1. Lawrence Livermore National Laboratory Pravesh Patel 10th Intl. Workshop on Fast Ignition of Fusion Targets June 9-13, 2008, Hersonissos, Crete Experimental measurements of electron energy spectra at FI-relevant intensities This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344

2. 2 Lawrence Livermore National Laboratory Acknowledgements T. Bartal, T. Ma, J. King, M.S. Wei, F. Beg K. Akli, R. Stephens T. Link, L. Van Woerkom, R.R. Freeman, D. Offermann, V. Ovchinnikov C. Chen, M. Porkolab, MIT, Cambridge, MA Y.Y. Tsui, University of Alberta, Canada D. Hey, A.J. Mackinnon, A. MacPhee, S. Le Pape, H. Chen, A.J. Kemp, M.H. Key, M. Tabak, R. Town, E. Storm

3. 3 Lawrence Livermore National Laboratory The mean energy of electrons produced by the ignitor laser is a critical parameter in fast ignition  We typically use ponderomotive scaling for the mean electron energy  Recent work (Sentoku, Kemp, Chrisman) indicates that steepening of the plasma density gradient will reduce T hot by a factor  (  n c /n p )  Degree of steepening dependent on a combination of laser intensity, pulselength, and pre-plasma  We have performed a study of T hot as a function of intensity and pre-pulse A. Kemp 100fs 200fs 300fs T hot 4  2  1 MeV

4. 4 Lawrence Livermore National Laboratory Experimental setup on the TITAN laser  150J in 0.6ps, 5µm FWHM focal spot  Intrinsic pre-pulse measured at ~10mJ (10 4 energy, 10 8 intensity contrast) Laser 10µm Al 25µm Cu 1000µm Al Electron spectrometer Bremsstrahlung spectrometer Absolute K-alpha yield  Intensity scan by varying laser energy (constant pulselength, spot size)  Pre-pulse scan by adding a 3ns long-pulse with varying energy 16˚S-pol

5. 5 Lawrence Livermore National Laboratory Focal spot is measured at low power OPCPA at target chamber center 15% 50% 150J, 0.6ps: 15% energy in 5µm FWHM spot  2x10 20 W/cm 2 150J, 0.6ps: 50% energy in 15µm diameter  7x10 19 W/cm 2

6. 6 Lawrence Livermore National Laboratory Electron spectrum measured with vacuum electron spectrometer (1-100 MeV) 121 J shot  Multi-temperature distribution

7. 7 Lawrence Livermore National Laboratory Electron spectrum measured with vacuum electron spectrometer 121 J shot  Multi-temperature distribution  Peak intensity of 1.5x10 20 W/cm 2  T hot ~5 MeV

8. 8 Lawrence Livermore National Laboratory Escaping electron spectrum shows strong dependence on pre-pulse level  High energy component (>5 MeV) increases with pre-pulse, consistent with acceleration from under- dense plasma [NOT ponderomotive acc.]  Low energy component (1-5 MeV) is relatively insensitive to pre-pulse (may be consistent with ponderomotive acc.) [caveat: only small frac. of electrons escape target – spectrum will be modified by target potentials]

9. 9 Lawrence Livermore National Laboratory Electron spectrum inside target can be inferred from bremsstrahlung measurements  Monte Carlo code ITS is used to compute response of target and detector to trial electron source function Target response Detector response 10keV  500keV 0.0010.010.1110100 Photon energy (MeV)

10. 10 Lawrence Livermore National Laboratory Bremsstrahlung data is generally well reproduced by a 1-Temp exponential distribution  Least squares fit gives unique solution for 1-T fits  Error on T hot ~  0.2 MeV  Caveat: 2-T fits with cold and hot components can also reproduce the data

11. 11 Lawrence Livermore National Laboratory T hot data as a function of laser intensity

12. 12 Lawrence Livermore National Laboratory T hot data as a function of laser intensity Ponderomotive scaling

13. 13 Lawrence Livermore National Laboratory T hot data as a function of laser intensity Ponderomotive scaling

14. 14 Lawrence Livermore National Laboratory Focal spot is measured at low power OPCPA at target chamber center 15% 50% 150J, 0.6ps: 15% energy in 5µm FWHM spot  2x10 20 W/cm 2 150J, 0.6ps: 50% energy in 15µm diameter  7x10 19 W/cm 2

15. 15 Lawrence Livermore National Laboratory T hot data as a function of laser intensity using mean laser intensity for 50% encircled energy Ponderomotive scaling

16. 16 Lawrence Livermore National Laboratory What intensity should we use?  We should start with the full energy on-shot focal intensity distribution (full energy spot may be larger than measurement due to thermal distortions in amplifiers and non-linear effects) Focal spot at TCC Equivalent plane measurement

17. 17 Lawrence Livermore National Laboratory Full energy focal spot intensity distribution Low power Full energy OPCPA Full shot  Focal spot does not degrade at full energy (with adaptive optic)

18. 18 Lawrence Livermore National Laboratory Full energy focal spot intensity distribution Low power Full energy OPCPA Full shot  Focal spot does not degrade at full energy (with adaptive optic)  Distribution of intensities  distribution of T hot s 1 MeV 4 MeV 2 MeV.5 MeV 3 MeV 6 MeV T hot

19. 19 Lawrence Livermore National Laboratory Electron spectrum calculated from measured focal spot using ponderomotive scaling  We can’t describe the electron energy distribution as a single temperature, or by a single mean energy  Actual electron spectrum may be better described as a ‘sum of exponentials’ kT~1 MeV kT~2 MeV kT~4 MeV Sum of electron spectra

20. 20 Lawrence Livermore National Laboratory We can perform forward calculation to test ponderomotive scaling theory against exp data Focal spot Power distribution Synthesized electron spectrum ITS brems calculation  Experimental spectrum is cooler, or lower temperature, than that calculated from pondoromotive scaling  we may be observing some degree of density steepening  Caveat: Monte Carlo modeling of electrons in target neglects field effects

21. 21 Lawrence Livermore National Laboratory Summary  Escaping electron spectra exhibit multi-temp distributions with a very hot component, kT>10 MeV, consistent with under-dense instabilities (NOT ponderomotive), and a lower temp component, kT~1 MeV; since escaping electrons are affected by potentials it’s questionable how to interpret this  Electron temperature, T hot, calculated from bremsstrahlung ranges from 0.1–1.2 MeV, many times lower than ponderomotive would predict using standard definition of focal spot intensity  Using the full focal intensity distribution demonstrates that there are effectively multiple hot electron temperatures, not a single T hot  Forward calculation suggests that we still observe slightly lower temperatures than standard ponderomotive scaling: may mean that we have some degree of density profile steepening occurring  Caveat: We still have some model dependency, primarily through using ITS, which neglects field effects – we will repeat with hybrid modeling