Proton Beams for Fast Ignition: Control of the Energy Spectrum

1. Proton Beams for Fast Ignition:Control of the Energy Spectrum A.P.L.Robinson1 D.Neely1, P.McKenna2, R.G.Evans1,4,C-G.Wahlström3,F.Linau3, O.Lundh3 1Central Laser Facility, Rutherford-Appleton Laboratory, UK 2 University of Strathclyde, Glasgow, UK 3Lund Laser Institute, Sweden 4Imperial College London, UK

2. Spectral Modification for Proton FI • Quasi-monoenergetic experimental results in 2006.(Hegelich et al. Nature 439 (2006)) • This may help proton driven Fast Ignition.(Temporal et al.,PoP 9 (2002)) • Spectral Modification w/o “Energy Slicing” + all optical approach. • We studied whether the use of multiple high-intensity laser pulses can produce useful spectral modification. • Carried out Vlasov and PIC simulations.

3. Is there a theoretical basis for this? Equal pulses: Why shouldn’t this just be very similar to one pulse? • Grismayer and Mora, PoP 13 (2006) • Single species • Hybrid • Exponential density profile • Zero velocity in pre-expanded tail • but … • Wave-breaking • Transient features in spectra 1.Max. Energy reduced. 2.Some part of the spectrum Is enhanced.

4. Vlasov simulations • 1D1P Eulerian Upwind method. • Large plasma near solid density (186μm); 40nm contamination layer • Contains a “Set-up” pulse of electrons + a “Main drive” pulse of electrons. • Sub-question: Does this work within TNSA alone? • 2 ion species; 2 temperature 186μm = rear surf. C4+ CH2 40nm SUP = Set-Up Pulse MDP = Main Drive Pulse MDP SUP

5. Results • See a reduction in Emax. • Fewer high energy protons. • Interestingly we have produced • a spectral peak. • Simulations run for 750fs. • Proton source layer close to • solid density and has 66% H. Where did these peaks come from? Seen at certain values of the set-up pulse temperature only (250-750keV) for standard conditions used. A.P.L.Robinson CLF

6. Two-stage Mechanism 186μm = rear surf. As the hotter MDP arrives → surge in protons across carbon Front → “wave breaking” + peak in proton density A.P.L.Robinson CLF

7. The Second stage Peak in proton density → “E-field alterations” (spike) → accumulation of protons in phase space. A.P.L.Robinson CLF 186μm = rear surf.

8. Sensitivity Also tried reducing density of SUP to 5 x 1026 and 2.5 x 1026m-3 Peaks still occur. Not a “chaotic” sensitivity to initial conditions

9. PIC simulations • 1D3P EM PIC code used. • 400nm foil at 4 x 1028 H & 4 x 1028 heavy ion (80ncrit) • Foil placed at 60μm • 40fs sin2 pulses MDP a0 = 4 • Comparison run with MDP only. SUP MDP

10. PIC Results We obtain similar results to Vlasov simulations Spectral Peaks Reduction in Emax SUP a0 = 2: RedSUP a0 = 1:Magenta Single Pulse Ref.: Black

11. But is this the same mechanism? Consider run II (SUP a0 = 2) Still see 2-stage mechansim. Proton density spike produced Protons Heavy ions A.P.L.Robinson CLF So the first stage is v.similar, but no `wave-breaking’

12. But is this the same mechanism? (II) Second Stage E-field Proton / Ion Density 2 pulse 1 pulse

13. But is this the same mechanism?(III) Second stage is then very similar in run II • ‘wave-breaking’ event • probably incidental to • some initial conditions. • Appears to be the same • mechanism. protons heavy ions This feature gives the peak.

14. …and some issues (I). Simulations at reduced density (10ncrit) result in over-optimistic predictions.

15. …and some issues (II). Heavy ions aren’t critical to this process: This is not a target composition effect! Red = Pure proton target. Black = Proton + Heavy Ion.

16. Conclusions • Can multiple 10-100fs ultraintense laser pulses result in a modified proton spectrum? • Yes, on the basis of our Vlasov and PIC simulations which both agree on this question. • Level of modification may be interesting to proton FI • Optical Approach:More practical + better for high rep. rate? • This is the start of an investigation that requires more work. • Future work needs more realism, but also a better • understanding so that we can control this. A.P.L.Robinson CLF