Abstract

Combination of the scheme of extraction during pumping (EDP) and the Thin Disk (TD) technology is presented to overcome the limitations associated with thermal cooling of crystal and transverse amplified spontaneous emission in high average power laser systems based on Ti:Sa amplifiers. The optimized design of high repetition rate 1-10 PW Ti:Sapphire EDP-TD power amplifiers are discussed, including their thermal dynamic behavior.

© 2016 Optical Society of America

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  4. W. P. Latham, A. Lobad, T. C. Newell, D. Stalnaker, and C. Phipps, “6.5 kW, Yb:YAG Ceramic Thin Disk Laser,” AIP Conf. Proc. 1278, 758–764 (2010).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  22. R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and H. P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quanum Electron. 34(6), 1046–1053 (1998).
    [Crossref]
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  24. R. Berman, E. L. Foster, and J. M. Ziman, “The Thermal Conductivity of Dielectric Crystals: The Effect of Isotopes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 237, 344–354 (1955).
    [Crossref]

2015 (1)

2014 (2)

C. J. Saraceno, F. Emaury, C. Schriber, M. Hoffmann, M. Golling, T. Südmeyer, and U. Keller, “Ultrafast thin-disk laser with 80 μJ pulse energy and 242 W of average power,” Opt. Lett. 39(1), 9–12 (2014).
[Crossref] [PubMed]

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

2013 (2)

2012 (3)

V. Chvykov and K. Krushelnick, “Large aperture multi-pass amplifiers for high peak power lasers,” Opt. Commun. 285(8), 2134–2136 (2012).
[Crossref]

C. J. Saraceno, F. Emaury, O. H. Heckl, C. R. E. Baer, M. Hoffmann, C. Schriber, M. Golling, T. Südmeyer, and U. Keller, “275 W average output power from a femtosecond thin disk oscillator operated in a vacuum environment,” Opt. Express 20(21), 23535–23541 (2012).
[Crossref] [PubMed]

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

2011 (1)

2010 (2)

J. H. Sung, S. K. Lee, T. J. Yu, T. M. Jeong, and J. Lee, “0.1 Hz 1.0 PW Ti:sapphire laser,” Opt. Lett. 35(18), 3021–3023 (2010).
[Crossref] [PubMed]

W. P. Latham, A. Lobad, T. C. Newell, D. Stalnaker, and C. Phipps, “6.5 kW, Yb:YAG Ceramic Thin Disk Laser,” AIP Conf. Proc. 1278, 758–764 (2010).
[Crossref]

2009 (2)

2007 (1)

2006 (1)

G. Mourou, T. Tajima, and S. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78(2), 309–371 (2006).
[Crossref]

2002 (1)

M. P. Kalachnikov, V. Karpov, H. Schönnagel, and W. Sandner, “100 – terawatt titanium-sapphire laser system,” Laser Phys. 12(2), 368–374 (2002).

1998 (1)

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and H. P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quanum Electron. 34(6), 1046–1053 (1998).
[Crossref]

1991 (1)

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002). A. Peter, “Schulz, Scott R. Henion, ”Liquid-Nitrogen-Cooled Ti: A12 O3 Laser,” IEEE J. Quantum Electron. 27(4), 1039–1047 (1991).

1990 (1)

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous‐wave end‐pumped solid‐state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[Crossref]

1955 (1)

R. Berman, E. L. Foster, and J. M. Ziman, “The Thermal Conductivity of Dielectric Crystals: The Effect of Isotopes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 237, 344–354 (1955).
[Crossref]

Ahmed, M. A.

Baer, C. R. E.

Bauer, D.

Behrendt, A.

Berman, R.

R. Berman, E. L. Foster, and J. M. Ziman, “The Thermal Conductivity of Dielectric Crystals: The Effect of Isotopes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 237, 344–354 (1955).
[Crossref]

Bulanov, S.

G. Mourou, T. Tajima, and S. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78(2), 309–371 (2006).
[Crossref]

Chambaret, J. P.

Chen, W.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002). A. Peter, “Schulz, Scott R. Henion, ”Liquid-Nitrogen-Cooled Ti: A12 O3 Laser,” IEEE J. Quantum Electron. 27(4), 1039–1047 (1991).

Chu, Y.

Chvykov, V.

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

V. Chvykov and K. Krushelnick, “Large aperture multi-pass amplifiers for high peak power lasers,” Opt. Commun. 285(8), 2134–2136 (2012).
[Crossref]

Deng, P.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002). A. Peter, “Schulz, Scott R. Henion, ”Liquid-Nitrogen-Cooled Ti: A12 O3 Laser,” IEEE J. Quantum Electron. 27(4), 1039–1047 (1991).

