1. International Workshop on Fast Ignition FIW 2008 16 to 18 Sept. Hernosissos, Crete Michael H. Key Lawrence Livermore National Laboratory This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. Fast ignition discussion points

2. Channeling / Hole boring The density profile of the plasma around the implosion is known from 1D hydro- point designs 3D PIC modeling has shown that a channel can be produced up to the critical density in the sub critical density plasma. Has modeling shown that the channel can be extended by hole boring to bring the laser to within <100  m of the ignition region ( requires ~200  m hole boring to few gcm -3 )? Shorter wavelength seems essential to bring laser close enough to compressed plasma ? Has the propagation of the main pulse in the semi - evacuated channel been modeled? Is there a credible integrated point design for high gain ?

3. Super penetration Modeling and small scale expts have shown the capability of the main pulse alone to penetrate somewhat beyond critical density with relativistic self focusing. Excessive T hot ( due to extreme case of extended preformed plasma) appears to be a problem but could it be mitigated with a shorter wavelength? The use shorter wavelength would allow penetration closer to the ignition region - is it a requirement ? Is there any point design for ignition?

4. Hydro design issues Density and pressure > 10x that in Gekko PW expt but cone tip thickness fixed by electron scattering and energy loss. Plasma jet penetration of tip is more severe due to higher pressure Dimensions of full size plasma >2x Gekko PW expt What are implications for stand off distance - tip to core - it seems it must be be considerably greater than in Gekko expt ? With divergent transport we should not therefore anticipate same 20% coupling eff. Design is hampered by numerical modeling difficulties in cone tip region - how viable solution ? Entrainment of cone material in to ignition region adds design issues - high Z filter in shell - low Z tamper on cone - effects on hydro instabilities ?

5. Most T hot measurements from electrons in vacuum - i.e. slope temperature, much data at >5MeV due to instrumental cut off at <4 MeV but new data with wider instrumental range show much cooler sometimes complex spectra at <4 MeV. Evidence that hot tail is pre- pulse related - increases with pre-pulse ? Data < 4MeV need quantitative model to correct for target potential Bremsstrahlung method may be better Should use power fraction v intensity to calculate electron spectra Data may be at threshold of showing profile steepening effects Cannot quite reach relevant regime in current 200 to 400J expts - need next generation experiments 5 to 10x more pulse energy Experimental methods T hot

6. Characteristic energy spectra have low slope kT at 4MeV (peak or plateau in transition region) Difficult to characterize by 1 or even 2 temperature fits Approx. kT~0.4 MeV for E 5 MeV

7. High kT region strongly enhanced by prepulse- suggests due to sub- critical interactions Difficult to characterize by 1 or even 2 temperature fits Approx. kT~0.4 MeV for E 5 MeV

8. Bremsstrahlung method may be better - electrons are detected INSIDE the target Should use power fraction v intensity to calculate electron spectra Data may be at threshold of showing profile steepening effects as modeled by Sentoku et al. Experimental methods T hot

9. Χ 2 /doF=23 Χ 2 /doF= 0.9 Pond Scaling Sentoku 60 (Tc)-40 (Th) Energy Split Shot 20080122s01 (121 J) Sentoku profile steepening model fits Bremsstrahlung data but Ponderomotive model does not

10. K alpha yield data plus MC modeling give efficiency estimates Need to include E and B fields for accurate results ( can be done with hybrid PIC). Hybrid PIC with electron injection does not include ponderomotive B field - how important is it - do we need explicit PIC modeling ? Experimental methods: conv. eff.

11. Considerable divergence in solid targets - 40 degree cone Very difficult to determine divergence for FI relevant case So far not able to reach high conductivity regime. Laser cone interaction is not at relevant intensity /pulse duration ? Divergence is critical parameter for efficiency Cone tip scattering sets lower bound ? Can self pinching mitigate divergence ? Integrated modeling credibility - what is lacking ? Electron divergence

12. No measurements have been made in integrated experiments - divergence may be different than in cool solid targets because of major resistivity difference. Needs new diagnostics We are developing Kalpha imaging of dopant in implosion. Needs higher photon energy than available with crystal imagers e.g Ag Kalpha at 22 keV Short pulse high energy Compton radiography complements Kalpha imaging for determination of transport cone angle and space resolved coupling efficiecy Electron divergence in integrated experiments

13. Issues for proton FI include several key steps not yet completed Hydrodynamic design for survival of the cone and proton foil rear surface? Proton focusing design which includes the walls of the cone and transmission thro the cone tip? Experimental validation of >15 % conversion to protons? Experimental validation of proton focusing to <60  m spot with f/1 segment of spherical shell enclosed in truncated cone? Laser focusing scheme to achieve sufficiently uniform intensity on source foil ?

