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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 1, Iss. 7 — Nov. 1, 2011
  • pp: 1341–1352
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Comparison of Nd:phosphate glass, Yb:YAG and Yb:S-FAP laser beamlines for laser inertial fusion energy (LIFE) [Invited]

A. C. Erlandson, S. M. Aceves, A. J. Bayramian, A. L. Bullington, R. J. Beach, C. D. Boley, J. A. Caird, R. J. Deri, A. M. Dunne, D. L. Flowers, M. A. Henesian, K. R. Manes, E. I. Moses, S. I. Rana, K. I. Schaffers, M. L. Spaeth, C. J. Stolz, and S. J. Telford  »View Author Affiliations


Optical Materials Express, Vol. 1, Issue 7, pp. 1341-1352 (2011)
http://dx.doi.org/10.1364/OME.1.001341


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Abstract

We present the results of performance modeling of diode-pumped solid state laser beamlines designed for use in Laser Inertial Fusion Energy (LIFE) power plants. Our modeling quantifies the efficiency increases that can be obtained by increasing peak diode power and reducing pump-pulse duration, to reduce decay losses. At the same efficiency, beamlines that use laser slabs of Yb:YAG or Yb:S-FAP require lower diode power than beamlines that use laser slabs of Nd:phosphate glass, since Yb:YAG and Yb:S-FAP have longer storage lifetimes. Beamlines using Yb:YAG attain their highest efficiency at a temperature of about 200K. Beamlines using Nd:phosphate glass or Yb:S-FAP attain high efficiency at or near room temperature.

© 2011 OSA

1. Introduction

Interest in the development of laser fusion energy has been increasing in recent years, for several reasons. Demand for electrical power, particularly power that is carbon free, has been increasing. The National Ignition Facility (NIF), which uses a solid-state laser driver, is soon expected to achieve fusion ignition and gain, thus demonstrating the feasibility of the basic process laser fusion power plants would use to generate electricity. Additionally, a sea change is occurring in the cost, availability and performance of diode lasers, which enable solid-state lasers to operate at the high efficiency and repetition rate required for fusion power plants. Given these trends, it is not surprising that several groups have proposed to develop laser fusion energy based on solid-state laser drivers [1

1. E. I. Moses, “The National Ignition Facility (NIF): A path to fusion energy,” Energy Convers. Manage. 49(7), 1795–1802 (2008). [CrossRef]

7

7. H. Matsui, T. Eguchi, T. Kanabe, M. Yamanaka, M. Nakatsuka, Y. Izawa, and S. Nakai, “Conceptual design of a laser diode-pumped Nd:glass slab laser driver for inertial fusion energy,” Fusion Eng. Des. 44(1-4), 401–405 (1999). [CrossRef]

].

A fusion power plant concept called Laser Inertial Fusion Energy (LIFE) has recently been put forward by engineers and scientists at the Lawrence Livermore National Laboratory (LLNL) [2

2. M. Dunne, E. I. Moses, P. Amendt, T. Anklam, A. Bayramian, E. Bliss, B. Debs, R. Deri, T. D. De La Rubia, B. El-Dasher, J. C. Farmer, D. Flowers, K. J. Kramer, L. Lagin, J. F. Latkowski, J. Lindl, W. Meier, R. Miles, G. A. Moses, S. Reyes, V. Roberts, R. Sawicki, M. Spaeth, and E. Storm, “Timely delivery of laser inertial fusion energy (LIFE),” Fusion Sci. Technol. 60, 19–27 (2011).

,8

8. T. M. Anklam, A. M. Dunne, W. R. Meier, S. Powers, and A. J. Simon, “LIFE: the case for early commercialization of fusion energy,” Fusion Sci. Technol. 60, 66–71 (2011).

10

10. A. Bayramian, S. Aceves, T. Anklam, K. Baker, E. Bliss, C. Boley, A. Bullington, J. Caird, D. Chen, R. Deri, M. Dunne, A. Erlandson, D. Flowers, M. Henesian, J. Latkowski, K. Manes, W. Molander, E. Moses, T. Piggott, S. Powers, S. Rana, S. Rodriguez, R. Sawicki, K. Schaffers, L. Seppala, M. Spaeth, S. Sutton, and S. Telford, “Compact, efficient laser systems required for laser inertial fusion energy,” Fusion Sci. Technol. 60, 28–48 (2011).

]. As currently envisioned, each LIFE power plant would have net electrical power generating capacity of 1 GW and use a 2.2 MJ, 384-beam, harmonically-converted Nd:glass laser to ignite cryogenically-cooled, indirect-drive fusion targets. Predicted overall laser efficiency, including power drawn by the laser cooling system, is greater than 15%. Details of the LIFE laser beamline design have been described before [10

10. A. Bayramian, S. Aceves, T. Anklam, K. Baker, E. Bliss, C. Boley, A. Bullington, J. Caird, D. Chen, R. Deri, M. Dunne, A. Erlandson, D. Flowers, M. Henesian, J. Latkowski, K. Manes, W. Molander, E. Moses, T. Piggott, S. Powers, S. Rana, S. Rodriguez, R. Sawicki, K. Schaffers, L. Seppala, M. Spaeth, S. Sutton, and S. Telford, “Compact, efficient laser systems required for laser inertial fusion energy,” Fusion Sci. Technol. 60, 28–48 (2011).

