PIC Simulations of Short-Pulse, High-Intensity Light Impinging on Structured Targets

1. PIC Simulations of Short-Pulse, High-Intensity Light Impinging on Structured Targets Presented to: 9th 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. 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. 30 40 20 10 20 10 0 20 30 30 0 10 20 0 First, we studied simple cone targets to assess the key physical processes. • 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 z(mm) • For these simulations, ne = 16nc, Te = 10 keV, Zmi/me = 3600, and ZTe/Ti = 20. laser • The incident laser propagates along the z-direction. • Beam spatial amplitude at the entrance plane is 1-sin8(x/(2xspot)) where xspot = 6mm. This spatial profile is relatively constant as the beam propagates. 5mm amp z(mm) The beam spot size is larger than the diameter of the inner wall of the cone. laser x(mm) • The temporal profile is flat, with a sharp rise to an intensity of 1019 W/cm2 for 1mm light. x(mm)

4. 2-D, 1019 W/cm2, 16nc, Te = 10 keV The incident laser is either pointed down the center of the cone or is shifted spatially by 3mm • 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, (Pz)s vs (x,z), at t=0.03 ps showing two problem initializations with the solid white lines indicating the initial plasma boundary. Shifted beam p-polarization • Have laser electric field in (p), or out (s) of the simulation plane for all 4 cases. Centered beam s-polarization Laser vacuum intensity on this color map. z(mm) z(mm) • At this early time, there is little reflected light. x(mm) x(mm)

5. 2-D, 1019 W/cm2, 16nc, Te = 10 keV Find light interference effects as the beam propagates. Centered beam s-polarization t = 0.09 ps. Shifted beam p-polarization t = 0.15 ps Poynting flux, (Pz)s, vs (x,z) z(mm) z(mm) Laser vacuum intensity on this color map. x(mm) x(mm) Beam has not yet reached the cone tip Significant reflection

6. 2-D, 1019 W/cm2, 16nc, Te = 10 keV The relativistic critical surface becomes deformed Centered irradiation onto flat inner surface cone; p-polarization; t = 0.38 ps ne vs (x,z) (Pz)s vs (x,z) Laser vacuum intensity on this color map. z(mm) z(mm) ncr x(mm) log(ne) vs (x,z) On this log scale, ne ranges from 0.03 to 33. and the change from red to green is at ne = 1.0 ncr z(mm) There is ~ 5 mm of plasma at ne ~ 0.3 in the beam path. x(mm)

7. 2-D, 1019 W/cm2, 16nc, Te = 10 keV For pointed cones, gouging out of the tip becomes visible before 0.5 ps Centered irradiation onto pointed inner surface cone; p-polarization; t = 0.46 ps ne vs (x,z) (Pz)s vs (x,z) Laser vacuum intensity on this color map. z(mm) z(mm) ncr x(mm) There is a sharp focus in the underdense plasma blowoff. log(ne) vs (x,z) On this log scale, ne ranges from 0.03 to 33. and the change from red to green is at ne = 1.0 ncr z(mm) x(mm)

8. 100 100 40 40 80 80 60 60 20 20 40 40 20 20 0 0 0 0 20 0 0 20 2-D, 1019 W/cm2, 16nc, Te = 10 keV Energetic particles have a wide angular distribution. Plot positions of electrons with energy > 0.8 MeV (g > 2.6) at t=0.15 ps from simulations in p-polarization. Centered irradiation z(mm) z(mm) 100 30 Shifted beam irradiation 80 60 20 z(mm) 40 z(mm) 10 20 0 0 30 0 10 20 x(mm) x(mm)

9. 2-D, 1019 W/cm2, 16nc, Te = 10 keV Static fields illustrate strong surface currents. Centered irradiation Shifted beam irradiation p-polarization p-polarization These static B fields are comparable to the laser field. (By)s vs (x,z) at t=0.25 ps z(mm) (Jz)s vs (x,z) at t=0.25 ps Note sign changes at the cone wall closer to the shifted incident beam. z(mm) x(mm) x(mm)

10. Pointed top, p-polarization Flat top, p-polarization 2-D, 1019 W/cm2, 16nc, Te = 10 keV Find little difference in absorption into hot electrons between centered and shifted beam pointings. Solid; Centered irradiation Dotted; Shifted irradiation Fraction of incident energy absorbed by electrons. Pointed top, s-polarization Flat top, s-polarization t(ps)

11. 2-D, 1019 W/cm2, 16nc, Te = 10 keV 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. • Absorption ( ) and reflection ( ) vs time; dotted curves are from the simulation with fixed ions. p-polarization Absorption into heated electrons with mobile ions. fraction Fixed ions. Reflection with mobile ions. t(ps)

12. 2-D, 1019 W/cm2, 16nc, Te = 10 keV The heated electrons are more collimated for flat top cone simulations with fixed ions. Plot positions of electrons with energy > 0.8 MeV (g > 2.6) at t=0.15 ps from simulations of centered beam in p-polarization. Fixed Ions Mobile Ions z(mm) z(mm) x(mm) x(mm)

13. 2-D, 1019 W/cm2, 16nc, Te = 10 keV 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 Absorption ( ) and reflection ( ) vs time; dotted curves are from the simulation with fixed ions. Positions of electrons with energy > 0.8 MeV (g > 2.6) at t=0.15 ps from centered irradiation in p-polarization. p-polarization Wide angular distribution as with mobile ions fraction z(mm) x(mm) t(ps) • Expect greater differences at later times.

