Abstract

Transverse plasma distribution with 1017 cm−3 maximum electron density and 150 μm transverse size in a plasma filament formed in air by an intense femtosecond laser pulse was measured by means of optical interferometry. Two orders of magnitude decay of the electron density within 2 ns was obtained by combined use of the interferometry and newly proposed terahertz scattering techniques. Excellent agreement was obtained between the measured plasma density evolution and theoretical calculation.

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References

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  1. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
    [CrossRef]
  2. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
    [CrossRef]
  3. F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006).
    [CrossRef] [PubMed]
  4. J. Yu, D. Mondelain, J. Kasparian, E. Salmon, S. Geffroy, C. Favre, V. Boutou, and J. P. Wolf, “Sonographic probing of laser filaments in air,” Appl. Opt. 42(36), 7117–7120 (2003).
    [CrossRef]
  5. S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).
    [CrossRef]
  6. J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
    [CrossRef] [PubMed]
  7. C. Y. Chien, B. La Fontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal, and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure the femtosecond ionization dynamics of air,” Opt. Lett. 25(8), 578–580 (2000).
    [CrossRef]
  8. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
    [CrossRef]
  9. A. Stepanov, N. Bochkarev, and A. Kabanov, “Spatial localization of the region of filamentation along the trace of propagation of focused femtosecond laser radiation in air,” Atmosphere. Oceanic Opt. J. 20, 859–862 (2007).
  10. I. A. Kossyi, A. Yu. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the non-equilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1(3), 207–220 (1992).
    [CrossRef]
  11. F. J. Mehr and M. A. Biondi, “Electron temperature dependence of recombination of O2+ and N2+ ions with electrons,” Phys. Rev. 181(1), 264–271 (1969).
    [CrossRef]
  12. L. M. Biberman, V. S. Vorobyev, and I. T. Yakubov, Kinetics of Nonequilibrium Low-Temperature Plasma (Nauka, Moscow, 1982 in Russian) [(Consultants Bureau, New York, 1987 in English)].
  13. N. L. Aleksandrov, S. V. Kindysheva, M. M. Nudnova, and A. Yu. Starikovskiy, “Mechanism of ultra-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields,” J. Phys. D Appl. Phys. 43(25), 255201 (2010).
    [CrossRef]
  14. N. A. Dyatko, I. V. Kochetov, A. P. Napartovich, and A. G. Sukharev, EEDF: the software package for calculations of the electron energy distribution function in gas mixtures. http://www.lxcat.laplace.univ-tlse.fr/software/EEDF/
  15. A. I. Florescumitchell and J. B. A. Mitchell, “Dissociative recombination,” Phys. Rep. 430(5-6), 277–374 (2006).
    [CrossRef]

2010

N. L. Aleksandrov, S. V. Kindysheva, M. M. Nudnova, and A. Yu. Starikovskiy, “Mechanism of ultra-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields,” J. Phys. D Appl. Phys. 43(25), 255201 (2010).
[CrossRef]

2007

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[CrossRef]

A. Stepanov, N. Bochkarev, and A. Kabanov, “Spatial localization of the region of filamentation along the trace of propagation of focused femtosecond laser radiation in air,” Atmosphere. Oceanic Opt. J. 20, 859–862 (2007).

2006

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006).
[CrossRef] [PubMed]

A. I. Florescumitchell and J. B. A. Mitchell, “Dissociative recombination,” Phys. Rep. 430(5-6), 277–374 (2006).
[CrossRef]

2005

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

2003

2000

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).
[CrossRef]

C. Y. Chien, B. La Fontaine, A. Desparois, Z. Jiang, T. W. Johnston, J. C. Kieffer, H. Pépin, F. Vidal, and H. P. Mercure, “Single-shot chirped-pulse spectral interferometry used to measure the femtosecond ionization dynamics of air,” Opt. Lett. 25(8), 578–580 (2000).
[CrossRef]

1992

I. A. Kossyi, A. Yu. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the non-equilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1(3), 207–220 (1992).
[CrossRef]

1982

1969

F. J. Mehr and M. A. Biondi, “Electron temperature dependence of recombination of O2+ and N2+ ions with electrons,” Phys. Rev. 181(1), 264–271 (1969).
[CrossRef]

Aleksandrov, N. L.