].

Nd-doped APG-1, a phosphate glass, was the gain medium chosen for the LIFE laser design because its properties meet requirements for efficient, high-average-power operation [11

11. Data sheet for APG-1 laser glass, (Schott North America, Inc., 2011). http://www.schott.com/advanced_optics/english/download/catalogs.html.

,12

12. J. H. Campbell, J. S. Hayden, and A. Marker, “High-power solid-state lasers: a laser glass perspective,” Int. J. Appl. Glass Sci. 2(1), 3–29 (2011). [CrossRef]

]. Specifically, storage lifetime is sufficient for pumping to be achieved using numbers of diodes that are affordable, when diodes are purchased in power-plant quantities. Saturation fluence is high enough for energy to be stored efficiently at high density, yet low enough for energy to be extracted efficiently at fluences below damage thresholds. Thermal shock resistance is sufficient to sustain laser operation at the required repetition rate of 16 Hz. Additionally, risks associated with the availability of Nd-doped phosphate glass slabs, in the quality and quantities needed for fusion power-plant lasers, is small relative to availability risks for most other gain-media. Over 110 metric tons of high-quality phosphate laser glass, distributed over 3072 slabs with dimensions of 4 cm x 44 cm x 74 cm, has already been fabricated for the NIF laser at LLNL. A similar quantity has been fabricated for the Laser Megajoule in Ceste, France. In comparison, the LIFE laser design uses only 27 metric tons of phosphate laser glass, which is distributed over 15,360 laser slabs with dimensions of 1 cm x 26 cm x 26 cm. The LIFE laser uses less phosphate glass than the NIF laser because stored energy density in the slabs is higher, and because less energy needs to be stored due to higher laser efficiency.

We have considered two other candidate gain media for use in LIFE laser beamline designs: Yb-doped yttrium aluminum garnet (Yb:YAG) and Yb-doped strontium fluorapatite (Yb:S-FAP). Both materials have been considered previously for use in fusion power plants and have potential performance advantages relative to Nd-doped phosphate glass [3

3. M. Dunne, N. Alexander, F. Amiranoff, P. Aguer, S. Atzeni, H. Azechi, V. Bagnoud, P. Balcou, J. Badziak, D. Batani, C. Bellei, D. Besnard, R. Bingham, J. Breil, M. Borghesi, S. Borneis, A. Caruso, J. C. Chanteloup, R. J. Clarke, J. L. Collier, J. R. Davies, J.-P. Dufour, P. Estraillier, R. G. Evans, M. Fajardo, R. Fedosejevs, G. Figueria, J. Fils, J. L. Feugeas, M. Galimberti, J.-C. Gauthier, A. Giulietti, L. A. Gizzi, D. Goodin, G. Gregori, S. Gus’kov, L. Hallo, C. Hernandez-Gomez, D. Hoffman, J. Honrubia, S. Jacquemot, M. Key, J. Kilkenny, R. Kingham, M. Koenig, F. Kovacs, K. Krushelnic, C. Labaune, K. Lancaster, C. Leblanc, P. H. Maire, W. Martin, A. McEvoy, P. McKenna, J. T. Mendonça, J. Meyer-ter-Vehn, K. Mima, G. Mourou, S. Moustaizis, Z. Najmudin, P. Nickles, D. Neely, P. Norreys, M. Olazabal, A. Offenberger, N. Papadogianis, J.-P. Perin, J. M. Perlado, J. Ramirez, R. Ramis, Y. Rhee, X. Ribeyre, A. Robinson, K. Rohlena, S. J. Rose, M. Roth, C. Rouyer, C. Rulliere, B. Rus, W. Sandner, A. Schiavi, G. Schurtz, A. Sergeev, M. Sherlock, L. Silva, R. A. Smith, G. Sorasio, C. Strangio, H. Takabe, M. Tatarakis, V. Tikhonchuk, M. Tolley, M. Vaselli, P. Velarde, T. Winstone, K. Witte, J. Wolowski, N. Woolsey, B. Wyborn, M. Zepf, and J. Zhang, “HiPER – technical background and conceptual design report” (HiPER Project, 2011). http://www.hiper-laser.org/docs/tdr/HiPERTDR2.pdf.