14. Point design issues What is the status of integrated point designs for the various facilities and ignition concepts? What are the most important issues needing further work to bring numerical point designs to readiness for experiments? What are the near term mid term and long term prospects for construction of facilities and for associated integrated experimental tests of point designs? What are the critical laser technology and target fabrication issues for ignition point designs? What is our overall confidence level for the feasibility of fast ignition? Do we have a credible vision for IFE based on FI ?

15. BACK UP VUGRAPHS from IFSA 2007 talk

16. SP Laser 113  m Fuel density and  R are primary choices For efficient burn with low driver energy1.5 <  R < 2 gcm -3 For high gain with low driver energy 300 <  < 500 gcm -3 Required  R and  with minimum central void are obtained with slow implosion of thick shells (e.g.1D modeling Betti and Zhou PoP) Ignition modeling shows scaling of minimum short pulse energy (e.g. Atzeni PoP, Tabak et al. Fus Sci Tech ) 300gcm -3,18 kJ in 23 ps,  =36  m, 1.1x10 20 Wcm -2 Target diameter is 113 micron >> 36 micron hot spot Cone tip to ignition hot spot separation ≥ target diameter for survival of cone tip Transport cone angle degrades coupling efficiency when distance>> hot spot diameter

17. Density increased to 500gcm -3 Target diameter reduced to 80  m Hot spot diameter increased to 60  m Ignition energy unchanged 18kJ, pulse shorter 14 ps Ignition intensity reduced 4.6x10 19 Wcm -2 SP Laser 80  m Require transport distance similar to hot spot diameter - ‘non ideal’ ignition may enable this Intensity Energy Original modeling by Tabak, figure from Atzeni (FIW 2006 )

18. Contamination of DT with high Z matter can quench fusion burn CH foam supported cryo- DT is attractive BUT require foam density 5x10 -2 gcm -3 Target fabrication issue ( Norimatsu et al Fus Sci Tech,49,483,(2006) Entrainment of cone material by imploding shell can contaminate ignition region Worst problem in Indirect drive - ablation due to M and L band radiation Mitigate with low z tamper layer on cone This is a key hydro design issue

19. Indirect and direct drive both have developing point designs Direct drive - higher drive efficiency- -prefered option for proposed new smaller scale facilities -driver energy ~200kJ ( HiPER, FirexII) Indirect drive- geometry advantages -good drive uniformity - compatible with e.g. NIF or LMJ Tabak hydro design IFSA 2007 Both require extensive hydro-design effort to optimize for FI - non uniform drive - cone tip separation - dense plasma structure…..

20. Typical ignition point design requires higher laser intensity than that for T hot For source area = hot spot area, (  =60  m) and 20% coupling intensity is 2.3x10 20 Wcm -2 for 14 ps The required laser wavelength is 0.3  m to make I 2 = 2x10 19 Wcm -2 ( ponderomotive T hot ) Third harmonic generation is possible ( =0.35  m ) and with R&D investment it may be feasible but it is not developed

21. Light pressure is 100 Gbar at 2x10 20 Wcm -2 - sweeps up preformed plasma and makes steep density gradient to high density with laser driven shock in cone tip ( 14  m travel at 10 gcm -3 in 14 ps ) Modeling (<1ns) predicts reduction of T hot by factor (  Nc/Ns) 0.5 ~ 1/30 and some reduction of conversion efficiency (Sentoku FIW2007) T hot increases with time and there is instability of critical surface ? More modeling is needed - longer duration 2D and 3D PIC Cannot quite reach relevant regime in current expts - need next generation experiments e.g 1kJ in  <6  m This uncertainty of T hot and conversion efficiency is CRITICAL and needs urgent attention There is large uncertainty in T hot at FI required intensity and pulse length due to effects of light pressure

22. Electron source characteristics are critical but not well understood for FI relevant irradiation T hot ~2MeV has coupling loss from low energy electrons in entry plasma and from hot tail to beyond ignition region. 70% of mono-energetic coupling ( Honrubia FIW2007) Transport reduces coupling by uncertain factor depending on transport distance (hydro design) and divergence ( source and transport physics ) Laser intensity,wavelength, preformed plasma, determine T hot and conversion efficiency Ponderomotive T hot requires I 2 = 2x10 19 Wcm -2 Electron range requirement is 1.2gcm -2 ( Atzeni, PoP ) Electron energy giving that range is 2 MeV ( Li and Pettrasso PoP )

