1. Pulse Shaping & Energy Capabilities of Angularly-Multiplexed KrF Lasers 17 th HAPL Meeting Naval Research Laboratory October 30-31, 2007 R. H. Lehmberg RSI/NRL Washington, DC Work supported by USDOE/NNSA/DP

2. One of the primary requirements for laser-driven inertial fusion energy (IFE) is the ability to produce high energy pulses with the temporal shapes needed to control hydrodynamic instabilities and target preheat. Although this capability has been well established on glass lasers such as the National Ignition Facility (NIF), it is less certain on Krypton Fluoride (KrF) lasers, where the large multi-beam angularly multiplexed amplifiers tend to have heavy saturation, high gains, & complicated gas kinetics. Saturation can produce severe pulse distortion, and high gains may allow excessive target preheat due to near-axial amplified spontaneous emission (ASE). This poster reviews the steps required to minimize pulse distortion & ASE, then describes and simulates a robust technique to produce the desired pulseshape by pre-compensating the distortion. Although the pulse shaping and ASE considerations are applicable to any large KrF laser, the simulations presented here apply to the ~30 kJ system designed for the recently-proposed NRL Fusion Test Facility (FTF). Introduction

3. Using the Orestes code, we have modeled the energy and pulse shaping capabilities of the KrF laser in our proposed Fusion Test Facility (FTF) We developed a simple & stable iteration technique for calculating the pre-distorted input pulseshape required to achieve the desired output pulseshape. The simulations show that KrF amplifiers can behave as quasi-storage lasers for 1 ns pulsewidths & pulse spacings Our FTF design allows energies up to 30 kJ from each of our 20 amplifier systems without excessive ASE prepulse on target It may be possible to generate the complicated pre-distorted input pulses by using an optical Kerr gate Main Results

4. 28 kJ KrF laser Amp (one of 20) Containment Vessel Laser Beam Ducts Reaction Chamber 28 kJ KrF Laser Amp (one of 20) Containment Vessel Laser Beam Ducts Reaction Chamber Conceptual Design of the FTF (M. W. McGeoch, Plex Corporation ) Laser energy on target: 500 kJ Fusion Power: 30 - 150 MW Rep Rate: 5 Hz Chamber radius: 5.5 m

5. FTF Optical Block Diagram (one of 20) T. Lehecka, Penn State Electro-Optics Center Front End Amp1 Mirror Fixed Amp Mirror Fixed Amp2 225ns, ~1kJ 225ns, ~30kJ Final Amplifier (100 x 100 cm 2 ) Driver Amplifier (30 x 30 cm 2 ) ~ 20  30 J input in 90 sequential pulses, one/beam ~ 30 kJ out ~ 1.2 kJ ~ 28 kJ in 90 synchronized pulses, one/beam  Target Chamber X615 Lenses 6X15 Convex Mirrors 6X15 Flat Mirrors 6X15 Convex Mirrors Oscillator 5Hz Rep Rate Beam Smoothing Pulse Shaping 2.5ns plus foot pulse Object 15beam splitter. 5 2 Amp4 ns ~2 J 15 beam Multiplexer – 38 ns 90 beam splitter Amp 3 38 ns 20 - 30 J 90 beam Multiplexer 225 ns 90 beam De-multiplexer 225 ns  2.5 ns Output optics The simulations deal primarily with the driver & final amplifier results

6. One of 90 Target Beams ASE Rays (cw)Mirror Pumped KrF (not drawn to scale) Input Array (6 X 15) Output Array (6 X 15) Because of its large angular divergence & cw time dependence, ASE can preheat the target via beam channels intended only for earlier pulses M. Karasik, et al, J. Appl. Phys. 98, 053101 (2005) On-target ASE intensity ramps up as: I ASE (t) J G DRVR (t)G FINL (t)N B (t ) G DRVR (t)G FINL (t) are the gains & N B (t) is the increasing number of beams whose demultiplexed paths allow light to reach the target at time t