6

6. C. D. Orth, S. A. Payne, and W. F. Krupke, “A diode pumped solid state laser driver for inertial fusion energy,” Nucl. Fusion 36(1), 75–116 (1996). [CrossRef]

]. With their longer storage lifetimes, Yb:YAG and Yb:S-FAP require fewer diodes for pumping. Since laser pump diodes are a major cost center for solid-state fusion lasers, this is an especially important consideration. Another advantage, which arises from the relatively simple, two-state electronic structure of Yb3+ ions, is immunity from several loss mechanisms that affect Nd3+ and other rare-earth lasers, including excited-state absorption, concentration quenching and upconversion. YAG also has much higher thermal conductivity and higher thermal shock resistance than phosphate glass. A disadvantage of Yb:YAG, however, is the necessity to cool slabs to temperatures well below room temperature for efficient operation. Cooling is required to reduce the thermal population of the lower laser level, which absorbs a portion of the extracting laser beam. Cooling also reduces the saturation fluence, so that stored energy can be extracted more efficiently without causing optical damage. Yb:S-FAP has more fortuitous spectral features than Yb:YAG that enable it to operate efficiently even at room temperature [13

13. L. D. DeLoach, S. A. Payne, L. K. Smith, W. L. Kway, and W. F. Krupke, “Laser and spectroscopic properties of Sr5(PO4)3F:Yb,” J. Opt. Soc. Am. B 11(2), 269–276 (1994). [CrossRef]

,14

14. A. J. Bayramian, “Development of trivalent ytterbium doped fluorapatites for diode-pumped laser applications,” doctoral thesis, University of California at Davis, UCRL-LR-139215, (June 21, 2000).

].

To date, Yb:YAG and Yb:S-FAP have been manufactured only in much smaller quantities and slab sizes than would be required for a LIFE power plant. However, excellent progress on the development of fabrication technology for these and similar materials has occurred. Fabrication of transparent ceramic YAG material using vacuum sintering is particularly salient [15

15. A. Ikesue, T. Kinoshita, K. Kamata, and K. Yoshida, “Fabrication and optical properties of high-performance polycrystalline Nd:YAG ceramics for solid-state lasers,” J. Am. Ceram. Soc. 78(4), 1033–1040 (1995). [CrossRef]

,16

16. A. Ikesue, Y. L. Aung, T. Yoda, S. Nakayama, and T. Kamimura, “Fabrication and laser performance of polycrystal and single crystal Nd:YAG by advanced ceramic processing,” Opt. Mater. 29(10), 1289–1294 (2007). [CrossRef]

], as this process appears readily scalable to large slab size. As the time required for fabrication is quite small, the vacuum sintering method appears amenable to mass production. Advances in technique have reduced scattering losses to ~0.1%/cm.

Progress has also been reported on the development of Yb:S-FAP crystals. Growth of the first small, high-quality crystal boules were reported in 1994 [17

17. S. A. Payne, L. D. DeLoach, L. K. Smith, W. L. Kway, J. B. Tassano, W. F. Krupke, B. H. T. Chai, and G. Loutts, “Ytterbium-doped apatite-structure crystals: a new class of laser materials,” J. Appl. Phys. 76(1), 497–503 (1994). [CrossRef]

]. Subsequently, a program was conducted, both at LLNL and at Northrup Grumman, to develop larger crystals for use in the Mercury laser system, at LLNL [18

18. K. Schaffers, A. J. Bayramian, J. A. Menapace, G. T. Rogowski, T. F. Soules, C. A. Stolz, S. B. Sutton, J. B. Tassano, P. A. Thelin, C. A. Ebbers, J. A. Caird, C. P. J. Barty, M. A. Randies, C. Porter, Y. Fei, and B. H. T. Chai, “Advanced material development for inertial fusion energy (IFE),” in Crystal Growth Technology, P. Capper and P. Rudolph, eds. (Wiley-VCH Verlag, 2010).

]. A number of crystal growth issues were discovered and addressed, but the issue of the occurrence of growth defects that cause small-scale wavefront features still remains. Nonetheless, crystals of sufficient size (0.7 cm x 4 cm x 6 cm) and quality were fabricated for use in the Mercury laser, which produced 60-J pulses at 10-Hz [19

19. K. I. Schaffers, J. B. Tassano, A. B. Bayramian, and R. C. Morris, “Growth of Yb: S-FAP [Yb3+: Sr5(PO4)3F] crystals for the mercury laser,” J. Cryst. Growth 253(1-4), 297–306 (2003), doi: , http://apex.jsap.jp/link?APEX/4/022703/. [CrossRef]

]. A recent development is the fabrication of C-FAP transparent ceramic [20

20. J. Akiyama, Y. Sato, and T. Taira, “Laser demonstration of diode-pumped Nd3+-doped fluorapatite anisotropic ceramics,” Appl. Phys. Express 4(2), 022703 (2011). [CrossRef]

]. C-FAP has the same crystalline structure as S-FAP but with calcium ions replacing strontium ions. Since C-FAP, like S-FAP, is uniaxial, it was necessary to align the constituent nano-crystals, to manage scattering losses. Alignment was achieved using a strong magnetic field. If successfully developed, this method has the potential for manufacturing laser slabs of the size needed for LIFE lasers, while avoiding the defect issues that attend Yb:S-FAP crystal growth.

