Abstract

The lifetime of a plasma channel produced by self-guiding intense femtosecond laser pulses in air is largely prolonged by adding a high voltage electrical field in the plasma and by introducing a series of femtosecond laser pulses. An optimal lifetime value is realized through adjusting the delay among these laser pulses. The lifetime of a plasma channel is greatly enhanced to 350 ns by using four sequential intense 100fs(FWHM) laser pulses with an external electrical field of about 350kV/m, which proves the feasibility of prolonging the lifetime of plasma by adding an external electrical field and employing multiple laser pulses.

© 2006 Optical Society of America

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References

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    [Crossref]
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    [Crossref]

2005 (2)

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

2004 (3)

X. Lu, Xi Ting Ting, Li Ying-Jun, and Zhang Jie, “Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air,” Acta Physica Sinica 53, 3404–3408 (2004).

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

2003 (2)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

2002 (1)

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

2001 (1)

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001).
[Crossref]

2000 (1)

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

1996 (1)

1995 (2)

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995).
[Crossref] [PubMed]

X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995).
[Crossref]

Ackermann, R.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Akozbek, N.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

André, Y.-B.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Bergmann, V.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Biondi, M.A.

M.A. BiondiG. Bekefi, “Recombination,” in Principles of Laser Plasmas, ed. pp.125–157 (New York, Wiley, 1976)

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Bourayou, Riad

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Braun, A.

Chen, Zhenglin

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Chien, C.-Y.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Chin, S.L.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

Comtois, D.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Curley, P. F.

Deng, Yunpei

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

Desparois, A.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Diels, Jean-Claude

X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995).
[Crossref]

Dong, Quanli

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Du, D.

Duan, Zuoliang

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

Eislöffel, Jochen

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Elizondo, Juan M.

X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995).
[Crossref]

Ferland, B.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

Franco, M. A.

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Grillon, G.

Hao, Zuoqiang

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Hatzes, Artie P.

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Hosseini, S. A.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

Jie, Zhang

X. Lu, Xi Ting Ting, Li Ying-Jun, and Zhang Jie, “Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air,” Acta Physica Sinica 53, 3404–3408 (2004).

Jin, Zhan

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Johnston, T. W.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Kalkner, W.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Kasparian, J.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Kasparian, Jérôme

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Kieffer, J.-C.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Korn, G.

Kumm, T.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

La Fontaine, B.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Laux, Uwe

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Li, Ruxin

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

Li, Y. J.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001).
[Crossref]

Li, Yingjun

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Li, Yutong

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Liu, Jiansheng

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

Liu, W.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

Liu, X.

Lu, X.

X. Lu, Xi Ting Ting, Li Ying-Jun, and Zhang Jie, “Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air,” Acta Physica Sinica 53, 3404–3408 (2004).

Luo, Q.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

Mechain, G.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Mejean, G.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Méjean, G.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Méjean, Guillaume

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Mercure, H. P.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Mourou, G.

Mysyrowicz, A.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62–64 (1996).
[Crossref] [PubMed]

Nibbering, E. T. J.

Prade, B. S.

Rethmeier, K.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Rizk, F. A.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Rodriguez, Miguel

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Rohwetter, P.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Roy, G.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

Salin, F.

Salmon, E.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Salmon, Estelle

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Sauerbrey, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Sauerbrey, Roland

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Schaper, S.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Scholz, Alexander

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Sheng, Zhengming

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Squier, J.

Stecklum, Bringfried

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Stelmaszcyk, K.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Teng, Hao

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Ting, Xi Ting

X. Lu, Xi Ting Ting, Li Ying-Jun, and Zhang Jie, “Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air,” Acta Physica Sinica 53, 3404–3408 (2004).

Vidal, F.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Wang, Cai Yi

X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995).
[Crossref]

Wei, Z. Y.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001).
[Crossref]

Wei, Zhiyi

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Weise, B.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Wolf, J. P.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

Wolf, J.-P.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Wolf, Jean-Pierre

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Wöste, L.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Wöste, Ludger

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Xie, Xinhua

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

Xu, Zhizhan

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

Yan, Fei

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Yang, H.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001).
[Crossref]

Yang, Hui

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Ying-Jun, Li

X. Lu, Xi Ting Ting, Li Ying-Jun, and Zhang Jie, “Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air,” Acta Physica Sinica 53, 3404–3408 (2004).

Yu, J.

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Yu, Jin

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Yu, W.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001).
[Crossref]

Zeng, Zhinan

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

Zhang, J.

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001).
[Crossref]

Zhang, Jie

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Zhang, Jun

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Zhao, X .M .

X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995).
[Crossref]

Acta Physica Sinica (2)

X. Lu, Xi Ting Ting, Li Ying-Jun, and Zhang Jie, “Lifetime of the plasma channel produced by ultra-short and ultra-high power laser pulse in the air,” Acta Physica Sinica 53, 3404–3408 (2004).

