1. 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. Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551-0808 Identifying Marker. 1 PIC Simulations of Short-Pulse, High-Intensity Light Impinging on Structured Targets Presented to: 9 th International Fast Ignitor Workshop Cambridge, Massachusetts Barbara F. Lasinski, A. Bruce Langdon, C. H. Still, Max Tabak, and Richard P. J. Town Lawrence Livermore National Laboratory November 5, 2006.

2. FIW/BFL et al. 2 PIC simulations of structured targets have high laser absorption. Simple cone target modeling shows light interference within the cone a wide angular spread of the energetic electrons. ion motion is important. beam pointing shifts don’t significantly change these results More realistic cone targets have similar properties. We find enhanced laser absorption with structured surfaces But the challenge is to find a shape which collimates the hot electrons. Two-dimensional grooves give higher absorption than three- dimensional divots.

3. FIW/BFL et al. 3 First, we studied simple cone targets to assess the key physical processes. 0 20 10 0 20 40 30 These initial PIC simulations were done in 2D(x,z) with our massively parallel code Z3. The cones each have a half-angle of ~13  For these simulations, n e = 16n c, T e = 10 keV, Zm i /m e = 3600, and ZT e /T i = 20. The incident laser propagates along the z-direction. z(  m) x(  m) laser Beam spatial amplitude at the entrance plane is 1-sin 8 (  x/(2x spot )) where x spot = 6  m. This spatial profile is relatively constant as the beam propagates. The beam spot size is larger than the diameter of the inner wall of the cone. The temporal profile is flat, with a sharp rise to an intensity of 10 19 W/cm 2 for 1  m light. 5m5m x(  m) amp

4. FIW/BFL et al. 4 The incident laser is either pointed down the center of the cone or is shifted spatially by 3  m In Z3, we apply a low pass temporal filter to fields and fluxes to highlight the low frequency component. These filtered quantities have the subscript s. Plots of the Poynting flux, (P z ) s vs (x,z), at t=0.03 ps showing two problem initializations with the solid white lines indicating the initial plasma boundary. x(  m) z(  m) Shifted beam p-polarization x(  m) z(  m) Centered beam s-polarization At this early time, there is little reflected light. 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV Have laser electric field in (p), or out (s) of the simulation plane for all 4 cases. Laser vacuum intensity on this color map.

5. FIW/BFL et al. 5 Find light interference effects as the beam propagates. x(  m) z(  m) Poynting flux, (P z ) s, vs (x,z) Centered beam s-polarization t = 0.09 ps. Shifted beam p-polarization t = 0.15 ps Beam has not yet reached the cone tip Significant reflection 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV Laser vacuum intensity on this color map. z(  m)

6. FIW/BFL et al. 6 n cr The relativistic critical surface becomes deformed x(  m) z(  m) Centered irradiation onto flat inner surface cone; p-polarization; t = 0.38 ps On this log scale, n e ranges from 0.03 to 33. and the change from red to green is at n e = 1.0 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV (P z ) s vs (x,z) n e vs (x,z) log(n e ) vs (x,z) There is ~ 5  m of plasma at n e ~ 0.3 in the beam path. Laser vacuum intensity on this color map. z(  m)

7. FIW/BFL et al. 7 For pointed cones, gouging out of the tip becomes visible before 0.5 ps x(  m) 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV On this log scale, n e ranges from 0.03 to 33. and the change from red to green is at n e = 1.0 n e vs (x,z) log(n e ) vs (x,z) (P z ) s vs (x,z) Centered irradiation onto pointed inner surface cone; p-polarization; t = 0.46 ps There is a sharp focus in the underdense plasma blowoff. z(  m) x(  m) Laser vacuum intensity on this color map. n cr

8. FIW/BFL et al. 8 Energetic particles have a wide angular distribution. x(  m) 0 10 20 30 0 10 20 30 20 40 60 80 100 0 0 20 0 40 20 40 60 80 100 0 0 20 0 40 20 40 60 80 100 0 Centered irradiation Shifted beam irradiation Plot positions of electrons with energy > 0.8 MeV (  > 2.6) at t=0.15 ps from simulations in p-polarization. 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV x(  m) z(  m)

9. FIW/BFL et al. 9 Static fields illustrate strong surface currents. x(  m) 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV z(  m) x(  m) (B y ) s vs (x,z) at t=0.25 ps (J z ) s vs (x,z) at t=0.25 ps Centered irradiation Shifted beam irradiation These static B fields are comparable to the laser field. Note sign changes at the cone wall closer to the shifted incident beam. z(  m) p-polarization

