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Appendix B: Supplemental Information on the Underlying Laser Technology
Pages 172-262

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From page 172...
... The host materials, besides keeping the laser-active ions in place, also interact with levels in several important ways. In a static sense, the atoms surrounding the active ions lower the symmetry of the paramagnetic-ion environment and "activate" transitions between the energy levels in the same shell, which would otherwise be dipole-forbidden in free-space surroundings.
From page 173...
... Each blue line represents a cluster of individual energy levels. SOURCE: Courtesy of Kansas State University, Department of Physics, http:// perg.phys.ksu.edu/vqm/laserweb/ch-6/6-15.gif.
From page 174...
... In the engineering of lasers, an important calculation is the power gain for amplifying the laser wavelength, G, in a length, z, of material (with only two energy levels participating) from stimulated emission.
From page 175...
... We will return to the discussion of cross sections after we consider the issue of linewidth. As discussed in the Technology History section, the development of laser mode-locking led to the generation of short pulses in the picosecond (ps)
From page 176...
... Since each ion is in the same surrounding, this type of broadening is called "homogeneous." We noted above that the energies of the ion levels depend on the ion environment, and when this varies from one ion to another then the overall laser linewidth becomes a superposition on all of the different energies, leading to another effect on linewidth, "inhomogeneous broadening." This effect can occur in crystals that have multiple environments for the ion, but it is most pronounced in glasses, where the lack of a well-ordered atomic structure, and thus a widely varying environment for the laser ions, leads to linewidths that are more than an order-of-magnitude larger than in single-environment crystals. The linewidths are large enough so that the structure evident in the absorption and emission spectra from Nd ions in crystals resulting from the existence of multiple, closely spaced energy levels is smoothed out to give the appearance of one continuous "band." FIGURE B.2  Gain cross section as a function of wavelength for two commonly used Nd-doped glasses.
From page 177...
... We plot the laser-ion energy level as a function of the distance from the surrounding ions, for the simple case where all of these ions change position in the same manner, the so-called "breathing mode" of ion motion. There is some minimum energy of the overall system, an equilibrium position, such that a displacement in either direction leads to a higher energy.
From page 178...
... The major drawback to these first vibronic lasers was that, because of thermally induced non-radiative processes between the laser energy levels, relatively low-threshold operation with lamp pumping required cooling of the laser crystals to cryogenic temperatures. Moulton reported the first laser operation from the 3d ion Ti3+ in the same host crystal Al2O3 (sapphire, the material, not the gemstone)
From page 179...
... The difference between the observed emission spectrum and the gain cross section reflects corrections needed to follow Einstein's formulation for gain from stimulated emission.5 Of note is the very broad gain linewidth, about 100 THz. This has allowed generation of 3.6-fsduration pulses at 800 nm,6 slightly more than one optical cycle, the shortest yet generated directly by a laser.
From page 180...
... For a laser pulse to efficiently extract the TABLE1 B.1  Key Characteristics of Common Solid-State Laser Materials Wavelength Storage time Cross section Gain linewidth Saturation Material (nm) (msec)
From page 181...
... The laser material must be capable of being optically pumped with good conversion of pump energy into stored energy. Until the last decade, the only practical, affordable pump source for high-energy systems was flashlamps or pump lasers based on flashlamps.
From page 182...
... Equation B.2 points out the fundamental relations between storage time, gain cross section (and hence saturation fluence) , and linewidth, and one result is the challenge in finding materials that have both large linewidth and a low Esat.
From page 183...
... . In terms of amplifier performance, Figure B.5 provides a good illustration of the relation among operating fluence, pulsewidth, and output energy, for the case of the present 1053-nm NIF final amplifier stage, which operates with a square beam cross section of 37.2 cm and a double-pass configuration.9 At short pulsewidths, energy limits come about from nonlinear effects in the glass, which lead to the generation of intensity peaks in the beam and optical damage to the material, while at long pulsewidths the limit is from the available input energy to the amplifier.10 The reduction in allowable output energy with shortening pulsewidth illustrates why the CPA technique is key to generating PW-class laser systems.
From page 184...
... Due to the lack of long-range structure, glass has poor thermal conductivity, as phonons that transport heat in electrically insulating materials like glasses cannot travel far without being scattered. The conductivities of common laser glasses are about 25x lower than for YAG, a common laser host, and about 50x lower than sapphire.
