t-V • But story a little more complicated:implosion doesn’t produce self-similar shape

  4. There are four stages in an implosion Uniform M~10 at end Ignore convergence P r R0 R R Uniformly accelerated equilibrium Adiabat shaping Convergent amplification ~3x in P 10x Hollow shell Ablation pressure a jump P r R R R Convergence harvests kinetic energy and breaks self-similarity stagnation

  5. The gain at fixed total energy(3 MJ) is determined by the IFAR and the compression intensity 100 I => vabl,Pabl, inflight,cs I,IFAR =>vimpl Vimpl,cs =>M Vimpl,IFAR,vabl =>hydro M => M,inflight =>stag stag =>Eigni Eigni,igni =>Eigni-laser Etotal, Eigni-laser =>Ecmp-las Ecomp-laser, hydro =>Ecomp Ecomp, stag,  => mass Mass, stag => R R => ,mass =>yield =>gain 400 200 IFAR 50 Intensity(1014W/cm2)

  6. How do maximum gain quantities depend on implosion laser intensity and total laser energy? gain(IFAR<100) gain IFAR 100 30 160 40 30 80 100 Intensity(1014W/cm2) 300 120 300 Energy(MJ) Energy(MJ) Energy(MJ)

  7. There are satisfactory design points for IFAR under 100 Implosion intensity 1014W/cm2 Implosion velocity 107cm/sec gain 3. 6 100 0.9 IFAR 4 0.3 300 2 Energy(MJ) Energy(MJ) Energy(MJ)

  8. Low required convergence ratios will allow relaxed illumination symmetry Convergence ratio Convergence ratio is measured after adiabat setting shocks have passed 40 20 IFAR 10 Energy(MJ)

  9. Maximum gains correspond to large ignition laser energies Fraction of energy in ignition laser Ignition laser energy(MJ) 0.03 IFAR 0.1 0.1 0.3 0.2 0.4 1.0 Energy(MJ) Energy(MJ)

  10. Low IFAR’s and high system energies lead to large spots and long stagnation and ignition energy delivery times Spot radius() Ignition time(ps) Stagnation time(ps) 30 10 10 100 IFAR 30 300 30 60 60 900 Energy(MJ) Energy(MJ) Energy(MJ)

  11. We explore the sensitivity of the optima to a number of model uncertainties and experimental details Nominal model Laser wavelength 0.33 m laser spot 10 Maximum IFAR 100 Short pulse laser coupling efficiency 0.25 Compression laser coupling  hydro model Ignition energy Atzeni model Particle range(gm/cm2) 0.6 E/MeV

  12. How does the wavelength of the implosion laser affect the gain curve? No restriction on ignition laser Eign-laser < 100 kJ  1.0,0.5 0.33,0.25  1.0,0.5 0.33,0.25 gain Elaser(MJ) Elaser(MJ)

  13. No restriction on ignition laser gain spot radius() 10,20,30,40,50 Elaser(MJ) How do the gain curves depend on the minimum radius of the ignition spot? Eign-laser < 100 kJ spot radius() 10,20,30,40,50 No solution for R > 10! Elaser(MJ) Current experiments show e- spreading to 20m spot from much smaller laser spot!

  14. Limiting the energy supplied by the ignition laser affects the total system gain No limitation 400 kJ 200 kJ 100 kJ gain Elaser(MJ)

  15. The system gain depends strongly coupling efficiency from laser to ignition region E ign < 100kJ No restriction on ignition laser gain  0.5 0.25 0.12 0.06 Elaser(MJ) Elaser(MJ)

  16. The system gain depends on the range of the relativistic electrons No restriction on ignition laser E ign < 100kJ Range multiplier 0.51.0 2.03.0 gain Range multiplier 0.51.0 2.03.0 Elaser(MJ) Elaser(MJ) Nominal range(gm/cm2) = 0.6 T(MeV) T=(I/1.2*1019W/cm2 )1/2