7. The simulations are based on our 30 kJ final amp design

8. Baseline Case: Desired pulseshapes (2.5 ns main pulse + 6 ns foot pulse) into the driver amplifier Time (ns) I IN (MW/cm 2 ) Control Beam Buffer Beam (I 0 ) I TOT Beams I 1,I 2,..,I 90 Time (ns) I IN (MW/cm 2 ) P EB P EB (MW/cm 3 ) Control beam loads down the amplifiers during e-beam ramp-up, thereby preventing high gains & large target ASE at early times Buffer beams (I 0 & I 90 ) minimize distortion of earliest & latest beams Total input energy of target beams (I 1,..,I 90 ) is 90 x 0.25 = 22.5 J

9. Time (ns) I OUT (MW/cm 2 ) P EB (MW/cm 3 ) I ASE (MW/cm 2 ) @ Final Amp I TOT I1I1 I3I3 I 88 I 90 In spite of their contiguous placement, the pulses out of the final amp are still distorted by saturation Total output energy of the 90 target beams is 30.4 kJ

10. Time (ns) I OUT (MW/cm 2 ) Pulse to pulse variations remain small, in spite of changes in the gas kinetics (e.g., Fluorine burnup) This suggests possible pre-compensation with a single input pulseshape

11. Iteration Technique First, estimate highest energy available from the final amp within constraints on driver input (Saturation  small changes in output energy require much larger % changes in input) E IN > 40 J would require an additional front end amplifier E IN < 20 J would lower efficiency and give higher driver gain & ASE (Estimates require only a single beam with a rectangular 225 ns pulse.) Then scale the intensity I S (t) of the desired pulseshape to give the estimated output energy in 90 beams. 0th iteration: Initially, the driver input pulses are the same shape as the desired output (baseline case) but scaled down to the 20-30 J input energy: I IN (0) (b,t-t b ) = η I S (t) (η ~ 10 -3 ) for each beam b = 0,1,..,90,91. The final amp output pulses I OUT (0) (b,t-t b ) will be distorted. Subsequent iterations: Choose one of the 92 beams b REF to represent all others (e.g., b REF = 34) Replace each driver input pulse by its partially compensated version; e.g. the 1st iteration uses I IN (1) (b,t-t b )=I IN (0) (b,t-t b )[I S (t)/I OUT (0) (b REF,t-t REF )] then recalculate to update the output pulses I OUT | (1) (b,t-t b ). Continue this procedure, replacing I IN (N) (b,t-t B )=I IN (N-1) (b,t-t b )[I S (t)/I OUT | (N-1) (b REF,t-t REF )] in each driver beam until the output I OUT (N) (b REF,t-t REF ) of the reference beam is close enough to the ideal pulseshape I S (t). The pre-distorted input pulse I IN (N) (b REF,t-t REF ) is then stored in a data file and subsequently used to generate the full 92 beam simulations shown here. This procedure could be modified to pre-correct each beam independently, if necessary.

12. Pre-distortion of the driver input pulses produces the desired output shape in the reference beam I IN (MW/cm 2 ) Time (ns) I OUT (MW/cm 2 ) Time (ns) Ref. Beam Ideal Pulse Time (ns) I IN (MW/cm 2 ) Control Beam Buffer Beam (I 0 ) I TOT Target Beams (I 1,I 2,…,I 90 ) Total input energy of target beams (I 1,..,I 90 ) is 90 x 0.25 = 25.2 J

13. The idea works well for all 90 beams Time (ns) I OUT (MW/cm 2 ) P EB (MW/cm 3 ) I ASE (MW/cm 2 ) I TOT I REF I45I45 I1I1 I3I3 I 88 I 90 Total output energy of the 90 target beams is 30.4 kJ

14. Time (ns) I OUT (MW/cm 2 ) Magnified views of selected beams show little distortion, even in the earliest pulses

15. On-target ASE is very low because the contiguous pulses continually load the amps and limit the gain Time (ns) Intensity on Target Fluence on Target I PULSE [10 13 W/cm 2 ] I ASE [10 5 W/cm 2 ] F PULSE [10 5 J/cm 2 ] F ASE [10  1 J/cm 2 ] There is enough margin here to allow lower input energies (e.g. ~ 10 J)

