Five-level argon&#x2013;helium discharge model for characterization of a diode-pumped rare-gas laser

Ben Eshel; Glen P. Perram

doi:10.1364/JOSAB.35.000164

Journal of the Optical Society of America B
Vol. 35,
Issue 1,
pp. 164-173
(2018)
•https://doi.org/10.1364/JOSAB.35.000164

Five-level argon–helium discharge model for characterization of a diode-pumped rare-gas laser

Ben Eshel and Glen P. Perram

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Ben Eshel and Glen P. Perram, "Five-level argon–helium discharge model for characterization of a diode-pumped rare-gas laser," J. Opt. Soc. Am. B 35, 164-173 (2018)

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Abstract

A five-level discharge kinetics model is developed to characterize the scaling potential of the diode-pumped rare-gas laser. The predicted excited state populations are examined as functions of the gas pressure, gas temperature, electron density, and electron temperature. The density of the metastable $Ar (1 s_{5})$ level is a sensitive function of electron temperature, increasing from $10^{12} {cm}^{- 3}$ at 1 eV to $5 \times 10^{13} {cm}^{- 3}$ at 1.2 eV, for a total pressure of 400 Torr and a gas temperature of 440 K. This is in contrast to the distribution among excited states, which are most sensitive to the electron density and result from the interplay of the electron-impact and neutral-impact spin-orbit mixing rates. The model is benchmarked using absorption, emission, and gain data from recent laser demonstrations. A metastable number-density/path-length product of $1 \times 10^{14} {cm}^{- 2}$ is required for optimal lasing performance at a strong pump intensity of $20 kW / {cm}^{2}$ . This system requires an aperture of $6.9 {cm}^{2}$ in order to sustain 100 kW performance in the total volume of $69 {cm}^{3}$ . The primary difficulty in the development of such a discharge system is due to the combined requirements of a large-volume, homogeneous, atmospheric pressure discharge with sufficient electron temperature to sustain significant production of the metastable $1 s_{5}$ state.

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Mechanism	Rate Coefficient, $γ$ ( $10^{- 9} {cm}^{3} / s$ )	References
$Ar (1 S_{0}) + e^{-} \to Ar (1 s_{5}) + e^{-}$	$2.7 Exp (\frac{- 11.9}{T_{e}})$	[15]
$Ar (1 S_{0}) + e^{-} \to Ar (1 s_{4}) + e^{-}$	$3.5 Exp (\frac{- 12.3}{T_{e}})$	[15]
$Ar (1 S_{0}) + e^{-} \to Ar (2 p_{10}) + e^{-}$	$2 Exp (\frac{- 13.0}{T_{e}})$	[15]
$Ar (1 S_{0}) + e^{-} \to Ar (2 p_{9}) + e^{-}$	$1.9 Exp (\frac{- 13.5}{T_{e}})$	[15]
$Ar (1 S_{0}) + e^{-} \to Ar (2 p_{8}) + e^{-}$	$2.2 Exp (\frac{- 13.6}{T_{e}})$	[15]
$Ar (1 s_{5}) + e^{-} \to Ar (2 p_{10}) + e^{-}$	$190 Exp (\frac{- 1.69}{T_{e}})$	[15]
$Ar (1 s_{4}) + e^{-} \to Ar (2 p_{10}) + e^{-}$	$150 Exp (\frac{- 2}{T_{e}})$	[15]
$Ar (1 s_{4}) + e^{-} \to Ar (2 p_{9}) + e^{-}$	$86 Exp (\frac{- 1.85}{T_{e}})$	[15]
$Ar (1 s_{5}) + e^{-} \to Ar (2 p_{8}) + e^{-}$	$86 Exp (\frac{- 1.73}{T_{e}})$	[15]
$Ar (1 s_{4}) + e^{-} \to Ar (2 p_{8}) + e^{-}$	$100 Exp (\frac{- 2}{T_{e}})$	[15]
$Ar (2 p_{8}) + e^{-} \to Ar (2 p_{9}) + e^{-}$	$400 T_{e}^{0.6}$	[15]
$Ar (2 p_{8}) + e^{-} \to Ar (2 p_{10}) + e^{-}$	$400 T_{e}^{0.6}$	[15]
$Ar (2 p_{9}) + e^{-} \to Ar (2 p_{10}) + e^{-}$	$400 T_{e}^{0.6}$	[15]
$Ar (1 s_{5}) + e^{-} \to Ar (1 s_{4}) + e^{-}$	$100 T_{e}^{0.6}$	[15]