Dong, J.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002). A. Peter, “Schulz, Scott R. Henion, ”Liquid-Nitrogen-Cooled Ti: A12 O3 Laser,” IEEE J. Quantum Electron. 27(4), 1039–1047 (1991).

Emaury, F.

Fields, R. A.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous‐wave end‐pumped solid‐state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[Crossref]

Fincher, C. L.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous‐wave end‐pumped solid‐state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[Crossref]

Fisch, N. J.

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

Foster, E. L.

R. Berman, E. L. Foster, and J. M. Ziman, “The Thermal Conductivity of Dielectric Crystals: The Effect of Isotopes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 237, 344–354 (1955).
[Crossref]

Gan, Z.

Golling, M.

Graf, T.

Heckl, O. H.

Hoffmann, M.

Innocenzi, M. E.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous‐wave end‐pumped solid‐state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[Crossref]

Jamelot, G.

Jeong, T. M.

Jung, R.

Kalachnikov, M. P.

M. P. Kalachnikov, V. Karpov, H. Schönnagel, and W. Sandner, “100 – terawatt titanium-sapphire laser system,” Laser Phys. 12(2), 368–374 (2002).

Karpov, V.

M. P. Kalachnikov, V. Karpov, H. Schönnagel, and W. Sandner, “100 – terawatt titanium-sapphire laser system,” Laser Phys. 12(2), 368–374 (2002).

Keller, U.

Khazanov, E. A.

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

Killi, A.

Krushelnick, K.

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

V. Chvykov and K. Krushelnick, “Large aperture multi-pass amplifiers for high peak power lasers,” Opt. Commun. 285(8), 2134–2136 (2012).
[Crossref]

Latham, W. P.

W. P. Latham, A. Lobad, T. C. Newell, D. Stalnaker, and C. Phipps, “6.5 kW, Yb:YAG Ceramic Thin Disk Laser,” AIP Conf. Proc. 1278, 758–764 (2010).
[Crossref]

Le Garrec, B.

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

Lee, J.

Lee, S. K.

Leng, Y.

Li, R.

Liang, X.

Liu, Y.

Lobad, A.

W. P. Latham, A. Lobad, T. C. Newell, D. Stalnaker, and C. Phipps, “6.5 kW, Yb:YAG Ceramic Thin Disk Laser,” AIP Conf. Proc. 1278, 758–764 (2010).
[Crossref]

Lu, H.

Lu, X.

Ma, L.

Mac Donald, M.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and H. P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quanum Electron. 34(6), 1046–1053 (1998).
[Crossref]

Malkin, V. M.

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

Mourou, G.

G. Mourou, T. Tajima, and S. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78(2), 309–371 (2006).
[Crossref]

Mourou, G. A.

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

Nees, J.

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

Negel, J.-P.

Neuenschwander, B.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and H. P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quanum Electron. 34(6), 1046–1053 (1998).
[Crossref]

Newell, T. C.

W. P. Latham, A. Lobad, T. C. Newell, D. Stalnaker, and C. Phipps, “6.5 kW, Yb:YAG Ceramic Thin Disk Laser,” AIP Conf. Proc. 1278, 758–764 (2010).
[Crossref]

Nickles, P. V.

Phipps, C.

W. P. Latham, A. Lobad, T. C. Newell, D. Stalnaker, and C. Phipps, “6.5 kW, Yb:YAG Ceramic Thin Disk Laser,” AIP Conf. Proc. 1278, 758–764 (2010).
[Crossref]

Pittman, M.

Plé, F.

Qiu, H.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002). A. Peter, “Schulz, Scott R. Henion, ”Liquid-Nitrogen-Cooled Ti: A12 O3 Laser,” IEEE J. Quantum Electron. 27(4), 1039–1047 (1991).

Roos, M. B.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and H. P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quanum Electron. 34(6), 1046–1053 (1998).
[Crossref]

Sandner, W.

J. Tümmler, R. Jung, H. Stiel, P. V. Nickles, and W. Sandner, “High-repetition-rate chirped-pulse-amplification thin-disk laser system with joule-level pulse energy,” Opt. Lett. 34(9), 1378–1380 (2009).
[Crossref] [PubMed]

M. P. Kalachnikov, V. Karpov, H. Schönnagel, and W. Sandner, “100 – terawatt titanium-sapphire laser system,” Laser Phys. 12(2), 368–374 (2002).

Saraceno, C. J.

Schönnagel, H.

M. P. Kalachnikov, V. Karpov, H. Schönnagel, and W. Sandner, “100 – terawatt titanium-sapphire laser system,” Laser Phys. 12(2), 368–374 (2002).