In this paper, we examine and compare the predicted performance of laser beamlines that use laser slabs of Nd:APG-1, Yb:YAG and Yb:S-FAP. A goal of our work is to provide materials developers with a measure of the relative performance of these three different gain media, when they are used in a laser architecture that enables high efficiencies to be attained. We have attempted to make these calculations comprehensive by including all laser energy transfer processes as well as the electrical power consumed by the cooling system. The remaining sections of this paper are as follows. In Section 2, we describe the LIFE laser beamline design. In Section 3, we describe our model for calculating efficiency. In Section 4, we describe calculations performed using our model. We present our modeling results in Section 5 and we provide a summary in Section 6.

2. Laser design

Since requirements for the LIFE laser’s efficiency and repetition rate are more demanding (>12% and 16 Hz, respectively) than performance characteristics of the NIF laser (~1% efficiency and ~10−4 Hz, respectively), the LIFE laser design is different from the NIF laser design in several respects. While the NIF laser slabs are pumped by flashlamps, the LIFE laser slabs are pumped by laser diodes. Diode laser light is more directional and more spectrally narrow than flashlamp light, and is transported to the laser slabs and is absorbed more efficiently. Diode light also reduces the quantum defect (energy difference between pump photons and extracting laser photons), particularly when pumping within the red-most pump band of Nd3+ at ~873 nm, as is the case for the LIFE laser. Further, while the NIF laser slabs are passively cooled, the LIFE laser slabs are actively cooled by forced convection of helium gas over slab surfaces. The technological basis for pumping with diodes and cooling with helium gas is well established and has been used before in the Mercury laser at LLNL [24

24. A. Bayramian, P. Armstrong, E. Ault, R. Beach, C. Bibeau, J. Caird, R. Campbell, B. Chai, J. Dawson, C. Ebbers, A. Erlandson, Y. Fei, B. Freitas, R. Kent, Z. Liao, T. Ladran, J. Menapace, B. Molander, S. Payne, N. Peterson, M. Randles, K. Schaffers, S. Sutton, J. Tassano, S. Telford, and E. Utterback, “The Mercury Project: A high average power, gas-cooled laser for inertial fusion energy development,” Fusion Sci. Technol. 52, 383–387 (2007).

].

Amplifiers comprise a stack of face-pumped Nd:APG-1 glass laser slabs, oriented at near normal incidence to the laser beam. APG-1 is a phosphate glass that has high thermal shock resistance relative to most other phosphate laser glasses. Slab thickness is one cm, thin enough to ensure that tensile stresses at the large slab surfaces are less than ~25% of the yield stress. Slabs are separated by two-mm-thick cooling channels in which helium gas is flowed to remove waste heat. Cooling channels for the outward-facing surfaces of the outer two slabs are defined by fused-silica windows, which are sufficiently thick (~7 cm) to hold off the difference between the helium cooling gas pressure and the outside ambient pressure (~4 times atmospheric pressure). A high helium gas pressure reduces power consumption by the helium compressor, under the constraint that the helium mass-flow rate is sufficient to limit the caloric temperature rise of the gas as it flows over the slabs, to 10 K. Slabs are edge mounted using a low-modulus transparent material that transmits amplified spontaneous emission from the slab to a liquid-cooled absorbing edge cladding. All transmissive optics have anti-reflective coatings.

Laser slab stacks are pumped on each end by pump-light modules, which produce intense, high-fill-factor, flat-top pump distributions. Diode light originates in closely-packed, high-power arrays of diode bars, which use microlenses to achieve low divergence (4° fast axis x 10° slow axis). On each amplifier end, light from two different arrays are combined using a polarizer, which nearly doubles the irradiance available from a single array. A half-wave plate is placed in front of one array to implement this polarization-combining method. A telescope images light from the two diode arrays onto the slab stack. Diode arrays are offset parallel to their emitting surface, to blur imprinting of individual diode tile structures onto the pump profile.

We used the beamline design, as shown in Fig. 1, to model performance with Nd:APG-1 slabs and Yb:YAG slabs. Both gain media are anisotropic and transmit circularly polarized light without difficulty. When modeling performance with Yb:S-FAP, which is uniaxial, the quarter-wave plate, Q1, was removed so that the beam propagating through the slabs was linearly polarized. The beam is polarized in the direction of the high-gain extraordinary axis on the first and fourth passes through the system, and in the direction of low-gain, ordinary axis on the second and third passes.