From page 185...
... Typical laser glasses have values of the thermal shock parameter in the 40-140 W/m range, while crystal hosts such as YAG and sapphire have values of 1,450 and 3,400, respectively.11 The problems of poor thermal conductivity in glass are magnified by the large material volumes required for high energies, which lead to relatively long paths for heat flow and thus large temperature gradients. High-energy systems, to date, mainly operate at such low pulse rates (several per min to per day)
From page 186...
... The ultimate limitations due to thermal fracture remain the limit to pulse rate and hence laser average power. Petawatt Glass System Examples At present there are a number of PW-class, Nd:glass-based systems worldwide, as shown in Table 4.2 from Chapter 4.
From page 187...
... energy levels of the laser transition, and thus a broader linewidth, shifted 14   M.D.Perry, et al., 1999, Petawatt laser pulses.
From page 188...
... For the latter, the devices are referred to as optical parametric chirped-pulse amplifiers (OPCPAs)
From page 189...
... The general approach to building the higher-energy "custom" systems is to employ multiple identical pump lasers, each of which is engineered to operate at an energy and average power limited by the choice of the laser technology, at this writing based on either lamp-pumped Nd:YAG or Nd:glass lasers. Energy- and average-power scaling is done by adding more pump lasers, up to technical limits set by ASE, thermal effects in the Ti:sapphire final stage amplifier, or practical limits set by funding.
From page 190...
... 8235, doi: 10.1117/12.908127. © 2012 Optical Society of America.
From page 191...
... At present the system, a photograph of which appears in Figure 2.3, operates at the 40 J output level with a 30-ps pulse, for a peak power of > 1.3 PW. While Ti:sapphire systems can operate at lower energies to reach the PW level compared to Nd:glass, the larger gain cross section of the gain medium presents an ASE challenge, notably in the large-diameter disk-configuration final stages where the gain transverse to the extraction beam can lead to significant losses in stored energy and/or parasitic oscillations arising from reflections at the disk edges.
From page 192...
... ,22 which makes use of the timing of multiple extraction passes through the amplifier to control the excited-state population in the laser material. EDP is only available to ns-pulse-pumped lasers such as Ti:sapphire.
From page 193...
... starting when all the pump energy has been accumulated in the gain medium, is timed to extract some of the stored energy at different times during the pumping process. The timing of the two pump pulses also helps to manage the peak stored energy in the 5.3-PW system.
From page 194...
... Wang, X Wang, et al., 2015, High-energy large-aperture Ti:sapphire amplifier for 5 PW laser pulses, Opt.
From page 195...
... Appendix B 195 At present there are a number of 0.1 PW and higher Ti:sapphire-based systems worldwide, as shown in Table 3.3 in Chapter 3. We return to a discussion of this technology in Appendix B3 in terms of future advances.
From page 196...
... The linear term for polarization has the effect of making light propagate through the material at a slower speed than in a vacuum which varies with wavelength λ, where the speed is c/n, with c the vacuum speed of light and n the refractive index of the material. At higher intensi ties, the accurate modeling of the displacement, or polarization, requires the inclu sion of terms that include the square, cube, and higher-orders of the electric field.
From page 197...
... Energy conservation requires that the power conversion of pump to signal and pump to idler is given by the ratio of the signal to pump and idler to pump frequencies, often referred to as the Manley-Rowe relation, which was derived from early work at radio frequencies. The same equations show that to produce appreciable amounts of amplification as the light travels through the material, all the electric fields of the light waves involved need to maintain a constant phase relationship.
From page 198...
... The simplest birefringent crystal is uniaxial, that is, there is an "optic axis" in the material along which the refractive index experienced by the light in that direction is independent of its polarization. Light going along any other direction experiences a refractive index that is polarization dependent, where the difference in refractive index between different polarizations depends on the specific direction of propagation.
From page 199...
... The other criterion is that the parametric gain has sufficient bandwidth to amplify an ultrashort pulse. If one utilizes a narrow-band pump laser, the bandwidth of an OPA is determined by how rapidly the phase-matching condition deviates from the condition set by equation B.7 as the signal frequency changes.
From page 200...
... P Wild, 1995, Noncollinear parametric gen eration in LiIO3 and b-barium borate by frequency-doubled, femtosecond Ti:sapphire laser pulses, Opt.
From page 201...
