1. A/XDiv-IDMARKING–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. –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 E K 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

4. –4 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,  =5/3  jumps by M 1/2 M-t-V and Schalk, Kemp and M-t-V But story a little more complicated:implosion doesn’t produce self-similar shape

5. –5 There are four stages in an implosion P R Adiabat shaping  R Uniformly accelerated equilibrium Uniform M~10 at end Ignore convergence R0R0 P R Ablation pressure Convergent amplification Convergence harvests kinetic energy and breaks self-similarity  jump R  R Hollow shell stagnation 10x ~3x in P

6. –6 The gain at fixed total energy(3 MJ) is determined by the IFAR and the compression intensity I => v abl,P abl,  inflight,c s I,IFAR =>v impl V impl,c s =>M V impl,IFAR,v abl =>  hydro M =>  M,  inflight =>  stag  stag =>E igni E igni,  igni =>E igni- laser E total, E igni-laser =>E cmp-las E comp-laser,  hydro =>E comp E comp,  stag,  => mass Mass,  stag =>  R  R =>  ,mass =>yield =>gain IFAR Intensity(10 14 W/cm 2 ) 50 100 200 400

7. –7 How do maximum gain quantities depend on implosion laser intensity and total laser energy? IFAR gain(IFAR<100) gain 40 80 120 160 30 100 300 30 100 300 Intensity(10 14 W/cm 2 ) Energy(MJ)

8. –8 There are satisfactory design points for IFAR under 100 Implosion velocity 10 7 cm/sec Implosion intensity 10 14 W/cm 2 gain IFAR Energy(MJ) 2 4 6 0.3 0.9 3. 100 300

9. –9 Low required convergence ratios will allow relaxed illumination symmetry Convergence ratio 10 20 40 Energy(MJ) IFAR Convergence ratio is measured after adiabat setting shocks have passed

10. –10 Maximum gains correspond to large ignition laser energies Ignition laser energy(MJ) Fraction of energy in ignition laser IFAR Energy(MJ) 0.03 0.1 0.3 0.1 0.2 0.4 1.0

11. –11 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) Energy(MJ) IFAR 30 100 300 900 10 30 10 30 60

12. –12 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 IFAR100 Short pulse laser coupling efficiency 0.25 Compression laser coupling  hydro model Ignition energyAtzeni model Particle range(gm/cm 2 )0.6 E/MeV

13. –13 How does the wavelength of the implosion laser affect the gain curve? E laser (MJ) gain No restriction on ignition laser E ign-laser < 100 kJ  1.0,0.5 0.33,0.25  1.0,0.5 0.33,0.25

14. –14 How do the gain curves depend on the minimum radius of the ignition spot? E ign-laser < 100 kJ E laser (MJ) No restriction on ignition laser gain E laser (MJ) spot radius(  ) 10,20,30,40,50 spot radius(  ) 10,20,30,40,50 No solution for R > 10  ! Current experiments show e - spreading to 20  spot from much smaller laser spot!

15. –15 Limiting the energy supplied by the ignition laser affects the total system gain No limitation 400 kJ 200 kJ 100 kJ E laser (MJ) gain

16. –16 The system gain depends strongly coupling efficiency from laser to ignition region No restriction on ignition laser E ign < 100kJ E laser (MJ) gain    0.5 0.25 0.12 0.06

17. –17 The system gain depends on the range of the relativistic electrons No restriction on ignition laserE ign < 100kJ E laser (MJ) gain Nominal range(gm/cm 2 ) = 0.6 T(MeV) T=(I/1.2*10 19 W/cm 2 ) 1/2 Range multiplier 0.5 1.0 2.0 3.0 Range multiplier 0.5 1.0 2.0 3.0

18. –18 What is the effect of reducing the coupling between the compression laser and the fuel? No restriction on ignition laser E ign-laser < 100 kJ Indirect drive has lower  H but smaller adiabat jump Cone focus implosions forming high  core may have reduced  H E laser (MJ)  H multipliers 1. 0.75 0.5 0.25 gain