10. FIW/BFL et al. 10 Find little difference in absorption into hot electrons between centered and shifted beam pointings. Pointed top, s-polarization Solid; Centered irradiation Dotted; Shifted irradiation Pointed top, p-polarization Flat top, p-polarization Flat top, s-polarization t(ps) Fraction of incident energy absorbed by electrons. 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV

11. FIW/BFL et al. 11 With fixed ions, simulations of flat top cones lead to lower absorption. We ascribe this difference to the role of the deformation of the relativistic critical surface in the absorption process. t(ps) fraction Absorption ( ) and reflection ( ) vs time; dotted curves are from the simulation with fixed ions. Absorption into heated electrons with mobile ions. Reflection with mobile ions. 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV Fixed ions. p-polarization

12. FIW/BFL et al. 12 The heated electrons are more collimated for flat top cone simulations with fixed ions. z(  m) x(  m) Plot positions of electrons with energy > 0.8 MeV (  > 2.6) at t=0.15 ps from simulations of centered beam in p-polarization. 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV Fixed Ions Mobile Ions x(  m)

13. FIW/BFL et al. 13 For cones with pointed tops, little difference between fixed and mobile ion simulations. We infer that relativistic critical surface deformation is less important for cones with pointed tops at these early time as the laser is efficiently absorbed along the upper side walls in both cases Expect greater differences at later times. Absorption ( ) and reflection ( ) vs time; dotted curves are from the simulation with fixed ions. fraction t(ps) 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV x(  m) Wide angular distribution as with mobile ions z(  m) p-polarization Positions of electrons with energy > 0.8 MeV (  > 2.6) at t=0.15 ps from centered irradiation in p-polarization.

14. FIW/BFL et al. 14 Results so far are insensitive to beam and cone shapes. (P z ) s vs (x,z) at t=0.08 ps With wings, whose intensity is ¼ that of the central region, this entire beam profile is wider than the cone inner wall. Curved plasma surfaces; the initial plasma boundary is shown by the green and red curves. 2D simulations at an intensity of 10 19 W/cm 2, p-polarization, 15  cone half angle, n e = 16n c, T e = 10 keV, Zm i /m e = 3600 and ZT e /T i = 20. x(  m) z(  m) A companion simulation with a Gaussian beam gives similar results. Positions of electrons with energy > 0.8 MeV at t=0.5 ps Intense part of the beam is approximately half the width of the cone inner wall. Proportions are closer to those in experiments z(  m)

15. FIW/BFL et al. 15 Do textured surfaces help? x(  m) z(  m) We have seen that the cone geometry with the pointed top produces high absorption into heated electrons. Will shaped surfaces increase the absorption into heated, collimated electrons? Conditions: n e =25n c, T e =10 keV, Zm i /m e = 3600, and ZT e /T i = 20 at an incident intensity of 10 19 W/cm 2 in both s- and p-polarization. Series of simulations of plane waves interacting with a “divot.” Varied depth of divot from 2  m to 8  m. Divot shapes with depth of 6  m. Depth

16. FIW/BFL et al. 16 There is strong focusing in the plasma that blows off the sides of the divot in this p-polarization simulation. Divots impact the laser-matter interaction. x(  m) z(  m) Model one divot, but take advantage of periodicity transverse to the laser beam when making snapshot plots. 2-D, 10 19 W/cm 2, 25n c, T e = 10 keV (P z ) s vs (x,z) at t=0.08 ps (P z ) s vs (x,z) at t=0.21 ps n e vs (x,z) at t=0.21 ps x(  m) z(  m) Laser vacuum intensity on this color map. n cr

17. FIW/BFL et al. 17 Divots increase the absorption into heated electrons compared to a flat slab. 2-D, 10 19 W/cm 2, 25n c, T e = 10 keV x(  m) z(  m) Absorption fraction into heated electrons. t(ps) 8  m deep, p-polarization 4  m deep, p-polarization 6  m deep, p-polarization 2  m deep, p-polarization 6  m deep, s-polarization no divot, p-polarization no divot, s-polarization fraction

18. FIW/BFL et al. 18 Unfortunately the heated electrons are not very collimated. 2-D, 10 19 W/cm 2, 25n c, T e = 10 keV Positions of electrons with energy > 0.8 MeV (  > 2.6) at t=0.15 ps from simulation in p-polarization. z(  m) x(  m) Heated electrons appear to be produced in a ~ 30  cone near the tip of the divot.