3. Efficiency model

We performed detailed efficiency calculations in which all energy transfer processes were taken into account, beginning with input electrical power and ending with optical power delivered to the final optic, which focuses light onto the target. See Table 1

Table 1. Efficiency Factors for Beamlines Using Slabs of Nd:APG-1 Phosphate Glass at 326 K, Yb:YAG at 200 K, and Yb:S-FAP at 295 K

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. The efficiency for conversion of alternating current to direct current (AC-DC) reflects the current state of commercial rectification technologies. The efficiency for the electrical pulser reflects results of recent prototype pulser tests, which have demonstrated 90% efficiency. However, circuit simulations show that anticipated improvements in the series resistance of capacitors and other components will increase pulser efficiency to 95% [25

25. A. Bayramian, B. Deri, S. Fulkerson, R. Lanning, and S. Telford, “Compact, efficient, low-cost diode power conditioning for laser inertial fusion energy,” Proc. SPIE 7916, 79160B (2011).

]. The efficiency for diodes reflects industry consensus on diode performance that will be achieved with mass-produced, low-cost diodes within a few years, and on efficiencies reported in the literature for diode lasers operating at 808 nm and 940-970 nm [e.g., 26

26. R. Feeler, J. Junghans, and E. Stephens, “Low-cost diode arrays for the LIFE project,” Proc. SPIE 7916, 791608 (2011).

29

29. M. Kanskar, T. Earles, T. J. Goodnough, E. Stiers, D. Botez, and L. J. Mawst, “73% CW power conversion efficiency at 50W from 970nm diode laser bars,” Electron. Lett. 41(5), 245–247 (2005). [CrossRef]

] and at 850-980 nm [30

30. P. Crump, J. Wang, S. Patterson, D. Wise, A. Basauri, M. DeFranza, S. Elim, W. Dong, S. Zhang, M. Bougher, J. Patterson, S. Das, M. Grimshaw, J. Farmer, M. DeVito, and R. Martinsen, “Diode laser efficiency increases enable > 400-W peak power from 1-cm bars,” Proc. SPIE 6104, 610409 (2006). [CrossRef]

], which have exceeded 70%. Pump light delivery and absorption efficiencies were calculated using ray-trace simulations of the pump delivery system described above, and measured absorption spectra for Nd-doped APG-1 glass [11

11. Data sheet for APG-1 laser glass, (Schott North America, Inc., 2011). http://www.schott.com/advanced_optics/english/download/catalogs.html.

], Yb:YAG [31

31. Temperature-dependent absorption spectra of Yb:YAG were provided by J. Kawanaka of the Institute of Laser Engineering, Osaka University, Osaka, Japan.

] and Yb:S-FAP [14

14. A. J. Bayramian, “Development of trivalent ytterbium doped fluorapatites for diode-pumped laser applications,” doctoral thesis, University of California at Davis, UCRL-LR-139215, (June 21, 2000).

]. Diode emission spectra were calculated assuming an instantaneous Gaussian distribution with a full-width, half-maximum bandwidth of 5 nm, and a time-dependent spectral chirp due to rising diode temperature during the pump pulse. Overall decay rates for excited ions were found by summing decay rates for all known significant decay channels, including spontaneous radiative decay rates [11

11. Data sheet for APG-1 laser glass, (Schott North America, Inc., 2011). http://www.schott.com/advanced_optics/english/download/catalogs.html.

,13

13. L. D. DeLoach, S. A. Payne, L. K. Smith, W. L. Kway, and W. F. Krupke, “Laser and spectroscopic properties of Sr5(PO4)3F:Yb,” J. Opt. Soc. Am. B 11(2), 269–276 (1994). [CrossRef]

,32

32. J. Dong, M. Bass, Y. Mao, P. Deng, and F. Gan, “Dependence of the Yb3+ emission cross section and lifetime on temperature and concentration in yttrium aluminum garnet,” J. Opt. Soc. Am. B 20(9), 1975–1979 (2003). [CrossRef]

], concentration quenching rates (for Nd:APG-1 only) [11

11. Data sheet for APG-1 laser glass, (Schott North America, Inc., 2011). http://www.schott.com/advanced_optics/english/download/catalogs.html.

], and amplified spontaneous emission rates. Amplified spontaneous emission (ASE) and radiation trapping rates were calculated using Monte-Carlo ray-tracing techniques that include both spectral and geometric effects, including transfer of radiation from slab to slab within the slab stack.