23. Cone electron source has many design facets that have not yet been optimized in point designs Convergence of electron flux to cone tip with reduction of required laser intensity Surface magnetic field guiding electrons along preformed plasma Sentoku et al PoP, Habara et al PRL Hot, low Z, low resistivity pre -formed plasma in cone guiding electron flux (Tabak) Enhanced laser intensity at cone tip by oblique plasma mirror reflection Nature of cone tip : open? -  R? - Z - surface finish -? - trade off with closeness of compressed plasma

24. Pre- formed plasma in cone is an important design variable ASE from 1  m laser is typically 10 -4 of main pulse energy - 10 J at 100kJ - what effect on interaction physics in cone ? May lead to laser requirement for either major suppression of ASE at 1  m or harmonic conversion of short pulse Some pre- plasma could be advantageous - control of T hot and wall electron transport Powerful pre-pulse might hold back plasma at open or thin cone tip - easier than hole boring ( Tabak) prepulse Light pressure blocks plasma penetration from implosion or thin cone tip

25. Benchmarked integrated modeling is required to predict the laser to hot spot coupling efficiency Credible benchmark will require next phase integrated experiments Firex I, Omega EP, Petal, NIF ARC Quasi integrated hybrid PIC modeling ( heuristic assumptions for divergence of injected electrons and 150  m separation of source and ignition region based on 2D hydro design) implies high ignition laser energy e.g 60kJ electrons therefore 180kJ laser. ( Honrubia - FIW 2006) PIC modeling of idealized ignition configuration has self consistent electron source - shows light pressure effects on T hot but lacks hydro details and needs longer run time(Sentoku - FIW 2006) Example from LLNL Town talk ?

26. Short pulse laser focal spot characteristics should be included in point designs Multiple short pulse beams are required Wavefront quality, relative phase and relative pointing determine focal spot produced by superposition of foci Engineering determines cone angle New technology is needed for phase and pointing control e.g. 65kJ 5 quads of NIF ARC with phasing designed to give FI required intensity

27. Conceptual design shows the requirements for proton FI XUV PW laser Laser Proton heating Cu K  image  m Laser 100kJ,3 ps 10 20 Wcm -2 50kJ electrons kT=3 MeV 20 kJ protons kT= 3 MeV Radially uniform proton plasma jet required for smallest focal spot Proton source foil protects rear surface from pre-pulse -thickness limits conv. efficiency Cone maintains vacuum region for proton plasma jet formation and protects surface of proton source foil DT fuel at 500g/cc 60  m ignition spot (same as electron ignition) Scattering limits thickness of cone tip and separation from fuel Requirements based on Ignition with protons : Atzeni et al.Nucl Fus 42,(2002)

28. Modeling of focusing suggests that 80% of energy at >3MeV can be delivered to 60  m focal spot from an f/1 segment of a 300  m radius spherical shell 10  m Au,1  m H, T hot 3 MeV, 47% conversion to protons >3MeV Hybrid PIC modeling by M Foord LLNL using LSP code See R Stephens paper for experimental focusing data

29. ErH 3 layer can replace cryo-H layer with similar efficiency Electron to Proton eff. H 35% ErH 3 30% See A MacKinnon paper for expts. with hydrides Hybrid PIC modeling by M Foord LLNL using LSP code

30. hyper-velocity impact fast ignition Modeling has shown the outline feasibility of accelerating a converging thin foil segment to the velocity, density and energy required for ignition. Many detailed issues are not yet studied in sufficient depth for a point design - limits on velocity and density due to preheat and instability, limits on focussing of the energy. Murakami et al PoP 2005

31. Conclusions Point designs for high gain are important and set the near term physics agenda The status of FI point designs is immature with many details lacking Electron/cone ignition is most advanced - T hot is uncertain therefore short pulse laser wavelength. We do not know the coupling efficiency and required short pulse energy Proton FI and hypervelocity impact have (rather primitive) point designs Channeling /hole boring and super penetration lack point designs FI is potentially VERY ADVANTAGEOUS - developed POINT DESIGNS are needed for SUCCESS

32. International Workshop on Fast Ignition FIW 2008 16 to 18 Sept. Hernosissos, Crete Michael H. Key Lawrence Livermore National Laboratory This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. Fast ignition discussion points