1. A.P.L.Robinson CLF Proton Beams for Fast Ignition: Control of the Energy Spectrum A.P.L.Robinson 1 D.Neely 1, P.McKenna 2, R.G.Evans 1,4,C- G.Wahlström 3,F.Linau 3, O.Lundh 3 1 Central Laser Facility, Rutherford-Appleton Laboratory, UK 2 University of Strathclyde, Glasgow, UK 3 Lund Laser Institute, Sweden 4 Imperial College London, UK

2. A.P.L.Robinson CLF 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. A.P.L.Robinson CLF Is there a theoretical basis for this? 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 Equal pulses: Why shouldn’t this just be very similar to one pulse? 1.Max. Energy reduced. 2.Some part of the spectrum Is enhanced.

4. A.P.L.Robinson CLF 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 SUP = Set-Up Pulse MDP = Main Drive Pulse C 4+ CH 2 40nm 186μm = rear surf. SUPMDP

5. A.P.L.Robinson CLF Results A.P.L.Robinson CLF See a reduction in E max. 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.

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

7. A.P.L.Robinson CLF 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. A.P.L.Robinson CLF Sensitivity Also tried reducing density of SUP to 5 x 10 26 and 2.5 x 10 26 m -3 Peaks still occur. Not a “chaotic” sensitivity to initial conditions

9. A.P.L.Robinson CLF PIC simulations 1D3P EM PIC code used. 400nm foil at 4 x 10 28 H & 4 x 10 28 heavy ion (80n crit ) Foil placed at 60μm 40fs sin 2 pulses MDP a 0 = 4 Comparison run with MDP only. MDP SUP

10. A.P.L.Robinson CLF PIC Results SUP a 0 = 2: Red SUP a 0 = 1:Magenta Single Pulse Ref.: Black We obtain similar results to Vlasov simulations Reduction in E max Spectral Peaks

11. A.P.L.Robinson CLF But is this the same mechanism? A.P.L.Robinson CLF Consider run II (SUP a 0 = 2) So the first stage is v.similar, but no `wave-breaking’ Still see 2-stage mechansim. Proton density spike produced Protons Heavy ions

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

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

14. A.P.L.Robinson CLF …and some issues (I). Simulations at reduced density (10n crit ) result in over-optimistic predictions.

15. A.P.L.Robinson CLF …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. A.P.L.Robinson CLF 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. A.P.L.Robinson CLF 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.