Extraction efficiency was calculated using the Frantz-Nodvik formalism [33

33. L. M. Frantz and J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34(8), 2346–2349 (1963). [CrossRef]

,34

34. A. E. Siegman, Lasers (University Science Books, 1986), Chap. 8.

], which was applied to individual slabs and with transmission losses taken into account at the input and output surfaces of each slab. To model pulse shape and nonlinear phase shift of the beam as it propagates through the beamline, laser pulses were divided into over one-hundred time slices. An iterative routine was used to adjust the input pulse shape and energy to achieve the desired output pulse. The extraction efficiency reported in Table 1 is the extracted fluence at the centerline of the laser aperture, divided by the centerline stored fluence. Stored fluence was calculated by multiplying the gain in nepers by the saturation fluence. The effect on efficiency of imperfect overlap between the gain distribution and the extracting beam was captured by the mode overlap factor. Mode overlap factor and the impact of gain nonuniformity were calculated using simulation codes [35

35. R. A. Sacks, M. A. Henesian, S. W. Haney, and J. B. Trenholme, “The PROP92 Fourier beam propagation code,” in ICF Annual Report, UCRL-LR-105821–96 (Lawrence Livermore National Laboratory, Livermore, CA, 1996), pp. 207–213.

,36

36. O. Morice, “Miro: Complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Eng. 42(6), 1530–1541 (2003). [CrossRef]

] that have been extensively validated against high-energy pulse laser systems, and which include spatial variations across the beam profile.

The slab pumping simulations incorporated heating and cooling effects. Heat sources included waste heat generated by the diodes, waste heat generated by pump processes and thermalized within the laser slabs, and absorption of spontaneous emission and amplified spontaneous emission by edge claddings surrounding each slab. Our simulations used standard techniques [37

37. W. M. Kays and A. L. London, Compact Heat Exchangers, 3rd ed. (Krieger Publishing, 1998).

,38

38. K. A. Manske, D. T. Reindl, and S. A. Klein, “Evaporative condenser control in industrial refrigeration systems,” Int. J. Refrig. 24, 676–691 (2001). [CrossRef]

] to calculate power consumption of chillers, compressors, pumps,and heat exchangers, as required for cooling diodes, slabs and edge claddings. Coolant pump power was calculated using pressure drops for specific cooling-channel dimensions and coolant mass-flow rates needed to limit temperature rise along flow paths. The caloric temperature rise of helium gas flowing over the laser slabs was limited to 10 K. The caloric rise of liquid coolant flowing over the edge claddings was limited to 20 K. Slab temperature distributions and tensile stresses at the large faces were approximated using standard formulas for uniform heat deposition and cooled faces [39

39. J. L. Emmett, W. F. Krupke, and W. R. Sooy, The Potential of High-Average-Power Solid-State Lasers, UCRL-53571 (Lawrence Livermore National Laboratory, Livermore, CA, 1984).

].

4. Calculations

Using the model described above, energetics calculations were performed iteratively to determine combinations of design parameters that meet laser energy and power requirements while producing high overall efficiency. The beamline designs we analyzed use the same 1ω beam size (25 cm x 25 cm, including apodized borders) and the same values for efficiencies that are independent of gain medium, such as harmonic conversion efficiency and 3w beam transport efficiency. Square pulse distortion, the ratio of small-signal gain at the beginning of the pulse to small-signal gain at the end of the pulse, was limited to ~30-40, to ensure that output pulse shapes can be controlled accurately, given limitations on the dynamic range of pulse-shaping hardware in the laser front end. In turn, the limit on square pulse distortion gave limits on 1ω output fluences, which were different for the three different gain media due todifferences in saturation fluence. Thus, the three different gain media produced different output energies per beamlines and required different numbers of beamlines to meet the overall 3w output energy requirement of 2.2 MJ.

Values of amplifier gain and stored energy were scanned to determine near-minimum values needed to produce 1ω output fluences. For each value of amplifier gain and stored energy tested, the injected energy from the front end was adjusted until the maximum output energy and extraction efficiency were obtained. Next, with stored energy set at the near-minimum value, the average gain coefficient was adjusted to determine the minimum value consistent with nonlinear phase shift < 2 radians, for the desired pulse shape. Nonlinear phase shift is limited to avoid beam breakup into small intensity features, which can degrade beam quality and increase damage risk. Using the minimum value of gain coefficient has the advantage of minimizing amplified spontaneous emission loss, which increases nonlinearly with gain coefficient. As gain coefficient was adjusted, the total thickness of glass in the amplifier was also adjusted, to keep overall gain and stored energy constant.

Following the extraction calculations, pumping calculations were performed. First, the average ion doping concentration in the gain medium was scanned until the desired absorption efficiency was obtained (for APG-1), or until the product of the absorption efficiency and the transparency efficiency factor was maximized (for Yb:YAG and for Yb:S-FAP). The transparency efficiency factor, which is important for quasi-three-level lasers, accounts for absorption of the extracting beam by the lower laser level, which increases as doping concentration increases. Using trial values for pump-pulse duration, slab thickness and number of slabs, doping concentrations of individual slabs were adjusted until all slabs had approximately the same gain. Diode pump power was adjusted to determine the value required to produce the specified gain. Pump pulse duration was scanned, to determine efficiency vs. diode pump-power curves. If necessary, calculations were repeated, using adjusted slab thicknesses and slab counts, to ensure that thermal stresses in slabs were a small fraction (less than 25%) of the estimated yield stress.