... Luchinin, et al., 2007, Compact 0.56 Petawatt laser system based on optical parametric chirped pulse amplification in KD* P crystals, Laser Physics Letters 4(6)
From page 202...
... Collier, 1997, The prospects for ultrashort pulse duration and ultrahigh intensity using optical parametric chirped pulse amplifiers, Opt. Commun.
From page 203...
... Kirsanov, G.A. Luchinin, et al., 2007, Compact 0.56 Petawatt laser system based on optical parametric chirped pulse amplification in KD*
From page 204...
... : Optical Parametric Chirped-Pulse Amplification In contrast to the Russian OPCPA work, the SIOM has reported a 1-PW peak power system employing a large-aperture LBO crystal.27 The source, as shown in Figure B.15, employs a Ti:sapphire CPA system to provide a 800-nm-centered, 1.9-ns-duration chirped pulse with as much as 2.25 J of energy. A single OPCPA stage, employing a 100 x 100 mm-aperture, 17-mm-thick crystal, amplifies the CPA signal input to an energy of about 45 J, compressed to 32.6 J of energy with a 32-fs-duration pulse.
From page 205...
... Hu, C Wang, et al., 2015, Optimization for high-energy and high-efficiency broadband optical parametric chirped-pulse amplification in LBO near 800 nm, Opt.
From page 206...
... This results in less heat left in the laser material compared to lamps, which, especially for near-infrared lasers, pump a multitude of higher-lying energy levels. In addition, lamps produce a large fraction of power that does not pump the laser material at all.
From page 207...
... A narrow spatial beam compared to the incoherent emission in all directions from a lamp, allowing better matching of the pump energy to the desired region in the solid-state gain medium, and thus higher conversion of pump power into laser power for some laser configurations. The net result of the use of diodes is a much higher overall electrical efficiency for diode-pumped solid-state lasers, at least an order-of-magnitude, and, for a given power output, a much reduced level of waste heat in the laser material.
From page 208...
... laser, so the amount of pump power density needed to achieve gain is higher compared to Nd-doped lasers. This can be overcome with the high pump power densities possible with diode pumping or by cooling the laser material to reduce the population of the lower level and hence the absorption.
From page 209...
... For PW-level, high-energy systems, which have been, with the exception of BELLA, based on flashlamp-pumped Nd:glass, the pump laser has relied on passive air cooling for the laser material as well as the flashlamps. The firing of the next shot has to wait until components have returned to ambient temperature.
From page 210...
... Figure B.18 and Figure B.19 show two approaches used for large-aperture designs, involving flow ing a coolant between a series of relatively thin disks of laser material. The first employs rapid flow of helium gas through the disks, which was demonstrated at 31   R
From page 211...
... The issue is of concern since nonlinear materials in general do not have good thermo-mechanical properties. As an example, the thermal shock parameters of KD*
From page 212...
... For fused silica, which has a very low thermal expansion coefficient, the thermal shock parameter (1,450 W/m) is similar to materials such as YAG, but more importantly, for typical cladding-pumped fiber lasers the length of material used in a laser is in the 120m range, about 1,000x that of typical rod lasers.
From page 213...
... While the overall electrical efficiencies, high average power, and high beam quality of fiber lasers make them unique as solid-state lasers, the small diameter of the single-mode active core (on the order of 10-100 µm) limits the pulsed, peakpower outputs of individual fiber lasers.
From page 214...
... For that, multiple sources must be coherently combined, either spatially to get higher brightness or spectrally to produce shorter pulses and hence higher peak powers. Coherent combining of cw lasers requires precise control over the relative phases of the lasers so that the rapidly varying electric fields of the lasers all peak at the same time as well as overlap in space.
From page 215...
... The latter allow operation at high enough pulse rates to enable effective feedback control of beam and/or spectral combining. However, given the mJ-level of pulse energy now available from individual fibers, the absolute numbers of fiber lasers required to reach the PW-peak-power region goes well beyond the current state of the art.
From page 216...
... Spatial -- Common Pulse 22 GW of peak power has been obtained through the coherent combina tion of four very-large mode-area (80 µm) Yb:fiber lasers.44 An optical schematic of the system, Figure B.20 shows a CPA system, where a common, low-energy, stretched pulse is amplified, spectrally optimized by a spatial-light-modulator based "Pulse-Shaper" (also seen in Figure B.7)
From page 217...
