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 UCRL-PRES-204413 Simulations of Electron Transport Experiments for Fast Ignition using LSP Presented to: 15 th International Symposium on Heavy Ion Inertial Fusion Princeton University, NJ Richard P. J. Town AX-Division Lawrence Livermore National Laboratory June 7, 2004

2. UCRL-PRES-204413-2 The LSP code has been used to study fast ignition relevant transport experiments A critical issue for Fast Ignition is understanding the transport of the ignitor electrons to the fuel. Experiments have shown a rapid increase in beam width followed by reasonable collimation with a 20° half angle. We have used the LSP code to: – generate simulated K  images; – model XUV images; and – model cone focus experiments. The LSP code has been used to study the effect on beam transport of: – non-Spitzer conductivity; and – the initial beam divergence.

3. UCRL-PRES-204413-3 A critical issue for fast ignition is understanding the transport of the ignitor electrons to the fuel Laser couples efficiently to the core Laser couples inefficiently to the core 1.1x10 21 cm -3 10 26 cm -3 This is a major driver on the short-pulse laser specification.

4. UCRL-PRES-204413-4 The XUV image can be used to estimate the temperature of the rear surface XUV image A series of LASNEX calculations of isochorically heated Al targets establishes the relationship between temperature and intensity.

5. UCRL-PRES-204413-5 Stephens et al. 1 used a Bragg crystal mirror to image a Cu fluor layer embedded in Al with a CCD camera Fast electron transport is diagnosed by burying a layer of of high-Z (e.g., Cu or Ti) material within a low-Z plasma matrix (e.g., Al or CH). Electrons reaching the layer cause K-shell ionization and the emitted photons are imaged with a camera, thus characterizing energy transport within a dense plasma. CCD cameraBragg crystal mirror Laser electrons K  fluorescence layer 1 R.B. Stephens, et al, to appear in Phys. Rev. E.

6. UCRL-PRES-204413-6 Experiments on MeV electron transport have been performed by researchers around the world Experimental data 1 show: – a rapid increase in beam size in the first few microns; and – a fairly collimated (20º half angle) beam in the bulk of the material. 1 M. H. Key, et al, 5th Workshop on Fast Ignition of Fusion Targets (2001). 0200400 200 50 250 150 100 Thickness (  m) Spot Radius (  m) X-ray (CH) X-ray (Al) XUV K  fluorescence Laser spot

7. UCRL-PRES-204413-7 LSP 1 is a hybrid particle code used extensively in the ion beam community Performed simulations using 2-D in cylindrical (r-z) geometry. Employs a “direct implicit” energy conserving electromagnetic algorithm. Hybrid fluid-kinetic descriptions for electrons with dynamic reallocation. Scattering between the beam and background plasma included. – Ionization and excitation ignored. LSP has been coupled to ITS to enable the generation of K  images to enable direct comparison with experimental data. Beam created by injection at the target boundary or by promotion within the plasma. 1 D. R. Welch, et al, Nucl. Inst. Meth. Phys. Res. A464, 134 (2001).

8. UCRL-PRES-204413-8 We have performed simulations of generic electron transport experiments The targets are based on the experiments performed by Martinolli et al 1 on the LULI and Vulcan laser. The big uncertainty is the initial hot electron beam parameters. Al 3+ Cu 2+ R Z 20 μm VACUUM 300μm 20μm 100μm Hot Electron Beam 1 E. Martinolli, et al., Laser & Part. Beams 20, 171 (2002).

9. UCRL-PRES-204413-9 A significant “halo” surrounds the short-pulse high intensity spot Typical data from Nova Petawatt laser shows about 30 to 40% of the laser energy in the central spot. We have approximated the laser intensity pattern as two Gaussians. 0.040.080.0120.0 10 0 10 2 10 4 10 6 Displacement (  m) Energy density (counts/pixel) Airy function CCD image of Focal spot

10. UCRL-PRES-204413-10 Determining the input electron distribution is based on experimental measurements The conversion efficiency into hot electrons has been measured by many experimentalists over a wide range of intensities:  = 0.000175 I(W/cm 2 ) 0.2661

11. UCRL-PRES-204413-11 There are two well-known scaling laws for hot electron temperature which we have used Pondermotive scaling: T hot (MeV)= (I 2 /(10 19 W/cm 2  m 2 )) 1/2 Beg scaling: T hot (MeV)= 0.1(I 2 /(10 17 W/cm 2  m 2 )) 1/3 Pondermotive Beg