19. –19 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”  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

20. –20 How would the gain curves change if requirements could be reduced below Atzeni’s fit? No restriction on ignition laser E ign-laser < 100 kJ gain E laser (MJ) 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? Atzeni x 0.5 x 0.25 x 0.125

21. –21 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

22. –22 How does the cost of ignition laser joules relative to compression driver joules affect the optima in yield/cost ? Yield/cost Cost* *MJ equivalent of compression driver Cost* Fractional cost of Ignition driver (MJ) Relative cost/J 0.5 1.0 3.0 10.

23. Identifying Marker. 23 What happens when we Fast Ignite an ion distributed radiator target rbrb rhrh E wall ~r h 2 T 3.3  0.62 E conv ~r h 2 T E escape Pr~3T 3.5 2r beam  ~r b /v imp 2-sided illumination scaled from normal DRT laser Ion beam

24. Identifying Marker. 24 Gain distribution and short pulse laser requirements Total input energy(MJ) T R (100 eV) 30 100 200 0.1 0.3 0.5 Total input energy(MJ) Gain Short pulse energy(MJ) Short pulse energy can be reduced with small gain reduction

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

26. –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) Ponderomotive E K 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

27. –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) “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

28. –28 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 E K 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

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34. –34 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

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36. –36 Lasnex calculations showing laser propagation in cone and intensity distribution

37. –37 Rays injected from f/5 focus into 30 o cone have only one bounce R(cm) Z(cm) Ray paths Ray pathlength Fraction of ray power 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

38. –38 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 H n e =10 26 100 TW e- power 2MeV drift in z 1 MeV temperature

39. –39 Hot electron current flows along inner edge of cone* Density of relativistic electrons Temperature of hot electrons *Consistent with Sentoku collisionless lower density PIC simulations

40. –40 Heating is mainly on inner edge of cone T Au H T e-thermal t H Electron thermal wave begins to penetrate dense(10 26 /cc) H

41. –41 The surface fields and currents are very large E radial EzEz rB 

42. –42 For 3 MJ total laser energy, the optima depend most strongly on the in-flight-aspect-ratio(IFAR) Hydrodynamic efficiency(%) is a function of IFAR,I Implosion Velocity (10 7 cm/sec)  (gm/cc) IFAR laser intensity 10 14 W/cm 2 laser intensity 10 14 W/cm 2 laser intensity 10 14 W/cm 2 0.04 0.08 0.15 1.5 3. 4.5 6 60. 120 300 900 0.11

43. –43 Optimized designs show tradeoffs among hydroefficiency, density,column density and IFAR  (%)  R(gm/cm 2 )  (gm/cm 3 ) 40 100 300 2 4 6 8 6 9 12 IFAR Laser energy(MJ)

44. IFSA_03_Haan–44 Through Innovative Laser Pulse Shaping we have Significantly Improved the Stability of High-Gain Direct-Drive Targets for Inertial Fusion Energy Yield350MJ E laser 2.9MJ Gain120 Shell breakup fraction: -Standard pulse~1.8 - Picket pulse ~0.15 DT gas DT fuel 2.38mm DT ablator (+ CH foam) 1.0 0.1 0.01 0.001 Time KrF or DPSSL laser “Picket stake” prepulse Laser Power Pulse Shape Standard 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

45. –45 Long pulse plastic slab coupling efficiencies were used *  1.0,0.5 0.33,0.25 Laser intensity(W/cm 2 ) Absorption fraction * See W.L.Kruer,ThePhysics of Laser Plasma Interactions,Westview Press, Boulder,CO

46. –46 Are small laser focal spots consistent with final optics protection? 1 cm thick SiO 2 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/cm 2 => 10 5 cm 2 => 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 10 15 W/cm 2 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