... in 2-ns-duration pulses in the amplifiers, the nonlinear effect of the high peak power on the refractive index and hence the optical phase in the final amplifiers (self-phase modulation, or SPM) was significant, about 5 radians of shift, and thus the phase delay through the amplifiers depended strongly on the pulse peak power.
From page 218...
... The image presented to the camera is a set of spatially distinct interference patterns that can be processed to derive the phase control for each fiber amplifier. The present plan seeks a short-term demonstration of a 61-fiber system with pulse energy of 10 mJ, with 50-kHz pulse rate, 350-fs pulses.
From page 219...
... In one system separate splitting and combining optics were used to produce 4 pulses, with path-length control provided by a LOCSET control system, and individual control of pulse amplitudes in the optics provided some compensation for gain saturation in the Yb:fiber amplifier.48 The system generated 380-fs-duration compressed pulses of 1.25 mJ (2.9 GW) at a 30-kHz rate, with a recombination efficiency of 75 percent.
From page 220...
... Leemans, and A Galvanauskas, 2016, "Progress in Coherent Pulse Stacking: A Pathway Toward Compact kHz Repetition Rate LPA Drivers," 17th Advanced Accelerator Concepts Workshop, Aug.
From page 221...
... Leemans, and A G ­ alvanauskas, 2016, "Progress in Coherent Pulse Stacking: A Pathway Toward Compact kHz Repetition Rate LPA Drivers," 17th Advanced Accelerator Concepts Workshop, Aug.
From page 222...
... Hu, C Wang, et al., 2015, Optimization for high-energy and high-efficiency broadband optical parametric chirped-pulse amplification in LBO near 800 nm, Opt.
From page 223...
... Dividing the input pulse spectrum into several spectral regions can allow Yb:fiber lasers to produce shorter pulses. In one low-power demonstration,56 a broadband input source was split into two spectral bands, which peaked at 1,026 and 1,040 nm, and each was input to a Yb:fiber CPA and then combined, with phase control on one beam provided to lock the phases.
From page 224...
... External Cavity Peak Power Enhancement Pulses repetitively injected into an external, low-loss resonator, if synchronized with the resonator round-trip time, can build up in peak power through addi tive combination, or "pulse stacking," which can be viewed as a variation on the technique of divided pulse amplification. For fiber lasers, pulse stacking allows the device to operate with relatively low-energy pulses at a high pulse rate -- a favorable operating condition for this technology.
From page 225...
... gratings, essentially a form of coherent spatial beam combination. The technique requires the same level of alignment, path-length, and phase control applied to coherent beam-combining.
From page 226...
... In the top of the figure, a high-energy, long-pulse pump beam, moving from left to right in the plasma, encounters a low-energy, short-duration seed pulse at the signal frequency, moving in the opposite direction. The bottom of the figure represents a later point in time when the amplified seed pulse becomes large enough in energy to remove a large fraction of the pump energy, essentially compressing a portion of the pulse energy into roughly the same duration as that of the seed.
From page 227...
... A Norreys, ­ 2011, Production of picosecond, kilojoule, and petawatt laser pulses via Raman amplification of nanosecond pulses, Phys.
From page 228...
... Li, and S Suckewer, 2007, A new method for generating ultraintense and ultrashort laser pulses, Nature Phys.
From page 229...
... Sergeev, 2014, Single cycle thin film compressor opening the door to ZeptosecondExawatt physics, Eur.
From page 230...
... Figure B.29 is a functional block diagram of the system, showing the staging and details of the energetics and pulse/spectral properties, and Figure B.30 is an optical schematic of the design. The goal is to generate 150-fs-duration pulses FIGURE B.29  Block diagram of 10-PW Nd:glass laser under construction at National Energetics.
From page 231...
... and 30-cm-aperture, Nd:phosphate glass final amplifier stages (Power amplifier 2)
From page 232...
... The laser requirements for Laser Ignition Fusion Energy (LIFE) called for a megajoule-class, ns-pulse laser that would operate at a pulse rate of 16 Hz.
From page 233...