16. I IN (MW/cm 2 ) Time (ns) Now apply the idea to something more challenging: an RX pulse with a 2:1 shock ignition spike at the end I IN (MW/cm 2 ) I OUT (MW/cm 2 ) Ref. Beam Ideal Pulse Time (ns) Control Beam Buffer Beam (I 0 ) I TOT Target Beams (I 1,I 2,…,I 90 ) Total input energy of target beams (I 1,..,I 90 ) is 90 x 0.31 = 27.9 J

17. Time (ns) I OUT (MW/cm 2 ) P EB (MW/cm 3 ) I ASE (MW/cm 2 ) I TOT I REF I MID No unpleasant surprises here Total output energy of the 90 target beams is 30.3 kJ

18. Time (ns) I OUT (MW/cm 2 ) Significant distortion occurs only in the 1 st pulse, which can be fixed by modifying the control beam

19. Time (ns) For something even more challenging, the pulses are now only 1ns FWHM and non-contiguous I IN (MW/cm 2 ) Time (ns) I OUT (MW/cm 2 ) Ref. Beam Ideal Pulse I IN (MW/cm 2 ) Control Beam Buffer Beam (I 0 ) I TOT Target Beams (I 1,I 2,…,I 90 ) Total input energy of target beams (I 1,..,I 90 ) is 90 x 0.31 = 29.7 J

20. Time (ns) I OUT (MW/cm 2 ) P EB (MW/cm 3 ) I ASE (MW/cm 2 ) I TOT I REF I MID This regime demonstrates KrF storage laser capability for pulses ~1 ns, but enhanced ASE may be an issue Total output energy of the 90 target beams is 26.9 kJ

21. Time (ns) I OUT (MW/cm 2 ) Shape fidelities are not as good as those of the longer pulses, but the pulse energies are still ~90% as large.

22. Intensity on Target Fluence on Target F PULSE [10 5 J/cm 2 ] F ASE [10  1 J/cm 2 ] Time (ns) I PULSE [10 13 W/cm 2 ] I ASE [10 6 W/cm 2 ] On-target ASE is enhanced because inter-pulse spacing allows high transient gains, but it is still not a problem

23. z E I (ISI, t-dep. pol.) E C (coherent pulse, 1054 nm, 45 o pol.)  (3) Medium E I (ISI cw, 248 nm, x-pol.) x E Iy (ISI pulse, y-pol.) x x y-Polarizer @ 248 nm x So how can we generate those ugly pre-distorted input pulseshapes? Take advantage of NIF fiber optic technology @ 1054 nm, then transfer pulseshape to 248 nm ISI light via an optical Kerr gate The proposed Kerr gate would allow a coherent pulsed 1  m control beam of high intensity I C (t) to impose the desired pulseshape on the envelope of a cw 248 nm ISI beam via polarization rotation. The time-dependent ISI intensity transmission at the exit of the y-polarizer is: T(t) = sin 2 [  (t)/2] where  (t) J L  248 (  xxyy +  xyyx ) I C (t)

24. Summary & Conclusions Using the Orestes code, we have modeled the energy and pulse shaping capabilities of the KrF laser in our proposed Fusion Test Facility (FTF). We developed a simple & stable iteration technique for calculating the pre-distorted input pulseshape required to achieve the desired output pulseshape. It may be feasible to carry out this technique experimentally on the rep-rated laser. The simulations show that KrF amplifiers can behave as quasi-storage lasers for 1 ns pulsewidths. Our FTF design allows energies up to 30 kJ from each of our 20 amplifier systems without excessive ASE prepulse on target. The ASE is so small that it might be feasible to use lower energy input pulses (at a minor loss in efficiency). It may be possible to generate the complicated pre-distorted input pulses by using an optical Kerr gate.