19. FIW/BFL et al. 19 In 3D simulations, grooves (2D structures) are better than divots (full 3D structures). Titan experiments on divots are planned to look for optimum structures and to use K  signature to investigate hot electrons. 3-D, 10 19 W/cm 2, 25n e, T e = 40 keV fraction Fraction of light reflected, or absorbed into heated electrons. Solid: groove with laser electric field in the plane of the groove Dotted: divot We identify these results on 2D vs 3D structures with experiments reported by Ditmire, Cowan et al on s- and p-polarization irradiations of wedge targets and the accompanying PIC simulations by Sentoku et al. t(ps)

20. FIW/BFL et al. 20 PIC simulations of structured targets have high laser absorption. Simple cone target modeling shows light interference within the cone a wide angular spread of the energetic electrons. ion motion is important. beam pointing shifts don’t significantly change these results More realistic cone targets have similar properties. We find enhanced laser absorption with structured surfaces But the challenge is to find a shape which collimates the hot electrons. Two-dimensional grooves give higher absorption than three- dimensional divots.

21. FIW/BFL et al. 21 Backup viewgraphs.

22. FIW/BFL et al. 22 From the incident and net fluence at the entrance plane, we compute the fraction of reflected light. Example: cone with flat inner surface, centered irradiation. In the code, accumulate in time the net fluence at the incident (z = 0) plane and compare to the incident fluence to find the fraction of reflected light. t(ps) incident fluence net fluence In these simulations with a relativistic overdense plasma, what is not reflected appears as field and particle energy. 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV p-polarization little reflection fraction more reflection s-polarization t(ps)

23. FIW/BFL et al. 23 The energetics of the simulation are monitored. Particle kinetic energy Electron kinetic energy Field energy Energy error Net fluence at the incident plane. The change in each quantity is plotted. Energy; arbitrary units. Example: cone with flat inner surface, centered irradiation. p-polarization s-polarization t(ps) Readily observe that p-polarization has higher absorption and lower reflection than s-polarization 2-D, 10 19 W/cm 2, 16n c, T e = 10 keV

24. FIW/BFL et al. 24 Geometric ratios in this cone irradiation study are guided by experiment. Plot Poynting flux with laser frequency filtered out, (P z ) s vs (x,z), at t=0.08 ps, to show the problem initialization for this beam with a central intense region and lower intensity wings. With wings, whose intensity is ¼ that of the centered region, this entire beam profile is wider than the cone inner wall. 2D (x, z) Z3 simulations in p-polarization at 10 19 W/cm 2, 15  cone half angle, n e = 16 n c, T e = 10 keV, Zm i /m e = 3600, and ZT e /T i = 20. At this early time, only the wings of the beam are interacting with the inner cone walls. x(  m) z(  m) Companion simulation with a Gaussian beam produces similar results. Intense part of the beam is approximately half the width of the cone inner wall.

25. FIW/BFL et al. 25 The laser-plasma interaction is predominantly at the inner cone wall at 0.7 ps. n e vs (x,z) x(  m) z(  m) 2-D, 10 19 W/cm 2, p-polarization, 16n c, T e = 10 keV (P z ) s vs (x,z) x(  m) z(  m) Laser vacuum intensity on this color map. Green and white curves show the initial plasma boundary. There is reflection along the sides of the beam Relativistic critical surface now has complex structure.

26. FIW/BFL et al. 26 Energetic electrons appear to come from the inner cone wall with a wide angular distribution. x(  m) z(  m) 2-D, 10 19 W/cm 2, p-polarization, 16n c, T e = 10 keV Plot positions of electrons with energy > 0.8 MeV (  > 2.6) t = 0.55 ps t = 0.5 ps t = 0.4 ps x(  m)

27. FIW/BFL et al. 27 There is ~ 25% reflection in this cone simulation. 2-D, 10 19 W/cm 2, p-polarization, 16n c, T e = 10 keV t(ps) Accumulate the net fluence at the incident plane (z = 0) and compare to the incident fluence to determine the fraction of reflected light. net fluence incident fluence absorption into heated electrons reflection fraction Fluences are normalized to the maximum incident fluence.

28. FIW/BFL et al. 28 What is optimum shape? This study is ongoing x(  m) z(  m) 2-D, 10 19 W/cm 2, 25n e, T e = 10 keV x(  m) z(  m) Have started looking at more complicated shapes; this new one still has problems. z(  m) Positions of electrons with energy > 0.8 MeV) at t=0.1125 ps (P z ) s vs (x,z) at t=0.03 ps (P z ) s vs (x,z) at t=0.3 ps Laser vacuum intensity on this color map.