14. Results so far are insensitive to beam and cone shapes. • 2D simulations at an intensity of 1019 W/cm2, p-polarization, 15 cone half angle, ne = 16nc, Te = 10 keV, Zmi/me = 3600 and ZTe/Ti = 20. • Proportions are closer to those in experiments • (Pz)s vs (x,z) at t=0.08 ps • Curved plasma surfaces; the initial plasma boundary is shown by the green and red curves. z(mm) • Intense part of the beam is approximately half the width of the cone inner wall. • Positions of electrons with energy > 0.8 MeV at t=0.5 ps • With wings, whose intensity is ¼ that of the central region, this entire beam profile is wider than the cone inner wall. z(mm) • A companion simulation with a Gaussian beam gives similar results. x(mm)

15. Do textured surfaces help? 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? Divot shapes with depth of 6mm. Series of simulations of plane waves interacting with a “divot.” Varied depth of divot from 2 mm to 8 mm. z(mm) Conditions: ne=25nc, Te=10 keV, Zmi/me = 3600, and ZTe/Ti = 20 at an incident intensity of 1019 W/cm2 in both s- and p-polarization. Depth x(mm)

16. 2-D, 1019 W/cm2, 25nc, Te = 10 keV Divots impact the laser-matter interaction. Model one divot, but take advantage of periodicity transverse to the laser beam when making snapshot plots. z(mm) x(mm) • ne vs (x,z) at t=0.21 ps • (Pz)s vs (x,z) at t=0.08 ps • (Pz)s vs (x,z) at t=0.21 ps z(mm) z(mm) z(mm) ncr x(mm) x(mm) x(mm) • There is strong focusing in the plasma that blows off the sides of the divot in this p-polarization simulation. Laser vacuum intensity on this color map.

17. 2-D, 1019 W/cm2, 25nc, Te = 10 keV Divots increase the absorption into heated electrons compared to a flat slab. z(mm) Absorption fraction into heated electrons. x(mm) 8 mm deep, p-polarization fraction 6 mm deep, p-polarization 4 mm deep, p-polarization 2 mm deep, p-polarization no divot, p-polarization 6 mm deep, s-polarization no divot, s-polarization t(ps)

18. 2-D, 1019 W/cm2, 25nc, Te = 10 keV Unfortunately the heated electrons are not very collimated. Positions of electrons with energy > 0.8 MeV (g > 2.6) at t=0.15 ps from simulation in p-polarization. Heated electrons appear to be produced in a ~ 30 cone near the tip of the divot. z(mm) x(mm)

19. 3-D, 1019 W/cm2, 25ne, Te = 40 keV In 3D simulations, grooves (2D structures) are better than divots (full 3D structures). Fraction of light reflected, or absorbed into heated electrons. Solid: groove with laser electric field in the plane of the groove fraction Dotted: divot t(ps) Titan experiments on divots are planned to look for optimum structures and to use Ka signature to investigate hot electrons. 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.

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. Backup viewgraphs.

22. 2-D, 1019 W/cm2, 16nc, Te = 10 keV From the incident and net fluence at the entrance plane, we compute the fraction of reflected light. • 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. • Example: cone with flat inner surface, centered irradiation. little reflection more reflection incident fluence s-polarization p-polarization net fluence fraction fraction t(ps) t(ps) • In these simulations with a relativistic overdense plasma, what is not reflected appears as field and particle energy.

23. 2-D, 1019 W/cm2, 16nc, Te = 10 keV The energetics of the simulation are monitored. • Example: cone with flat inner surface, centered irradiation. s-polarization p-polarization Particle kinetic energy Electron kinetic energy Energy; arbitrary units. Field energy Energy error Net fluence at the incident plane. t(ps) t(ps) • The change in each quantity is plotted. • Readily observe that p-polarization has higher absorption and lower reflection than s-polarization

24. Geometric ratios in this cone irradiation study are guided by experiment. • 2D (x, z) Z3 simulations in p-polarization at 1019 W/cm2, 15 cone half angle, ne = 16 nc, Te = 10 keV, Zmi/me = 3600, and ZTe/Ti = 20. • Plot Poynting flux with laser frequency filtered out, (Pz)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. • Intense part of the beam is approximately half the width of the cone inner wall. • With wings, whose intensity is ¼ that of the centered region, this entire beam profile is wider than the cone inner wall. z(mm) • At this early time, only the wings of the beam are interacting with the inner cone walls. x(mm) • Companion simulation with a Gaussian beam produces similar results.

25. 2-D, 1019 W/cm2, p-polarization, 16nc, Te = 10 keV The laser-plasma interaction is predominantly at the inner cone wall at 0.7 ps. (Pz)s vs (x,z) ne vs (x,z) z(mm) z(mm) x(mm) x(mm) 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. 2-D, 1019 W/cm2, p-polarization, 16nc, Te = 10 keV Energetic electrons appear to come from the inner cone wall with a wide angular distribution. • Plot positions of electrons with energy > 0.8 MeV (g > 2.6) t = 0.55 ps t = 0.5 ps t = 0.4 ps z(mm) x(mm) x(mm) x(mm)

27. 2-D, 1019 W/cm2, p-polarization, 16nc, Te = 10 keV incident fluence net fluence There is ~ 25% reflection in this cone simulation. • Accumulate the net fluence at the incident plane (z = 0) and compare to the incident fluence to determine the fraction of reflected light. fraction • Fluences are normalized to the maximum incident fluence. absorption into heated electrons fraction reflection t(ps)

28. 2-D, 1019 W/cm2, 25ne, Te = 10 keV What is optimum shape? This study is ongoing Have started looking at more complicated shapes; this new one still has problems. z(mm) x(mm) Positions of electrons with energy > 0.8 MeV) at t=0.1125 ps (Pz)s vs (x,z) at t=0.3 ps (Pz)s vs (x,z) at t=0.03 ps z(mm) z(mm) z(mm) x(mm) x(mm) x(mm) Laser vacuum intensity on this color map.