Calculations were performed for average slab temperatures of 326 K for Nd-doped APG-1 slabs, at temperatures of 150 K, 175 K, 200 K, and 232 K for Yb:YAG slabs and at a temperature of 295 K for Yb:S-FAP. Values for gain-medium parameters used in our calculations are presented in Table 2

Table 2. Key Properties Used for Modeling Performance of APG-1, Yb:YAG and Yb:S-FAP

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. For APG-1, emission cross section and saturation fluence have been adjusted slightly to account for the difference between average slab temperature and room temperature [40

40. A. C. Erlandson, G. F. Albrecht, and S. E. Stokowski, “Model predicting the temperature dependence of the gain coefficient and the extractable stored energy density in Nd:phosphate glass lasers,” J. Opt. Soc. Am. B 9(2), 214–222 (1992). [CrossRef]

,41

41. J. Dong, M. Bass, and C. Walters, “Temperature-dependent stimulated-emission cross section and concentration quenching in Nd3+-doped phosphate glasses,” J. Opt. Soc. Am. B 21(2), 454–457 (2004). [CrossRef]

], at which the spectroscopic properties of APG-1 were determined. Also, for APG-1, saturation fluence was adjusted to compensate for observed discrepancies between Frantz-Nodvik predictions and the results of saturated gain measurements for Nd glasses. It is believed that these discrepancies arise from the effects of inhomogeneous broadening, which occur in the glass matrix. Since no saturated gain measurements at high fluence have been reported for APG-1 glass, we used a correction factor of 0.9, which is the average value reported in the literature for eight different phosphate laser glasses [42

42. D. M. Pennington, D. Milam, and D. Eimerl, “Gain saturation studies in LG-750 and LG-770 amplifier glass,” Proc. SPIE 3047, 630–642 (1997).

45

45. W. E. Martin and D. Milam, “Gain saturation in Nd:doped laser materials,” IEEE J. Quantum Electron. 18(7), 1155–1163 (1982). [CrossRef]

]. For Yb:YAG, fits were made to reported temperature-dependent properties, including emission cross section and saturation fluence, radiative lifetime, and thermal conductivity [32

32. J. Dong, M. Bass, Y. Mao, P. Deng, and F. Gan, “Dependence of the Yb3+ emission cross section and lifetime on temperature and concentration in yttrium aluminum garnet,” J. Opt. Soc. Am. B 20(9), 1975–1979 (2003). [CrossRef]

,46

46. D. C. Brown, “The promise of cryogenic solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 11(3), 587–599 (2005). [CrossRef]

48

48. Y. Sato, J. Akiyama, and T. Taira, “Effects of rare-earth doping on thermal conductivity in Y3Al5O12 crystals,” Opt. Mater. 31(5), 720–724 (2009). [CrossRef]

], to allow modeling at arbitrary temperatures between 77K and 250K. Table 2 gives values for Yb:YAG only at the operating temperature that gave the highest efficiency, which was 200 K.

5. Results

Calculated laser efficiency is plotted vs. peak diode power in Fig. 2
Fig. 2 Efficiency vs. peak system diode power for beamlines using Nd:APG-1, Yb:YAG and Yb:S-FAP laser slabs. Since output fluence and energy per beamline depends upon the gain medium and operating temperature, the number of beamlines was varied to keep the total output pulse energy at 3w fixed, at 2.2 MJ. See text for details.
. Generally, as peak diode power increases, the pump pulselength required to produce the necessary gain and stored energy becomes shorter, which in turn causes decay loss to decrease and efficiency to increase. Since diodes are a major cost factor, the optimum design point for LIFE beamlines is not at the highest efficiency. Rather, it is a point that balances costs for adding diodes against costs for generating more electrical power that is recycled to the laser. Thus, the baseline design chosen for the LIFE laser system, which uses Nd:APG-1 glass, has ~15.6% overallefficiency and uses ~50 GW peak diode power, at a ~164-μs pulselength. As Fig. 2 shows, higher efficiency is possible but would require the purchase of additional diodes.

The highest predicted efficiencies for Yb:YAG are at an average slab operating temperature of 200 K. This optimum temperature occurs as a result of tradeoffs between several temperature-dependent factors. As temperature is increased, extraction efficiency falls due to greater absorption by the thermally-populated lower laser level and due to reduced emission cross section, which causes saturation fluence to be higher. On the other hand, as temperature is increased, ASE losses become smaller, due to the reduced emission cross section, and electrical power consumption by the refrigeration system becomes smaller, due to the increase in coefficient of performance for the refrigeration system. At the LIFE baseline efficiency of ~15.6%,Yb:YAG (at 200 K) requires ~45% fewer diodes than Nd:APG-1. Fewer diodes are required primarily because of the longer radiative lifetime of Yb:YAG (995 μs vs. 361 μs). In comparison, Yb:S-FAP requires 68% fewer diodes than Nd:APG-1, also at an efficiency of 15.6%. Yb:S-FAP has longer radiative lifetime than Yb:YAG (1100 μs vs. 995 μs). Additionally, radiation trapping increases storage lifetime relative to radiative lifetime by about 45%, compared with ~20% for Yb:YAG. However, the primary reason that Yb:S-FAP requires fewer diodes than Yb:YAG is operation at room temperature, which gives a significant efficiency boost due to reduced refrigerator power.