12. UCRL-PRES-204413-12 The current density and energy distribution can now be defined in terms of laser intensity Using the new Python front end to LSP the injected beam energy and current density can be calculated from: – conversion efficiency; and – hot temperature scaling law. A thermal spread is also added. rold = 0.0 for i in range(400): r = (i+0.5)*0.00002 intensity = Gaussian(r, 1.0e-3, 1.0e20, 0.0, 1.0e12) +Gaussian(r, 1.0e-2, 1.0e17, 0.0, 1.0e12) if intensity > 0.0: thot = BegScaling( intensity ) ehot = 1.6022e-16*thot area = pi*(r**2-rold**2) lpower = intensity*area epower = lpower*conversionEfficiency(intensity) Density =1.6022e-19*epower/(area*ehot) rold = r Pondermotive Beg

13. UCRL-PRES-204413-13 The LSP code uses Spitzer conductivity, which we know is not valid at low temperatures. The calculated resistivity of aluminum at solid density increases with temperature. 10 -8 10 -7 10 -6 10 -5 10 -1 10 0 10 1 10 2 10 3 Temperature (eV) Resistivity (  m) SpitzerNon-Spitzer

14. UCRL-PRES-204413-14 Reduced filamentation is observed when the conductivity is constant to 100eV Beam density at 1.6 ps

15. UCRL-PRES-204413-15 The K  diagnostic gives time-integrated images of the emission generated by the hot electron beam The diagnostic will record both K  photons generated by the forward going and backward going “refluxed” electrons.

16. UCRL-PRES-204413-16 K  images were generated at various times throughout the simulations A time history displaying the birth positions of the K  photons can be generated for each source. Photons created  0.5ps  1.5ps  3.0ps Base source case: Beg Temperature Scaling, 200keV transverse thermal energy X (  m) R (microns) X (  m) Y (  m) The time integrated diagnostic is a good measure of hot electron beam transport.

17. UCRL-PRES-204413-17 LSP calculations show reasonable agreement with experimental data for moderate Al thicknesses There appears to be moderate agreement in the trend of increasing spot diameter with Al thickness, based on the average between vertical and horizontal line-outs. The large asymmetry in the horizontal direction is under investigation. Spot Diameter (  m) Experimental Data LSP calculations Al Thickness (  m)

18. UCRL-PRES-204413-18 We can also compare these source scenarios using the K  spot diameter at half-max intensity A significant asymmetry was detected when taking similar line-outs in the horizontal direction, resulting in the relatively large error in spot diameter for many of the data points. 140 120 100 80 60 40 20 0 2D Source Injection Spot Diameter (microns) Thermal transverse temperature (keV) (I 2 ) 3/2 (I 2 ) 1/2 (I 2 ) 1/3 0 100 200 300 400 500 600 140 120 100 80 60 40 20 0 Spot Diameter (  m)

19. UCRL-PRES-204413-19 The LSP calculation matches the measured temperature pattern at the rear surface of the target 27J of hot electrons, in a 1-ps pulse, with Beg scaling and a thermal spread of 300keV injected into a 100  m Al 3+ plasma. The temperature was obtained by post-processing the LSP energy data at the rear surface with a realistic equation of state.

20. UCRL-PRES-204413-20 Z3 is being used to generate hot electrons from LASNEX-predicted pre-pulse plasmas 1-D line out of plasma formed by 10mJ prepulse on a CH target: (z,x) plots of electrons with energies > 12 MeV: 0.5 ps 1.0 ps UCRL-PRES-204413-20

21. UCRL-PRES-204413-21 Extracting the correct electron distribution function is more complicated for oblique incidence A 10 19 W/cm 2 laser incident on a 16 n c plasma (shown by white lines) at a 30 o angle of incidence. (z,x) phase space plot of electrons with energies > 5 MeV. 0.3 ps0.6 ps Electrons injected at a significant angle We are using Python to closely couple Z3 output to LSP input 0.5 ps 0.3 ps

22. UCRL-PRES-204413-22 We have recently started large scale cone calculations using LSP Background electron density profile of a gold cone touching a perfect conductor. 2MeV electrons promoted along surface

23. UCRL-PRES-204413-23 Hot electrons start on inner edge and then diffuse into the cone 0.16 ps1.4 ps Transport efficiency <20% of hot electron out of cone

24. UCRL-PRES-204413-24 The LSP code has been used to study fast ignition relevant transport experiments A critical issue for Fast Ignition is understanding the transport of the ignitor electrons to the fuel. Experiments have shown a rapid increase in beam width followed by reasonable collimation with a 20° half angle. We have used the LSP code to: – generate simulated K  images; – model XUV images; and – model cone focus experiments. The LSP code has been used to study the effect on beam transport of: – non-Spitzer conductivity; and – the initial beam divergence.

25. UCRL-PRES-204413-25 Collaborators: C. Chen, L. A. Cottrill, M. H. Key, W. L. Kruer, A. B. Langdon, B. F. Lasinski, B. C. McCandless, R. A. Snavely, C. H. Still, M. Tabak, S. C. Wilks, LLNL, Livermore, CA, USA. D. R. Welch, MRC, Albuquerque, NM, USA.