... At 10 Hz the system would operate the Ti:sapphire laser at the highest average power ever attained from the material. As of December 2016, the system had operated with the pump laser at an intermediate milestone of >100 J of fundamental energy, 75 percent conversion to the second harmonic, and operation of the Ti:sapphire source with < 30 fs pulsewidth.68 High Field-Petawatt, Extreme Light Infrastructure-Attosecond Pulse Light Source In contrast to the HAPLS system, the ELI-ALPS facility in Szeged, Hungary was scheduled to obtain a 10Hz, 2PW Ti:sapphire laser that employs flashlamp-pumped pump lasers, for the so-called HF PW System.69 A schematic of the system appears in Figure B.34.
From page 234...
... FIGURE B.33  Photograph of one of four 800-kW diode-laser array used in the HAPLS pump laser. SOURCE: Courtesy of Lawrence Livermore National Laboratory.
From page 235...
... in cooperation with their subsidiary, Continuum (San Jose, CA) , would include newly designed pump lasers providing 60 J of energy from a single beam.70 Also in contrast with the HAPLS system, the design would seek to operate with 17-fsduration pulses, thus requiring 34 J of pulse energy, compared to the 30 J design for the LLNL system.
From page 236...
... Nd:glass lasers. Figure B.37 shows a photograph of one completed ATLAS system, while Figure B.38 shows a drawing of the complete system as it will be installed at ELINP.
From page 237...
... at ELI-NP," presented at ELI Beamlines Summer School, Aug. 24-29, Prague, Czech Republic, http://www.eli-beams.eu/wp-content/uploads/2013/11/Dabu_high_power_laser_system_at_eli-np.pdf.
From page 238...
... FIGURE B.37  Photograph of ATLAS flashlamp-pumped Nd:glass laser providing 100 J of 527-nm energy at a pulse rate of 1/minute.
From page 239...
... © Optical Society of America. in a Yb:KYW regenerative amplifier and further amplified in a Yb:YAG thin-disk regenerative amplifier to 150 mJ.
From page 240...
... Druon, et al., 2015, Design and current progress of the Apollon 10 PW project, High Power Laser Science and Engineering 3:e2. to the OPCPA stage.76 The mJ-level OPCPA output pulse is then set to amplified further to provide an input to the high-energy Ti:sapphire amplifier chain.77 The use of diode-pumping for all of the lasers in the front-end enables a 100-Hz pulse rate, an aid to the use of diagnostics and feedback controls that provide for a high stability seed source, even when the entire system runs at a much lower rate.
From page 241...
... The major issue to be resolved is whether the required gain and stored energy can be achieved before parasitic losses arise in the amplifier. Optical Parametric Chirped-Pulse Amplifiers 10 Petawatts at the Shanghai Institute for Optics and Fine Mechanics Also under consideration at the Shanghai Institute for Optics and Fine M ­ echanics (SIOM)
From page 242...
... at a pulse rate of one shot every 20 seconds. For over a decade the CLF has been engaged in the development of an OPCPA based source that would utilize the Vulcan laser as a pump source.
From page 243...
... L Collier, 2008, Optical parametric chirped-pulse amplification source suitable for seeding high-energy systems, Opt.
From page 244...
... Miyanaga, and Gekko-EXA Design Team, 2016, Conceptual design of sub-exa-watt system by using optical parametric chirped pulse amplification, Journal of Physics: Conference Series 688: 012044. 1, 20, and 50 Petwatts Gekko-EXA Since 2009 a group at the Institute of Laser Engineering (ILE)
From page 245...
... crystals, arranged for slightly non-collinear phase-matching to provide 600-nm gain bandwidths around 1,053 nm. 75-Petawatt Extended Performance-Optical Parametric Amplifier Line, Laboratory for Laser Energetics LLE has presented a conceptual design to build an OPCPA-based 75-PW source (EP-OPAL)
From page 246...
... SOURCE: J Bromage, University of Rochester, "Ultra-High Intensity Laser Technology," presentation to the committee on July 14, 2016.
From page 247...
... subsequently amplified by three picosecond-pulsewidth-pumped NOPAs and then stretched to a 1.5-ns pulsewidth for further amplification by OPCPAs. The use of the relatively low-pulse-rate WLC makes possible a high pulse-contrast ratio compared to a mode-locked source, where the high pulse rate can make suppression of nearby (in time)
From page 248...
... , presumably OPCPA-based, as part of a facility called the Station of ­ xtreme Light Science (SEL) at X-ray FEL, where the possibility of combining E the source with an X-ray FEL will provide a unique experimental capability.89 Yb-doped Materials As discussed in Appendix B3, the development of diode pumping opened a variety of new approaches to the operation of solid-state lasers and a whole class of laser materials based on the rare-earth dopant Yb.
