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Computational fluid dynamics modeling of subsonic flowing-gas diode-pumped alkali lasers: comparison with semi-analytical model calculations and with experimental results Karol Waichman, Boris D. Barmashenko,* and Salman Rosenwaks Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel *Corresponding author:
[email protected] Received July 18, 2014; revised September 1, 2014; accepted September 1, 2014; posted September 3, 2014 (Doc. ID 217256); published October 13, 2014 Comprehensive analysis of kinetic and fluid dynamic processes in flowing-gas diode-pumped alkali lasers (DPALs) using two- and three-dimensional computational fluid dynamics (2D and 3D CFD) models is reported. The 2D model is applied to a Cs DPAL with optical resonator-flow field coaxial configuration and the 3D model is applied to an optical axis transverse to the flow configuration. The models take into account effects of temperature rise and losses of Cs atoms due to ionization. The 2D CFD model is applied to 1 kW flowing-gas Cs DPAL [Quantum Electron. 42, 95 (2012)] and the calculated results are in good agreement with the measurements. Comparison of the 2D CFD to semi-analytical model [J. Opt. Soc. Am. B 30, 1118 (2013)] shows that for low pump power both models predict very close values of the laser power; however, at higher pump power, corresponding to saturation of the absorption of the pump transition, the laser power calculated using the 2D CFD model is much higher than that obtained using the semi-analytical model. At high pump power, the heat convection out of the laser resonator is more efficient for the transverse case than the coaxial case, the temperature in the resonator is lower, and consequently the calculated laser power is higher. Optimization of the Cs DPAL parameters, using 3D CFD modeling, shows that applying high flow velocity and narrowband pumping, maximum lasing power as high as 40 kW can be obtained at pump power of 80 kW for transverse flow configuration in a pumped volume of ∼0.7 cm3 . © 2014 Optical Society of America OCIS codes: (140.1340) Atomic gas lasers; (140.3430) Laser theory; (140.6810) Thermal effects; (140.3460) Lasers. http://dx.doi.org/10.1364/JOSAB.31.002628
1. INTRODUCTION Diode-pumped alkali lasers (DPALs) operating at ∼800 nm, extensively studied during the last decade, combine the positive characteristics of gas lasers and solid-state/fiber lasers and are scalable to high power without suffering the negative properties of the latter [1,2]. These gas phase lasers operate at frequency νl of the D1 n2 P 1∕2 →n2 S 1∕2 transition of the alkali atoms (where n 4, 5, 6 for K, Rb, and Cs, respectively). They are pumped via absorption of unphased, low beam quality radiation of diode lasers at frequency νp of the D2 n2 S 1∕2 →n2 P 3∕2 transition, followed by rapid relaxation (by buffer gas) of the upper to the lower fine-structure level, n2 P 3∕2 to n2 P 1∕2 (designated as levels 3 and 2, respectively; the ground state n2 S 1∕2 is designated as 1). In spite of a rather high power and optical-to-optical conversion efficiency that has been achieved [2], operating efficient DPALs and scaling them to higher power (e.g., 10 kW and beyond) is hindered by the processes of heating of the gas mixture and photoexcitation and ionization of the alkali atoms. As shown experimentally [3] and theoretically [4–7], at high pumping power these processes result in temperature rise and losses of the neutral alkali atoms and hence in substantial decrease of the slope and of the overall optical-tooptical efficiencies of the DPAL. To avoid the temperature rise and replenish the lost neutral alkali atoms, there is a need to 0740-3224/14/112628-10$15.00/0
flow the gas mixture [1]. Recently the “first light” from such a laser [8] and a 1 kW flowing-gas Cs DPAL with ∼48% efficiency [9] were reported. The 1 kW power obtained in [9] is the maximum reported power of the DPAL, being much higher than the maximum reported value of 145 W reached in a static Rb DPAL [10]. Rough estimates of flowing-gas DPALs operation parameters were carried out in [11,12]. It was shown that for 3.7 MW pumping of longitudinal flow Rb DPAL [11] and for 1 MW pumping of transverse flow Rb DPAL [12], the rise of the temperature T in the gain medium is 20 kW even higher values of u ∼ 100 m∕s are required. B. Maximum Achievable Power in Cs Diode-Pumped Alkali Laser with Narrowband Pumping and Longitudinal and Transverse Flows To estimate the maximum achievable powers in flowing-gas DPALs we performed calculations of the power for narrowband pumping where the pump bandwidth, 10 GHz, was much smaller than the collisionally broadened linewidth of the D1 and D2 transitions. In this case the absorption of the pump beam is much larger than in the case of the broadband pumping studied in Subsection 3.A. Other parameters of the laser presented in Table 2 (examples 2 and 3) were optimized to reach the maximum values of P lase . In particular u 100 m∕s and T w 403°K, higher than in the 1 kW device [9], were chosen. We also found, using the semi-analytical model, that pure CH4 with optimal pressure p 4.5 atm should be used as the buffer gas and that the optimal coupling mirror reflection r 2 for the chosen flow parameters is 0.1. Both longitudinal and transverse flow geometries shown in Figs. 1(a) and 1(b), respectively, were studied. First we compared the values of P lase calculated by the semi-analytical and the 2D CFD model for the longitudinal flow (Fig. 9). The laser parameters are shown in Table 2 (example 2). Just as in the case of the broadband pumping for low P p < 20 kW the semi-analytical and the 2D CFD model predict very close values of P lase . However, at higher P p the values of P lase , calculated using the 2D CFD model, are much higher than those obtained using the semi-analytical model. Thus, the former model predicts much higher maximum achievable laser powers, >30 kW, rather than ∼20 kW predicted by the latter. To illustrate the influence of heating and ionization on P lase , Fig. 9 also shows the values of P lase at P p 60 kW calculated using the 2D CFD model without heating and ionization and with heating but without ionization. Heating and ionization result in substantial decrease of P lase ; at high P p > 20 kW, the influence of the heating being stronger than that of the ionization. The values of P lase for transverse flow calculated by the 3D CFD model are also shown in Fig. 9. They are by 25%–30% 2D CFD, longitudinal Semi-analytical, longitudinal
60000
Plase, W
2D CFD, longitudinal: constant T, no ionization
50000
2D CFD, longitudinal: no ionization
40000
3D CFD, transverse
higher than for the longitudinal flow with the same u, the maximum values of P lase being as high as 40 kW at P p 80 kW. This power is extracted from the very small active volume of 0.7 cm3 . The main reason for the higher P lase achieved for transverse flow is the much more efficient cooling caused by faster replacement of the hot active volume gas. This results in lower temperature of the gas in the lasing medium. For example, at P p 80 kW the average temperatures over the lasing volume for the longitudinal and transverse flows are 480 K and 410 K, respectively.
