Fast electron transport in fusion targets

1. Fast electron transport in fusion targets J.J. Honrubia1 and J. Meyer-ter-Vehn2 1 GIFI, ETSIA, Universidad Politécnica de Madrid, Spain 2Max-Planck-Institut für Quantenoptik, Garching, Germany Presented at 35th European Physical Society Conference on Plasma Physics and 10th International Workshop on Fast Ignition of Fusion Targets, June 9 – 18, 2008, Hersonissos, Crete, Greece

2. Target study group X. Ribeyre, G. Schurtz, M. Olazabal, R. G. Evans J.R. Davies, L. Silva, G. Sorasio J. Badziak IPPLM J. Meyer-ter-Vehn J.J. Honrubia, M. Temporal, R. Ramis S. Atzeni, A. Schiavi

3. Baseline specifications • Implosion energy: • 200 kJ in 5ns • 10 m chamber • 40 beam irradiation? • 2w or 3w? 2. PW beamlines: 70kJ in 10ps wavelength? number of beams?

4. Outline • Integrated simulation model. • Fast electron energy deposition. • Simulations of RAL experiments on fast electron beam divergence in solid targets. • Integrated simulations of fast ignition by electrons • Importance of collective effects. • Minimum ignition energies. • Integrated simulations of fast ignition by ions. • Protons. • Mono-energetic carbon beams. • Conclusions.

5. Integrated simulation model • Standardhybrid PIC model for fast electron transport (Bell, 1997). • Energy deposition by Coulomb collisions of fast electrons with background plasma and ohmic heating due to the return current. • Classical Spitzer resistivity (no ‘anomalous’ effects). • 2-D r-z hydrodynamics: • SESAME EoS. • Flux-limited thermal electron conduction. • multigroup radiation transport. • DT fusion reactions • kinetic a-particle transport. max depth a-particle energy deposition in DT at 400 g/cm3 and 50 keV

6. Fast electron energy deposition in DT • Solodov & Betti, PoP15, 042707 (2008): • Li & Petrasso, PoP13, 056314 (2006), multiple scattering theory 0.8 × 0.6 EMeV (g/cm2) • Deutschet al., PRL 77, 2483 (1996); Starikov & Deutsch, PRE 71, 0264907 (2005), relativistic electron stopping in quantum plasmas: • Atzeni, Schiavi & Davies: P5.106

7. Fast electron energy deposition in DT 1D relativistic Maxwellian with E = 2 MeV, q = 22º 2 MeV, q = 0º r = 300 g/cm3 beam Solodov & Betti

8. Simulation of fast electron transport experiments • Experiments with planar foils carried out at RAL by J.S. Green et al. [PRL 100, 015003 (2008)] and Lancaster et al. [PRL 98, 125002 (2007)]. • Cu and Al/Cu/Al foils, 4×1019 W/cm2 @  (1.5×1020 W/cm2 @ 2) with 5 ps pulse duration. Beam divergence measured by Ka diagnostics = 35º. • q-Gaussian radial beam distribution to mimic the radial energy distribution of the Vulcan laser [Nakatsutsumi, Davies et al, New J. Phys. 10, 043046 (2008)]. • the observed beam divergence is reproduced assuming an initial angle of 50 – 55º. Bq (Tesla) 920 0 - 920

9. Ignition energies vs. beam divergence • Experiments at LULI [Baton et al., PoP (2008)],RAL and Livermore state the non-existence of surface currents and beam focusing in cone targets. • If there are not other mechanisms to reduce beam divergence, ignition energies for ‘realistic’ target configurations can become quite high.

10. Electron beam parameters • Electron beam parameters: super-Gaussian distribution with spot radius = 20 - 23 mm (FWHM). Gaussian pulse in time with durations of 15 – 20 ps. • Initial divergence half-angles 30º, 35º and 40º (planar experiments q 50º) • Energy distribution: 1D relativistic Maxwellian with temperature given by 75% and 50% of the ponderomotive scaling. E  1 – 2.5 - 2 MeV, Beg’s law. • Peak intensity of the laser pulse 2×1020 W/cm2 @ 2w. • Laser-to-fast electron conversion efficiency = 0.4 • Multi-PW laser beam energy  100 kJ @ 2w.