Mechanism	Rate Coefficient, $γ$ ( $10^{- 11} {cm}^{3} / s$ )	References
$Ar (1 s_{5}) + Ar \to Ar (1 S_{0}) + Ar$	$2.5 {(\frac{T}{300})}^{0.5}$	Estimated
$Ar (2 p_{10}) + Ar \to Ar (1 s_{5}) + Ar$	$1.5 {(\frac{T}{300})}^{0.5}$	[15]
$Ar (2 p_{10}) + Ar \to Ar (1 s_{4}) + Ar$	$1.5 {(\frac{T}{300})}^{0.5}$	[15]
$Ar (2 p_{9}) + Ar \to Ar (1 s_{5}) + Ar$	$3 {(\frac{T}{300})}^{0.5}$	[15]
$Ar (2 p_{9}) + Ar \to Ar (1 s_{4}) + Ar$	$3 {(\frac{T}{300})}^{0.5}$	[15]
$Ar (2 p_{8}) + Ar \to Ar (1 s_{5}) + Ar$	$4 {(\frac{T}{300})}^{0.5}$	[15]
$Ar (2 p_{8}) + Ar \to Ar (1 s_{4}) + Ar$	$4 {(\frac{T}{300})}^{0.5}$	[15]
$Ar (2 p_{8}) + Ar \to Ar (2 p_{9}) + Ar$	$1.1 {(\frac{T}{300})}^{0.5}$	[16]
$Ar (2 p_{8}) + Ar \to Ar (2 p_{10}) + Ar$	$1.1 {(\frac{T}{300})}^{0.5}$	[16]
$Ar (2 p_{9}) + Ar \to Ar (2 p_{10}) + Ar$	$2.6 {(\frac{T}{300})}^{0.5}$	[16]
$Ar (2 p_{8}) + Ar \to Ar (1 S_{0}) + Ar$	$1.5 {(\frac{T}{300})}^{0.5}$	[16]
$Ar (2 p_{9}) + Ar \to Ar (1 S_{0}) + Ar$	$2.5 {(\frac{T}{300})}^{0.5}$	[16]
$Ar (2 p_{10}) + Ar \to Ar (1 S_{0}) + Ar$	$0.59 {(\frac{T}{300})}^{0.5}$	[16]

Mechanism	Rate Coefficient, $γ$ ( $10^{- 11} {cm}^{3} / s$ )	References
$Ar (1 s_{4}) + He \to Ar (1 s_{5}) + He$	0.01	[16]
$Ar (1 s_{5}) + He \to Ar (1 S_{0}) + He$	$0.2 {(\frac{T}{300})}^{0.5}$ [ $30 Exp (- \frac{2400}{T})$ ]	Estimated
$Ar (2 p_{8}) + He \to Ar (2 p_{9}) + He$	4.5[ $30 Exp (- \frac{570}{T})$ ]	[16]
$Ar (2 p_{8}) + He \to Ar (2 p_{10}) + He$	0.4[ $30 Exp (- \frac{1300}{T})$ ]	[16]
$Ar (2 p_{9}) + He \to Ar (2 p_{10}) + He$	1.6[ $30 Exp (- \frac{880}{T})$ ]	[16]
$Ar (2 p_{8}) + He \to Ar (1 S_{0}) + He$	$0.1 {(\frac{T}{300})}^{0.5}$	[16]
$Ar (2 p_{9}) + He \to Ar (1 S_{0}) + He$	$0.2 {(\frac{T}{300})}^{0.5}$	[16]
$Ar (2 p_{10}) + He \to Ar (1 S_{0}) + He$	$0.0041 {(\frac{T}{300})}^{0.5}$	[16]

Mechanism	Einstein A Coefficient, $γ$ ( $10^{7} s^{- 1}$ )	References
$Ar (1 s_{4}) \to Ar (1 S_{0})$	11.8 (0.057)	[18]
$Ar (2 p_{8}) \to Ar (1 s_{4})$	0.928	[18]
$Ar (2 p_{8}) \to Ar (1 s_{5})$	2.15	[18]
$Ar (2 p_{9}) \to Ar (1 s_{5})$	3.3	[18]
$Ar (2 p_{10}) \to Ar (1 s_{4})$	0.543	[18]
$Ar (2 p_{10}) \to Ar (1 s_{5})$	1.89	[18]

Case	Pressure $P$ [Torr]	Temperature $T$ [K]	Gain Length $l_{g}$ [cm]	Output Coupler $r$	Transmission $T_{w}$	Gain $g_{th}$ [ ${cm}^{- 1}$ ]	Inversion $Δ_{th}$ [ $10^{11} {cm}^{- 3}$ ]
PSI model	769	600	1.9	0.85	0.9	0.15	4.6
AFRL model	400	440	7.62	0.2	0.9	0.13	2.3
Optimized model	100–1000	750	10	0.2	0.98	0.085	0.29–2.9

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Journal of the Optical Society of America B