4. SUMMARY 2D and 3D CFD models of flowing-gas subsonic DPALs taking into account the rise of temperature, excitation of the alkali atoms to high electronic levels, and their losses due to ionization in the lasing medium are reported. Using these models, coupled equations for laser kinetics, laser optics, and gas flow were solved and the flow patterns and spatial distributions of the temperature and different species in the lasing region were calculated for Cs DPALs. The 2D CFD model applied to the 1 kW Cs DPAL with longitudinal gas flow [9] shows good agreement between the calculated and measured dependence of P lase on P p , p, and T w over a wide range of these parameters. Comparison with the semi-analytical model of the DPAL [7] shows that the main assumption of this model on the uniform densities of electronically excited Cs atoms, ions, and temperature in the lasing region appears to be inaccurate for high P p . For low P p both models predict very close values of P lase ; however, at higher pump power, when the absorption on the pump transition is saturated, the spatial variations of the temperature and densities strongly affect the power, and the values of the laser power calculated using the 2D CFD model become much higher than those obtained using the semi-analytical model. This indicates that CFD modeling has to be applied for predicting the maximum possible power for high power DPALs. Unfortunately, no measurements for high power are available as yet. Optimization of the Cs DPAL parameters showed that applying high longitudinal flow velocity and narrowband pumping, maximum P lase > 30 kW can be obtained at P p 80 kW. Calculations performed for Cs DPAL with high transverse flow velocity using the 3D CFD model show that even higher P lase ∼ 40 kW can be reached at the same P p 80 kW in the very small active volume of 0.7 cm3 . Estimates of the influence of the heating and ionization on P lase showed that these processes result in substantial decrease of P lase , the heating effect being stronger than that of the ionization.
APPENDIX A: DEFINITION OF THE RATES IN EQS. (3)–(7)
30000
A. Rates Involving Low S and P Levels (1, 2, and 3) Lasing rate:
20000 10000
W 21 g21
0 0
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10000 20000 30000 40000 50000 60000 70000 80000
Pp, W Fig. 9. Dependence of P lase on P p calculated using 2D (for the longitudinal flow) and 3D (for the transverse flow) CFD, and semianalytical models for t 0.98, u 100 m∕s, T 403°K, and pure CH4 . Other parameters as in Table 2 (examples 2 and 3).
− I l z I l z : hνl
Pumping rate: Z W 31
0
∞
g31 ν
− I p z; ν I p z; ν dν: hν
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Rate of relaxation of the upper to the lower fine-structure level, j 3→2: W 32 γ 32 n3 − ε32 n2 ; where γ 32 nCH4 σ 32 vr
r TK ; 298
vr is the average thermal velocity at 298 K and ε32 2 exp−ΔE32 ∕kB T. Quenching rate: j 2; 3→1:
Qj1 γ q nj ;
where pthe quenching rate coefficient γq nCH4 σ q vr TK∕298. Spontaneous emission rate: j 2; 3→1: S j1 Aj1 nj . B. Rates Involving High D and S Levels Photoexcitation j→i: I ji nj σ ji;l I l σ ji;p I p ; where σ ji;l and σ ji;p are the laser and pump radiation cross sections, respectively, for process 7 in Table 3, calculated in Eq. (13) of [7]: I l
− I l z I l z hνl
and I p
Z
∞ I z; ν p
0
I −p z; ν dν: hν
Pooling j→i: Poji k8;ji n2j . Spontaneous emission i→j: S ij Aij ni . C. Rates Involving Ionization and Recombination Photoionization: i→X : Phi σ ion ni I l I p . Penning ionization: i→X : Pnj;i k11 nj ni . Recombination: 2 R 2 k14 nX 2 ;
R k12 nX n1 nt k13 nX n1 nHe ; where nt ≡
i3 X
ni
i1
j6 X
nj :
j4
In the above expressions for the rates k8;ji , k11 , k12 , k13 , and k14 are the rate constants corresponding to reaction numbers 8, 11, 12, 13, and 14, respectively, in Table 3. σ 32 , σ q and σ ion are the cross sections corresponding to processes 2, 6, and 10, respectively, in Table 3.
ACKNOWLEDGMENTS Effort sponsored by the High Energy Laser Joint Technology Office (HEL JTO) and the European Office of Aerospace Research and Development (EOARD) under grant FA865513-1-3072.
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