As indicated above, Table 1 gives efficiency breakdowns for Nd:APG-1, Yb:YAG and Yb:S-FAP beamline designs that have approximately the same overall laser electrical-to-optical efficiency of ~15.6%. Absorption efficiencies for Yb:YAG and Yb:S-FAP are lower than for Nd:APG-1, since their ion concentrations were limited to avoid excessive reductions in transparency for the extracting beam. Nd:APG-1 is not significantly affected by transparency, as Nd3+ is a four-level laser. Extraction efficiency for Nd:APG-1 is lower than for Yb:YAG and Yb:S-FAP due to the application of the correction factor for saturation fluence to account for inhomogeneous broadening, as explained above. Overall electrical-to-optical conversion efficiency is higher for Yb:YAG than for either Nd:APG-1 or Yb:S-FAP, when the electrical power needed for cooling the laser is not included. The effect on efficiency of including cooling power is substantially greater for Yb:YAG than for Nd:APG-1 and Yb:S-FAP, due to operation of Yb:YAG at reduced temperature.

Table 3

Table 3. Beamline Properties

table-icon
View This Table
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provides addition information on APG-1, Yb:YAG (200 K) and Yb:S-FAP beamline designs. The 1ω output fluence and energy per beamline become progressively smaller as one progresses across the table, due to falling saturation fluence and corresponding reduction in the square-pulse-limited output fluence. As output fluence and energy become smaller, a larger number of beamlines are needed to produce the required pulse energy to drive fusion reactions. For example, the laser systems we analyzed, which produce 2.2 MJ at 3ω and which use slabs of Nd:APG-1, Yb:YAG and Yb:S-FAP, require 384, 390 and 500 beamlines, respectively. It should be noted that the numbers of beamlines needed could have been changed by adjusting the aperture size.

6. Summary

We have performed a side-by-side comparison of the efficiency of Nd:APG-1, Yb:YAG and Yb:S-FAP beamlines that have been designed for use in laser inertial fusion energy (LIFE) power plants. Our modeling accounts for 18 different efficiency factors, each representing an energy-transfer step or an energy loss mechanism. When multiplied together, these efficiency factors give the overall electrical-to-optical conversion efficiency of the laser. Two loss factors, one of which represents losses due to spontaneous decay while the other of represents losses due to amplified spontaneous emission, depend on the gain medium chosen as well as on the duration of the pump pulse. These losses can be reduced by using a higher diode peak power to pump the laser slabs for a shorter period of time, while still attaining the necessary population inversion. Provided sufficient numbers of diodes are used, beamlines using Nd:APG-1, Yb:YAG or Yb:S-FAP can achieve an electrical-to-optical conversion efficiency of at least 12-16%, well within the desirable range for the LIFE power-plant application. Due largely to differences in storage lifetime, the three different gain media require different numbers of diodes. For example, to achieve an overall electrical-to-optical conversion efficiency of about 15.6%, laser systems using gain media of Nd:APG-1, Yb:YAG and Yb:S-FAP require relative peak diode powers of 1, 0.55 and 0.32, respectively. Additionally, due to differences in saturation fluence, the three different gain media operate at different 1w fluences and require different numbers of beamlines.

Acknowledgments

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

References and links

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OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(160.3380) Materials : Laser materials

ToC Category:
Laser Materials

History
Original Manuscript: July 29, 2011
Revised Manuscript: October 10, 2011
Manuscript Accepted: October 15, 2011
Published: October 26, 2011

Citation
A. C. Erlandson, S. M. Aceves, A. J. Bayramian, A. L. Bullington, R. J. Beach, C. D. Boley, J. A. Caird, R. J. Deri, A. M. Dunne, D. L. Flowers, M. A. Henesian, K. R. Manes, E. I. Moses, S. I. Rana, K. I. Schaffers, M. L. Spaeth, C. J. Stolz, and S. J. Telford, "Comparison of Nd:phosphate glass, Yb:YAG and Yb:S-FAP laser beamlines for laser inertial fusion energy (LIFE) [Invited]," Opt. Mater. Express 1, 1341-1352 (2011)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-1-7-1341


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References

  1. E. I. Moses, “The National Ignition Facility (NIF): A path to fusion energy,” Energy Convers. Manage.49(7), 1795–1802 (2008). [CrossRef]
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