Schriber, C.

Sergeev, A. M.

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

Speiser, J.

Stalnaker, D.

W. P. Latham, A. Lobad, T. C. Newell, D. Stalnaker, and C. Phipps, “6.5 kW, Yb:YAG Ceramic Thin Disk Laser,” AIP Conf. Proc. 1278, 758–764 (2010).
[Crossref]

Stiel, H.

Südmeyer, T.

Sung, J. H.

Sutter, D.

Tajima, T.

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

G. Mourou, T. Tajima, and S. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78(2), 309–371 (2006).
[Crossref]

Toroker, Z.

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

Tümmler, J.

Voss, A.

Wagner, G.

Wang, C.

Wang, X.

Weber, H. P.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and H. P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quanum Electron. 34(6), 1046–1053 (1998).
[Crossref]

Weber, R.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and H. P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quanum Electron. 34(6), 1046–1053 (1998).
[Crossref]

Wulfmeyer, V.

Xu, J.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002). A. Peter, “Schulz, Scott R. Henion, ”Liquid-Nitrogen-Cooled Ti: A12 O3 Laser,” IEEE J. Quantum Electron. 27(4), 1039–1047 (1991).

Xu, L.

Xu, Y.

Xu, Z.

Yang, P.

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002). A. Peter, “Schulz, Scott R. Henion, ”Liquid-Nitrogen-Cooled Ti: A12 O3 Laser,” IEEE J. Quantum Electron. 27(4), 1039–1047 (1991).

Yin, D.

Yu, L.

Yu, T. J.

Yura, H. T.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous‐wave end‐pumped solid‐state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[Crossref]

Ziman, J. M.

R. Berman, E. L. Foster, and J. M. Ziman, “The Thermal Conductivity of Dielectric Crystals: The Effect of Isotopes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 237, 344–354 (1955).
[Crossref]

AIP Conf. Proc. (1)

W. P. Latham, A. Lobad, T. C. Newell, D. Stalnaker, and C. Phipps, “6.5 kW, Yb:YAG Ceramic Thin Disk Laser,” AIP Conf. Proc. 1278, 758–764 (2010).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modeling of continuous‐wave end‐pumped solid‐state lasers,” Appl. Phys. Lett. 56(19), 1831–1833 (1990).
[Crossref]

IEEE J. Quantum Electron. (1)

H. Qiu, P. Yang, J. Dong, P. Deng, J. Xu, and W. Chen, “The influence of Yb concentration on laser crystal Yb:YAG,” Mater. Lett. 55, 1–7 (2002). A. Peter, “Schulz, Scott R. Henion, ”Liquid-Nitrogen-Cooled Ti: A12 O3 Laser,” IEEE J. Quantum Electron. 27(4), 1039–1047 (1991).

IEEE J. Quanum Electron. (1)

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and H. P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quanum Electron. 34(6), 1046–1053 (1998).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Phys. (1)

M. P. Kalachnikov, V. Karpov, H. Schönnagel, and W. Sandner, “100 – terawatt titanium-sapphire laser system,” Laser Phys. 12(2), 368–374 (2002).

Opt. Commun. (3)

V. Chvykov, J. Nees, and K. Krushelnick, “Transverse amplified spontaneous emission: The limiting factor for output energy of ultra-high power lasers,” Opt. Commun. 312, 216–221 (2014).
[Crossref]

V. Chvykov and K. Krushelnick, “Large aperture multi-pass amplifiers for high peak power lasers,” Opt. Commun. 285(8), 2134–2136 (2012).
[Crossref]

G. A. Mourou, N. J. Fisch, V. M. Malkin, Z. Toroker, E. A. Khazanov, A. M. Sergeev, T. Tajima, and B. Le Garrec, “Exawatt-Zettawatt pulse generation and applications,” Opt. Commun. 285(5), 720–724 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (6)

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

R. Berman, E. L. Foster, and J. M. Ziman, “The Thermal Conductivity of Dielectric Crystals: The Effect of Isotopes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 237, 344–354 (1955).
[Crossref]

Rev. Mod. Phys. (1)

G. Mourou, T. Tajima, and S. Bulanov, “Optics in the relativistic regime,” Rev. Mod. Phys. 78(2), 309–371 (2006).
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Other (4)

C. Teisset, M. Schultze, R. Bessing, M. Haefner, S. Prinz, D. Sutter, and T. Metzger, “300 W Picosecond Thin-Disk Regenerative Amplifier at 10 kHz Repetition Rate,” in Advanced Solid-State Lasers Congress Postdeadline, G. Huber and P. Moulton, eds., OSA Postdeadline Paper Digest (online) (Optical Society of America, 2013), paper JTh5A.1.