N. L. Aleksandrov, S. V. Kindysheva, M. M. Nudnova, and A. Yu. Starikovskiy, “Mechanism of ultra-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields,” J. Phys. D Appl. Phys. 43(25), 255201 (2010).
[CrossRef]

Becker, A.

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006).
[CrossRef] [PubMed]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[CrossRef]

Biondi, M. A.

F. J. Mehr and M. A. Biondi, “Electron temperature dependence of recombination of O2+ and N2+ ions with electrons,” Phys. Rev. 181(1), 264–271 (1969).
[CrossRef]

Bochkarev, N.

A. Stepanov, N. Bochkarev, and A. Kabanov, “Spatial localization of the region of filamentation along the trace of propagation of focused femtosecond laser radiation in air,” Atmosphere. Oceanic Opt. J. 20, 859–862 (2007).

Boutou, V.

Chien, C. Y.

Chin, S. L.

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006).
[CrossRef] [PubMed]

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[CrossRef]

Deng, Y.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

Desparois, A.

Duan, Z.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

Favre, C.

Florescumitchell, A. I.

A. I. Florescumitchell and J. B. A. Mitchell, “Dissociative recombination,” Phys. Rep. 430(5-6), 277–374 (2006).
[CrossRef]

Franco, M.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).
[CrossRef]

Geffroy, S.

Ina, H.

Jiang, Z.

Johnston, T. W.

Kabanov, A.

A. Stepanov, N. Bochkarev, and A. Kabanov, “Spatial localization of the region of filamentation along the trace of propagation of focused femtosecond laser radiation in air,” Atmosphere. Oceanic Opt. J. 20, 859–862 (2007).

Kasparian, J.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[CrossRef]

J. Yu, D. Mondelain, J. Kasparian, E. Salmon, S. Geffroy, C. Favre, V. Boutou, and J. P. Wolf, “Sonographic probing of laser filaments in air,” Appl. Opt. 42(36), 7117–7120 (2003).
[CrossRef]

Kieffer, J. C.

Kindysheva, S. V.

N. L. Aleksandrov, S. V. Kindysheva, M. M. Nudnova, and A. Yu. Starikovskiy, “Mechanism of ultra-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields,” J. Phys. D Appl. Phys. 43(25), 255201 (2010).
[CrossRef]

Kobayashi, S.

Kossyi, I. A.

I. A. Kossyi, A. Yu. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the non-equilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1(3), 207–220 (1992).
[CrossRef]

Kostinsky, A. Yu.

I. A. Kossyi, A. Yu. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the non-equilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1(3), 207–220 (1992).
[CrossRef]

La Fontaine, B.

Li, R.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

Liu, J.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

Liu, W.

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006).
[CrossRef] [PubMed]

Matveyev, A. A.

I. A. Kossyi, A. Yu. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the non-equilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1(3), 207–220 (1992).
[CrossRef]

Mehr, F. J.

F. J. Mehr and M. A. Biondi, “Electron temperature dependence of recombination of O2+ and N2+ ions with electrons,” Phys. Rev. 181(1), 264–271 (1969).
[CrossRef]

Mercure, H. P.

Mitchell, J. B. A.

A. I. Florescumitchell and J. B. A. Mitchell, “Dissociative recombination,” Phys. Rep. 430(5-6), 277–374 (2006).
[CrossRef]

Mondelain, D.

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).
[CrossRef]

Nudnova, M. M.

N. L. Aleksandrov, S. V. Kindysheva, M. M. Nudnova, and A. Yu. Starikovskiy, “Mechanism of ultra-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields,” J. Phys. D Appl. Phys. 43(25), 255201 (2010).
[CrossRef]

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[CrossRef]

Pépin, H.

Prade, B.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).
[CrossRef]

Salmon, E.

Silakov, V. P.

I. A. Kossyi, A. Yu. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the non-equilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1(3), 207–220 (1992).
[CrossRef]

Simard, P. Tr.

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006).
[CrossRef] [PubMed]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[CrossRef]

Starikovskiy, A. Yu.

N. L. Aleksandrov, S. V. Kindysheva, M. M. Nudnova, and A. Yu. Starikovskiy, “Mechanism of ultra-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields,” J. Phys. D Appl. Phys. 43(25), 255201 (2010).
[CrossRef]

Stepanov, A.