11. Resistive collimation of the fast electron beam d = 100 mm, q = 30º, E = 1.5 MeV, e-beam energy = 37 kJ

12. energy deposition Ti d = 100 mm d = 125 mm d = 150 mm Anomalous deposition and filamentation • Ohmic heating by return currents is dominant in the halo, while Coulomb energy deposition prevails in the high density core. • Anomalous electron stopping [Honda et al. PRL 95, 2128, 2000) plays no role at high densities, in agreement with the advanced PIC calculations shown by Sentoku [PoP (2008)] • Resistive filamentation 3D hybrid simulation J.J. Honrubia and J. Meyer-ter-Vehn, Nuclear Fusion 46, L25 (2006).

13. Integrated ignition simulations • = 35º, E = 1.5MeV, d = 100 mm, 37 kJ Ti Bq r 250 g/cm3 r 100 g/cm3 r

14. Integrated ignition simulations • = 40º, E = 1MeV, d = 100 mm, 37 kJ Ti Bq r 250 g/cm3 r 100 g/cm3 r

15. Electron beam ignition energies

16. Fast ignition by laser-driven ion beams • Motivation: ion beam fast ignition presents over fast ignition by relativistic electrons: • interaction is well known • more flexibility: multiple pulses, additional hydrodynamic DT compression, etc. • Proton beam: • Maxwellian energy distribution with constant temperature in radius and time. • Instantaneous emission at 650 mm from the blob centre (FWHM ≈ 7 ps). • Carbon ion beam: • mono-energetic beam with 10% energy spread. • Gaussian pulse in time with FWHM = 5 ps. • Cone-target configuration r (g/cm3) 500 mm 150 mm multi-PW laser 10 g/cm3

17. Carbon and proton beam energy deposition

18. DT ignition by carbon ions E = 400 MeV, DE/E = 10%, d = 650 mm, rb = 15.5 mm, tb= 5 ps, Ep = 9.5 kJ Density Ion temperature r (g/cm3) Ti (keV) 200 660 1300 1900 0.4 8 16 24 r 250 g/cm3 Radius (mm) Z (mm) Z (mm)

19. DT ignition by carbon ions E = 400 MeV, DE/E = 10%, d = 650 mm, rb = 15.5 mm, tb= 5 ps, Ep = 9.5 kJ Density Ion temperature r (g/cm3) Ti (keV) 200 660 1300 1900 0.4 8 16 24 r 250 g/cm3 Radius (mm) Z (mm) Z (mm)

20. Proton ignition energies • Fuel ignition with laser beam energies lower than 100 kJ requires high densities r 600 g/cm3, assuming a laser-to proton beam energy conversion around 12% [Snavely et al., PRL 85, 2945 (2000)]. • High densities can be achieved in cone targets with compression laser energies about 200 kJ [HiPER Technical Report, 2007]. • Plasma surrounding the dense core absorbs a significant fraction of the beam energy ( 30%),two beams?.

21. Carbon beam ignition energies • We found optimal kinetic energies are in the range of 300 – 500 MeV (in agreement with J.C. Fernandez et al., IFSA 2007). • The laser energies required to ignite targets may be too high for the laser-to- carbon beam conversion efficiencies of a few percent reported by Yin et al. [PoP 14, 056706 (2007)] for the ‘laser breakout afterburner’ scheme. • Radiation pressure acceleration with overall conversion efficiencies around or higher than 10% may be a possibility (M. Hegelich et al.)

22. Comparison with fast electrons fast electrons ions hlaser-to-ion = 0.12 hlaser-to-electron = 0.4 Elaser (kJ) Elaser (kJ) 150 150 100 100 80 50 50

23. Summary • Fast electron energy deposition and target ignition have been studied by means of integrated hybrid simulations. • Beam energy deposition in the core is almost exclusively by classical Coulomb energy loss; ohmic energy loss by return currents prevails in the corona, and anomalous energy deposition due to instability growth plays almost no role because of the high-density plasma. • We have actually demonstrated ignition and burn of a DT core compressed to 500 g/cm3. • Ion beams are a good candidate to demonstrate fast ignition if laser to ion conversion efficiencies higher than10% can be demonstrated experimentally.