V. Chvykov, M. Kalashnikov, and K. Osvay, “Final EDP Ti:Sapphire Amplifiers for ELI Project,” SPIE Proceeding, LOO 9515–18 (2015).

http://inventions.umich.edu/technologies/6154_thin-disk-extraction-during-pumping-laser-amplifier

V. Chvykov, V. Yanovsky, S.-W. Bahk, G. Kalintchenko, and G. Mourou, “Suppression of parasitic lasing in multi-pass Ti-sapphire amplifiers,” in Proceedings of the OSA Technical Digest, CLEO 2003, paper CWA34 (2003).

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Figures (10)

Fig. 1
Fig. 1

Dependence of the transverse gain inside the Ti:Sa crystal on the angle between the longitudinal direction (normal to the crystal input surface) and direction of the ASE ray inside the crystal. The crystal is normally cut. The rays propagate in the plane that is perpendicular to the C-axis of the crystal and goes through the center of the pumped region., They start at the edge of the pumped region. Longitudinal gain Gl = 6, a – aspect ratio A = 2, b- A = 6, c –A = 10.

Fig. 2
Fig. 2

Dependences of transverse gain on crystal aspect ratios.

Fig. 3
Fig. 3

Dependences of the losses during pumping for crystals with the different aspect ratios. Dashed area corresponds to the pump pulse.

Fig. 4
Fig. 4

Losses calculated for the 200 TW/100 Hz 6-pass Ti:Sapphire EDP- power amplifier. Shaded area is the pump pulse.

Fig. 5
Fig. 5

Steady-state temperature distribution in a crystal with 2 mm thickness and 2 cm diameter (diameter of the pumped area is 1.9 cm) (a). Steady-state temperature profile in the transverse direction of the crystal for different longitudinal positions (from bottom to top) (b). Temporally resolved heating of 100 pulses producing the same steady-state temperature in the center (red) and at the edge of the pumped area (orange, below) of the crystal (c).

Fig. 6
Fig. 6

Steady-state temperature distribution in case of the coolant temperature of 77 °K and 1 kHz repetition rate (average pump power is 1.1 kW) (a). Steady-state temperature profile along the front surface of the crystal in case of 1 and 2 kHz repetition rate and 77 °K coolant temperature (b). Steady-state temperature distribution in case of 30 °K coolant temperature and 6 kHz repetition rate (average pump power is 6.6 kW) (c). Steady-state temperature profile along the front surface of the crystal in case of repetition rates from 5 to 10 kHz and 30 °K coolant temperature (d).

Fig. 7
Fig. 7

a. Steady-state temperature distribution in the crystal with 1 cm thickness and 11 cm diameter for 120 J pumping at 10 Hz repetition rate (1.2 kW pump power) in case of 15 °C coolant temperature. b. Steady-state temperature profiles in the 1 cm thick crystal in the transverse direction for different longitudinal positions .c. Steady-state temperature distribution in the crystal with 3 cm thickness and 12 cm aperture size for 30 J per side pumping at 10 Hz repetition rate and side surface cooling with 15 °C coolant temperature. d. Temperature profiles in this crystal in the transverse direction for different longitudinal positions.

Fig. 8
Fig. 8

a- Steady-state temperature distribution in the 2 PW, cryogenically cooled amplifier crystal with 1 cm thickness and 11 cm diameter for 120 J pumping at 100 Hz repetition rate (12 kW pump power) in case of 77 K coolant temperature. b. Steady-state temperature profiles for the 1 cm thick crystal in the transverse direction for different longitudinal positions.

Fig. 9
Fig. 9

a. Steady-state temperature distribution in the 10 PW, cryogenically cooled amplifier crystal with 1.5 cm thickness and 15 cm diameter for 500 J pumping at 10 Hz repetition rate (5 kW pump power) in case of 70 K coolant temperature. b. Steady-state temperature profiles in the 1.5 cm thick crystal in the transverse direction for different longitudinal positions.

Fig. 10
Fig. 10

Dependence of the peak temperature on thickness of the Ti:Sa crystal for different coolant temperatures.

Equations (4)

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ρ C p T t =( kT )+ Q v ,
ρ C p uT=( kT )+ Q v
Q v,TD (r,z,t)=αη P peak [ e αz + e α(Lz) ] f spatial (r,z) f temporal (t) 1 A(z)
Q V,S (r,z)=αη P peak [ e αz + e α(Lz) ] f spatial (r,z) 1 A(z)

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