A. Stepanov, N. Bochkarev, and A. Kabanov, “Spatial localization of the region of filamentation along the trace of propagation of focused femtosecond laser radiation in air,” Atmosphere. Oceanic Opt. J. 20, 859–862 (2007).

Takeda, M.

Théberge, F.

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006).
[CrossRef] [PubMed]

Tzortzakis, S.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).
[CrossRef]

Vidal, F.

Wolf, J. P.

Wolf, J.-P.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[CrossRef]

Xie, X.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

Xu, Z.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

Yu, J.

Zeng, Z.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

Appl. Opt.

Atmosphere. Oceanic Opt. J.

A. Stepanov, N. Bochkarev, and A. Kabanov, “Spatial localization of the region of filamentation along the trace of propagation of focused femtosecond laser radiation in air,” Atmosphere. Oceanic Opt. J. 20, 859–862 (2007).

J. Opt. Soc. Am.

J. Phys. D Appl. Phys.

N. L. Aleksandrov, S. V. Kindysheva, M. M. Nudnova, and A. Yu. Starikovskiy, “Mechanism of ultra-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields,” J. Phys. D Appl. Phys. 43(25), 255201 (2010).
[CrossRef]

Opt. Commun.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).
[CrossRef]

Opt. Lett.

Phys. Rep.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007).
[CrossRef]

A. I. Florescumitchell and J. B. A. Mitchell, “Dissociative recombination,” Phys. Rep. 430(5-6), 277–374 (2006).
[CrossRef]

Phys. Rev.

F. J. Mehr and M. A. Biondi, “Electron temperature dependence of recombination of O2+ and N2+ ions with electrons,” Phys. Rev. 181(1), 264–271 (1969).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

J. Liu, Z. Duan, Z. Zeng, X. Xie, Y. Deng, R. Li, Z. Xu, and S. L. Chin, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 026412 (2005).
[CrossRef] [PubMed]

F. Théberge, W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036406 (2006).
[CrossRef] [PubMed]

Plasma Sources Sci. Technol.

I. A. Kossyi, A. Yu. Kostinsky, A. A. Matveyev, and V. P. Silakov, “Kinetic scheme of the non-equilibrium discharge in nitrogen-oxygen mixtures,” Plasma Sources Sci. Technol. 1(3), 207–220 (1992).
[CrossRef]

Rep. Prog. Phys.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007).
[CrossRef]

Other

L. M. Biberman, V. S. Vorobyev, and I. T. Yakubov, Kinetics of Nonequilibrium Low-Temperature Plasma (Nauka, Moscow, 1982 in Russian) [(Consultants Bureau, New York, 1987 in English)].

N. A. Dyatko, I. V. Kochetov, A. P. Napartovich, and A. G. Sukharev, EEDF: the software package for calculations of the electron energy distribution function in gas mixtures. http://www.lxcat.laplace.univ-tlse.fr/software/EEDF/

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Figures (6)

Fig. 1
Fig. 1

Schematics of the experimental setups. Inset: the THz field spectrum generated in ZnTe crystal in the second setup.

Fig. 2
Fig. 2

(a) Phase shift map at the front edge of the filament (W 0 = 5.4 mJ.). (b) Phase shift averaged along the filament. (c) Transverse profile of electron density.

Fig. 3
Fig. 3

(a) Maximum plasma density Ne 0 and (b) FWHM diameter of the plasma channel along the filament. The pump pulse energy is W 0 = 5.4 mJ.

Fig. 4
Fig. 4

(a) Plasma density Ne 0 and (b) FWHM diameter of the filament as a function of the pump pulse energy W 0. Inset – the geometry of energy dependence measurements (see text).

Fig. 5
Fig. 5

(a) Plasma density decay at x = 0, W = 5.4 mJ. (b) Transverse plasma density distributions for t = 0 ps, 100 ps and 200 ps.

Fig. 6
Fig. 6

(a) Bolometer signal as a function of time delay. (b) Plasma density Ne 0 decay. Crosses and diamonds – terahertz and interferometric experimental measurements, respectively. Solid curve – theoretical calculation. Inset – electron temperature as a function of time.

Tables (1)

Tables Icon

Table 1 Reactions for Plasma Decay Calculation.

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