From page 249...
... Appendix B 249 FIGURE B.47  Optical schematic of proposed 200-PW XCELS system.
From page 250...
... in operation at the Helmholtz Institute in Jena, Germany, employs m a mix of diode-pumped Yb:glass and Yb:CaF2 media as amplifiers.90 The Yb:glass media are used for all but the final stage of the system because of their large gain bandwidth, but this does lead to a limited pulse rate of 0.02 Hz even with diode pumping. A schematic of the system, in Figure B.48, shows a double-CPA design, where pulses from a mode-locked Ti:sapphire laser at 1,030 nm are stretched to 20 ps, regeneratively amplified, compressed, and then passed through an XPW stage 90   M
From page 251...
... Thus the final stage of the system, with 1.2 MW of diode peak pump power, will utilize a pump energy of 1.8-5 kJ, leading to optical efficiencies well below 10 percent. Operation at the 0.1-PW level (15 J in 150 fs)
From page 252...
... Albach, and U Schramm, 2013, "PEnELOPE - a high peak-power diode-pumped laser system for laser-plasma experiments," in High-Power, High-Energy, and High-Intensity Laser Technology; and Research Using Extreme Light: Entering New Frontiers with Petawatt-Class Lasers, (J.
From page 253...
... To date, with gas cooling at 175 K, the system has generated a 10-ns output pulse with 107 J of energy. The pulse rate was limited to 1 Hz by issues with the cooling system, but the goal is 10Hz operation, and cooling to 150 K
From page 254...
... called, in one publication,95 for a 30-J/pulse, 30-fs output at kHz rates, but a later publication discussed goals of >10 J per pulse, a >10 kHz pulse rate with pulses of 100–200 fs duration.96 The longer pulsewidth in the later publication recognizes that, with the properties of Yb:fibers, a 30-fs pulse would require spectral beam combination in addition to spatial combination. Given the notional design of 1 mJ/fiber, the system requires > 10,000 fiber lasers to meet the output-energy requirements.
From page 255...
... fiber and the pulse intensity, adding in the need to match and control the energy out of each fiber. Obtaining a high pulse contrast is problematic, as ASE is a major issue with fiber lasers and there is no evident technique in ICAN to suppress ASE to the levels required by many applications.
From page 256...
... • About 103 photons/electron, at 1 Å, compared to about 10−2 for spontane ous radiation, more at longer wavelengths. Free Electron Laser Basic Concepts and Technology Free-electron lasers use relativistic electrons as a gain medium.
From page 257...
... Wavelength range 0.11–4.4 0.275–0.063 5.1–0.04 0.6–0.1 7–0.1 1.2–0.05 (nm) X-ray pulse energy 1–3 for 0.1<λ<1.5 0.2–0.4 for 0.67–8.5 for 0.81–1 for 0.5–1.3 for 1–4.5 for (mJ)
From page 258...
... 0.5@λmin 0.1@λmin 0.01@λmin 0.4@λmin 0.02@λmin Pulse duration, 15–100@λmax, Depending on seed pulse duration 6–50 6–50 rms (fs) 15–100@λmin and harmonic order, typically 40–100 Linewidth, rms 0.2@λmax, 0.1 0.2–0.05 (%)
From page 259...
... For the present, however, current sources such as LCLS are not Fourier transform limited at the highest energy levels, and also the technology of X-ray mirrors prevents focusing to waists on the order of the wavelength,104 and so the highest focused intensity for an X-ray FEL is far below this limit. Measured 102   L.R.Elias et al., 1976, Observation of stimulated emission.
From page 260...
... LCLSII-1.1-DR-0001-R0, 2014. intensities are in the range of 1020 W/cm2, which is below the highest intensity available with optical frequency lasers.105 Average Power The current average power for these sources is on the order of fractions of a watt (millijoules at 120 Hz)
From page 261...
... H Yu, 1991, Generation of intense UV radiation by subharmonically seeded single-pass free electron lasers, Physical Review A 44(8)
From page 262...
... Penn, 2005, Obtaining attosecond x-ray pulses using a self-amplified spontaneous emission free electron laser, Physical Review Special Topics - Accelerators and Beams 8(5)


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