“Sizing” of solid state laser driver requirements for inertial fusion energy 1) Efficiency > %, including cooling Key issue is recycled power: f recycle = 1 / [  M  eff G] For fusion gain G = 100 and thermal-to-electrical e M = 0.45: -  eff = 0.10 gives recycled power fraction f recycle =  eff = 0.15  f recycle =  eff = 0.07  f recycle = 0.21 (for G = 150) 2) Cost < $ 1B for 2 MJ laser driver, or $500/J [E 3w / (  opt  em )] C diode = $0.5 B (E 3w = 2 MJ, t em = 1 msec,  opt = 0.2, C diode =5¢/W) “Rest of laser” cost taken as $0.5 B (Orth, et al.) 3) Repetition rate of ~10 Hz Limited by clearing rate of chamber, highest feasible rate 5) Beam smoothness of <0.1 % in 1 nsec on-target Beam smoothness can roughly be described with: * 1 /  ( 0  ℓ ) 2 = (  t )  tot ( d targ / ℓ ) 2 (  / 2) Using  = s -1 (bandwidth), t = s (target response time),  tot = N beams / (F#) 2 = 0.05, d targ = 0.4 cm, ℓ = 200 (ℓ-mode)  yields  = 0.1 % Smoothing by spectral-dispersion (SSD) and phase plates (using several color cycles) needed to produce suitable beam SSD requires that: d spot = d target / 5 * J. Rothenberg 4) Reliability of >10 8 shots ~10 10 needed for diode arrays >10 8 shots needed for other components, depending on cost Learning curve analysis suggests that diode bar prices will continue to drop as the market grows IFE plant uses ~ 25M bars operating at 400W/bar “Bottoms –up” estimate of diode bars is ~3 ¢/W for fusion economy Mercury price IFE goal IRE “soft” quote of 35 ¢/W 59% learning curve Experience in the semiconductor industry is that price for “minimum function” experiences ~60% slope learning curve, IEEE Spectrum, June 1980, p.45. Anticipated diode bar price for IFE is judged reasonable from learning curve analysis Relative “figures of merit” (FOM) for gain media 1) Emission lifetime,  em -1 impacts diode costs If  pump =  em, pump efficiency is  pump = 63 % Total cost ($B) = 0.5 / [  em (msec)] 2) Saturation fluence, F sat impacts risk of optical damage For F out = 3.0 F sat, extraction efficiency   ext = (1 + F sat / F out ) -1 = 0.75 Damage is statistical, depending on optic and beam modulation (~1.5x) Peak output fluence is F peak = 4.5 F sat It is desirable for the optical fluence to be below 30 J/cm 2 to avert damage 3) Beam line energy, E beam impacts architectural complexity Nonlinear B-integral accumulation and ASE are “balanced” by optimizing the doping and optical path length Larger E beam simplifies the beam line, leading to an overall reduction in optics and mechanical part count On the other hand, it may be more difficult to “handle” higher power E beam =  ext (3 / 64) (  ℓ /  ) 2 F sat -1 4) Fill factor,  fill impacts efficiency Approach considers efficiency in terms of overlap of diode pump and laser beam FOMs for representative 1  m laser materials (a)Yb:S-FAP is further limited by stimulated Raman scattering (b) Nd concentration is limited due to clustering Colored boxes are favorable Where does beam modulation come from? One cause – nonlinear refractive index at high intensities can cause small scale focusing (filamentation) Why do we care? Optical damage and focusibility of the beam 0.75 cm 0.1 cm Mercury-like layout Reconstructed Image planes 25 cm NIF-like layout Now we compare two fusion laser concepts to minimize intensity modulation 0.75 cm Image plane (9 cm long) Slab spacing is a key cause of nonlinear ripple growth. The “B-integral” is a figure of merit for determining when a beam will filament For similar B-integral, the proximity of the laser slabs in Mercury-like architecture reduces nonlinear ripple The Mercury-like architecture will produce beams with less intensity modulation than the NIF-like architecture (assuming no pinholes) Far field for B = 3.8 radians If pinholes are used, then the Mercury-like architecture offers decreased pinhole loading relative to NIF-like architecture NIF-like architecture Mercury-like >1000 GW/cm 2 < 1 Pinholes are needed to control ripple growth and to avoid optical damage Design of Solid State Lasers for Inertial Fusion Energy Andy Bayramian, Stephen A. Payne, Ray Beach, and Camille Bibeau Lawrence Livermore National Laboratory, Livermore, California Figures of Merit Nonlinear beam propagation Amplifier material selection 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. Nd:SrF 2 performance versus aperture size 10 x 15 cm 2, 1.3 kJ 20 x 30 cm 2, 3.6 kJ 30 x 45 cm 2, 6.6 kJ B max Efficiency is limited by high saturation fluence of 10.6 J/cm 2 (i.e. B max < 3 radians) and low gain (i.e. losses) Doping level is limited to 3.8 x cm -3 by Nd clustering Path length = cm E B = 3 radians I pump = 21.3 kW/cm 2 Nd:glass performance versus aperture size Nd:glass is a favorable gain medium for fusion, although it demands reduced cost for the diode array pumps Doping = 2 x cm -3 Path length = 8.75 cm E B = 3 radians I pump = 21.3 kW/cm 2 10 x 15 cm 2, 1.2 kJ 20 x 30 cm 2, 3.3 kJ 30 x 45 cm 2, 5.3 kJ B max Yb:S-FAP performance versus aperture size, taking into account ASE, emission, extraction, losses and beam overlap Doping = 2 x cm -3 Path length = 7.9 cm E B = 3 radians I pump = 21.3 kW/cm 2 Assumes stimulated Raman scattering is not a limiting factor 10 x 15 cm 2, 1.7 kJ 20 x 30 cm 2, 4.2 kJ 30 x 45 cm 2, 8.3 kJ B max Yb:S-FAP is the most favorable gain medium, although stimulated Raman scattering may be an issue for apertures > 10 x 15 cm 2 Phase distortions introduced in image plane Phase transformed into amplitude modulation by propagation Nonlinear growth of amplitude ripples Image is relayed Original phase distortions reconstructed Out-of-relay ripples grow further I  Propagation and nonlinear effects I  Reconstructed Image planes Image plane (200 cm long) B = 8 Calculation doesn’t include lenses (small effect) = + + ….. Fourier decomposition Yb:YAG performance versus aperture size B max Efficiency is limited by high saturation fluence of 9.6 J/cm 2 (i.e. B max < 3 radians), low gain (i.e. losses), and high n2 Doping = 5 x cm -3 Path length = 10.5 cm E B = 3 radians I pump = 66.6 kW/cm 2 10 x 15 cm 2, 1.3 kJ UCRL-MI