  17. What is the effect of reducing the coupling between the compression laser and the fuel? No restriction on ignition laser Eign-laser < 100 kJ H multipliers 1. 0.75 0.5 0.25 gain Elaser(MJ) Elaser(MJ) Indirect drive has lower H but smaller adiabat jump Cone focus implosions forming high  core may have reduced H

  18. Current techniques to deflate imploded capsules expel significant energy • It is natural for implosion of shell to lead to low density-high entropy hotspot • About half of stagnated energy resides in hotspot • Eliminating low density core by “flatulent stagnation” wastes this energy and can halve gain • Need to lower “hotspot” a by factor 100 before final stagnation • Options • Radiative cooling • Holey shell so low density core can escape early. Tricky implosion calculation • Have low Mach # implosion so hollow core doesn’t form; e.g., bare drop driven at high intensity. Use large short pulse laser to compress and light ignition region

  19. How would the gain curves change if requirements could be reduced below Atzeni’s fit? No restriction on ignition laser Eign-laser < 100 kJ Atzeni fit ~ 6x ignition energy in isobaric model Recent calculations show 2x reduction for cylindrical implosion driven by short pulse How well can we do? gain Atzeni x 0.5 x 0.25 x 0.125 Elaser(MJ) Elaser(MJ)

  20. Original Fast Ignitor paper had suprathermal electrons drive implosion with most of yield coming at stagnation • Similar effect rediscovered in 2-D calculations by Herrmann and Hatchett with a cylindrical reimplosion of original blob • Factor 2 reduction of ignition energy relative to direct core heating • Probably room for further optimization

  21. How does the cost of ignition laser joules relative to compression driver joules affect the optima in yield/cost ? Fractional cost of Ignition driver Ignition driver (MJ) Yield/cost Relative cost/J 0.5 1.0 3.0 10. Cost* Cost* Cost* *MJ equivalent of compression driver

  22. What happens when we Fast Ignite an ion distributed radiator target 2-sided illumination scaled from normal DRT Eescape 2rbeam Ion beam rh Pr~3T3.5 t~rb/vimp rb Econv~rh2 T Ewall~rh2T3.3t0.62 laser

  23. Gain distribution and short pulse laser requirements Short pulse energy(MJ) Gain 0.1 200 0.3 100 0.5 TR(100 eV) 30 Total input energy(MJ) Total input energy(MJ) Short pulse energy can be reduced with small gain reduction

  24. We obtain the spot size and pulse length dependence of gain Gain Gain 30 Spot radius(cm) Pulse length(10-8sec) 30 200 100 200 100 Total input energy(MJ) Total input energy(MJ) Hybrid target has ~3-4X beam spot with 25%lower coupling efficiency

  25. We constructed a Fast Ignitor gain model based on a few ingredients • Atzeni ignition power,intensity,energy model • Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket equation using degenerate gas DT EOS(summarized in Lindl’s book) • Ponderomotive EK scaling model • “Adjusted” version of Meyer-ter-Vehn, Kemp imploding shell self-similar stagnation model • Found dependence of gain on IFAR, total laser energy, drive intensity, ignition laser energy, ignition spot size, laser wavelength, short pulse coupling efficiency, short pulse laser cost, compression laser coupling efficiency for laser direct drive targets • Fast Ignition gain curves driven by distributed radiator HIF target given • Detailed calculations are required to validate these optima

  26. We constructed a Fast Ignitor gain model based on a few ingredients • Atzeni ignition power,intensity,energy model • Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket equation using degenerate gas DT EOS(summarized in Lindl’s book) • “Adjusted” version of Meyer-ter-Vehn, Kemp imploding shell self-similar stagnation model • Found dependence of gain on IFAR, total laser energy, drive intensity, ignition laser energy, ignition spot size, laser wavelength, short pulse coupling efficiency, short pulse laser cost, compression laser coupling efficiency • Detailed calculations are required to validate these optima • Suggested options to increase fast ignition gain