Quanli Dong, Fei Yan, Jie Zhang, Zhan Jin, Hui Yang, Zuoqiang Hao, Zhenglin Chen, Yutong Li, Zhiyi Wei, and Zhengming Sheng, “The measurement and analysis of the prolonged lifetime of the plasma channel formed by short pulse laser in air,” Acta Physica Sinica 54, 3247–3250 (2005).

Appl. Phys. B (1)

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Akozbek, G. Roy, and S.L. Chin, “Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules,” Appl. Phys. B 77, 697–702 (2003).
[Crossref]

Appl.Phys. Lett. (1)

R. Ackermann, K. Stelmaszcyk, P. Rohwetter, G. Mejean, E. Salmon, J. Yu, J. Kasparian, G. Mechain, V. Bergmann, S. Schaper, B. Weise, T. Kumm, K. Rethmeier, W. Kalkner, L. Wöste, and J. P. Wolf, “Triggering and guiding of megavolt discharges by laser-induced filaments under rain conditions,” Appl.Phys. Lett. 85, 5781–5783 (2004).
[Crossref]

IEEE J. Quantum Electron. (1)

X .M . Zhao, Jean-Claude Diels, Cai Yi Wang, and Juan M. Elizondo, “Femtosecond Ultraviolet Laser Pulse Induced Lightning Discharges in Gases,” IEEE J. Quantum Electron. 31.599–612(1995).
[Crossref]

IEEE Trans. Plasma Sci. (1)

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28, 418–433 (2000).
[Crossref]

Opt. Lett. (2)

Phy. Rev. E (1)

Miguel Rodriguez, Riad Bourayou, Guillaume Méjean, Jérôme Kasparian, Jin Yu, Estelle Salmon, Alexander Scholz, Bringfried Stecklum, Jochen Eislöffel, Uwe Laux, Artie P. Hatzes, Roland Sauerbrey, Ludger Wöste, and Jean-Pierre Wolf. “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phy. Rev. E 69, 036607 (2004).
[Crossref]

Phys. Rev. E (3)

Hui Yang, Jie Zhang, Yingjun Li, Jun Zhang, Yutong Li, Zhenglin Chen, Hao Teng, Zhiyi Wei, and Zhengming Sheng, “Characteristics of self-guided laser plasma channels generated by femtosecond laser pulses in air,” Phys. Rev. E 66, 016406(2002).
[Crossref]

Jiansheng Liu, Zuoliang Duan, Zhinan Zeng, Xinhua Xie, Yunpei Deng, Ruxin Li, and Zhizhan Xu, “Time-resolved investigation of low-density plasma channels produced by a kilohertz femtosecond laser in air,” Phys. Rev. E 72, 026412 (2005).
[Crossref]

H. Yang, J. Zhang, W. Yu, Y. J. Li, and Z. Y. Wei, “Long plasma channels generated by femtosecond laser pulses,” Phys. Rev. E 65, 016406(2001).
[Crossref]

Science (1)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Other (1)

M.A. BiondiG. Bekefi, “Recombination,” in Principles of Laser Plasmas, ed. pp.125–157 (New York, Wiley, 1976)

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup; Electrodes a, b, and probe c are set close to the path of the plasma channel induced by femtosecond laser pulse.

Fig. 2.
Fig. 2.

(a) Measured electrical signals (solid line a, dashed line b, and dash-dotted line c correspond to electrical fields of 0V/m, 250kV/m, 350kV/m respectively); (b) Theoretical calculation with initial condition that n e =×1017 cm -3.

Fig. 3.
Fig. 3.

Electrical signals in double-pulse scheme. The energies of two pulses with the delay of 20 ns are 0.5 mJ and 0.4 mJ respectively. The energies of two pulses with the delay of 40 ns are also 0.5 mJ and 0.4 mJ respectively.

Fig. 4.
Fig. 4.

Electrical signals in double-pulse scheme. The energies of two pulses with the delay of 60 ns are 0.5 mJ respectively. The energies of two pulses with the delay of 100 ns are 0.3 mJ respectively.

Fig. 5.
Fig. 5.

Electrical signal in four-pulse scheme. The energy of the first pulse is 0.4 mJ, and the energies of later pulses are all about 0.1 mJ. The delay between two contiguous pulses is 70 ns.

Fig. 6.
Fig. 6.

Theoretical simulation with α=7.4×104 s -1 and η=2.5×107 s -1 [11]; Solid line a, dashed line b and dash-dotted line c correspond to different dissociative recombination rates 2.2×10-13 m 3/s, 0.8×10-13 m 3/s and 0.3×10-13 m 3/s respectively.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

n e t = α n e η n e β ep n e n p
n p t = α n e β ep n e n p β np n n n p
n n t = η n e β np n n n p
β 1 ( m 3 s ) = 2.035 × 10 12 Te 0.39 , ( e N 2 + )
β 2 ( m 3 s ) = 1.138 × 10 11 Te 0.70 , ( e O 2 + )
β ep = 0.79 β 1 + 0.21 β 2

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