  27. We constructed a Fast Ignitor gain model based on a few ingredients • Atzeni ignition power,intensity,energy model • Hydrodynamic efficiency, in-flight-aspect-ratio(IFAR) from rocket equation using degenerate gas DT EOS(summarized in Lindl’s book) • Ponderomotive EK scaling model • “Adjusted” version of Meyer-ter-Vehn, Kemp imploding shell self-similar stagnation model • Found dependence of gain on IFAR, total laser energy, drive intensity, ignition laser energy, ignition spot size, laser wavelength, short pulse coupling efficiency, short pulse laser cost, compression laser coupling efficiency for laser direct drive targets • Fast Ignition gain curves driven by distributed radiator HIF target given • Detailed calculations are required to validate these optima

  28. LSP calculations showing electron transport in cones Spatial distributions shown: Hot electron temperature Thermal electron temperature Ion temperatures Particle densities Magnetic field Electrical current Electric field

  29. Lasnex calculations showing laser propagation in cone and intensity distribution

  30. Rays injected from f/5 focus into 30o cone have only one bounce Ray paths Fraction of ray power R(cm) Ray pathlength Z(cm) Try other acceptor shapes or incident angles to get more bounces Increase roughness at micron scale--ponderomotively formed bubbles have much higher absorption in PIC calculations

  31. The implicit,hybrid PIC code LSP from MRC was used to calculate the transport of hot electrons in a cone to high density fuel Au Z*=30 100 TW e- power 2MeV drift in z 1 MeV temperature H ne=1026

  32. Hot electron current flows along inner edge of cone* Temperature of hot electrons Density of relativistic electrons *Consistent with Sentoku collisionless lower density PIC simulations

  33. Heating is mainly on inner edge of cone Te-thermal TAu Te-thermal t H H Electron thermal wave begins to penetrate dense(1026/cc) H

  34. The surface fields and currents are very large rBq Eradial Ez

  35. For 3 MJ total laser energy, the optima depend most strongly on the in-flight-aspect-ratio(IFAR) Implosion Velocity (107cm/sec) Hydrodynamic efficiency(%) is a function of IFAR,I (gm/cc) 6 900 4.5 300 0.11 3. 0.15 IFAR 120 0.08 1.5 60. 0.04 laser intensity 1014W/cm2 laser intensity 1014W/cm2 laser intensity 1014W/cm2

  36. Optimized designs show tradeoffs among hydroefficiency, density,column density and IFAR (%) R(gm/cm2) (gm/cm3) 300 8 6 100 IFAR 4 12 40 2 6 9 Laser energy(MJ) Laser energy(MJ) Laser energy(MJ)

  37. Through Innovative Laser Pulse Shaping we have Significantly Improved the Stability of High-Gain Direct-Drive Targets for Inertial Fusion Energy KrF or DPSSL laser Laser Power Pulse Shape 1.0 0.1 0.01 0.001 “Picket stake” prepulse Standard 2.38mm DT ablator (+ CH foam) DT fuel Time DT gas • Yield 350MJ • Elaser 2.9MJ • Gain 120 • Shell breakup fraction: • Standard pulse ~1.8 • - Picket pulse ~0.15 • Picket fence pulse shape drives decaying through shell • High adiabat in ablator • Low adiabat in fuel • IFAR 100 => 40 without loss of fuel density • Comparable to indirect drive

  38. Long pulse plastic slab coupling efficiencies were used* Absorption fraction  1.0,0.5 0.33,0.25 Laser intensity(W/cm2) * See W.L.Kruer,ThePhysics of Laser Plasma Interactions,Westview Press, Boulder,CO

  39. Are small laser focal spots consistent with final optics protection? • 1 cm thick SiO2 at 15m from capsule will become opaque due to neutron loading after 2 months of reactor yields • Thin films may tolerate longer exposures • 200 kJ at 2J/cm2 => 105cm2 => 3m final optic =>f/5 • Diffraction limit allows small spot • Pointing accuracy ~ 1 microradian for a moving target! • G.Logan suggested 1 cm scale conical plasma mirror at 1015W/cm2 to focus light from large area • Scanning the surface maintains a smooth surface for long pulse • High intensity simulations show absorption between 30-90% (Sentoku small scale, LASNEX--preliminarylarge scale) • Electron transport calculations have begun

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