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Numerical method of electron-positron pairs generation in photon-photon collider

## Numerical method of electron-positron pairs generation in photon-photon collider

Li Ang, Yu Jin-Qing, Chen Yu-Qing, Yan Xue-Qing
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• #### Abstract

The creation of positron and electron pairs through photon-photon collision, named Breit-Wheeler process, has been well understood in the theories of quantum electrodynamics for nearly 100 years. The photon-photon collision, which is one of the most basic processes of matter generation in the universe, has not been observed yet. The study on photon-photon collision can promote the development of two-photon physics, quantum electrodynamics theories and high energy physics. To observe photon-photon collision in the laboratory, one needs to collimate a huge number of energetic γ-ray photons into a very small spot. Recently, the development of highly collomated source generated by 10 PW laser makes photon-photon collider much more possible than before. In photon-photon collider, the study of numerical simulation plays a critical role since no experiment has achieved such a process. In this paper, a new numerical method is developed to handle the two-photon Breit-Wheeler process. This method is based on the exact two-photon collision dynamic principle, including energy threshold condition, cross-section condition, Lorentz transformation, etc. In the method, the photons are divided into quantitative photon blocks based on the spatial coordinates. Firstly, one needs to find the collision blocks according to the spatial motion law. Secondly, the ergodic method is used to look up the photons that satisfy the energy threshold condition and the cross-section condition from the blocks. Then, one can calculate the electron yield of the photon collision, and the kinetic parameters of the positrons and electrons. This method rigorously follows the physical principle so it has high precision. On the other hand, this method determines the collision of the block in advance, which can reduce the computational requirement a lot. A series of tests is carried out to confirm the accuracy and feasibility of this numerical method by calculating the collision between mono-energetic photon beams. In the tests, the collision angle is assumed to 180° and 60° separately, the results of pair momentum distribution are discussed. We also simulate the collision of the γ-ray beams generated through the interaction between ultra-intense laser and narrow tube targets. In the simulations, the collision angle is changed from 170° to 30° to see its effect on pair production. It is found that the yield of electron-positron pairs decreases with collision angle increasing, which has also been reported in previous work. Therefore, this numerical method can be efficiently used for modeling photon-photon collider, and provide theoretical reference and suggestion to the future experimental design of γ-ray collision.

#### References

 [1] Marklund M, Shukla P K 2006 Rev. Mod. Phys. 78 591 [2] Ehlotzky F, Krajewska K, Kamiński J 2009 Rep. Prog. Phys. 72 046401 [3] Piazza A D, Müller C, Hatsagortsyan K Z, Keitel C H 2012 Rev. Mod. Phys. 84 1177 [4] 黄金书, 罗鹏晖, 鲁公儒 2009 物理学报 58 12 Huang J S, Luo P H, Lu G R 2009 Acta Phys. Sin. 58 12 [5] Burke D L, Field R C, Smith G H, Spencer J E, Walz D 1997 Phys. Rev. Lett. 79 1626 [6] Breit G, Wheeler J A 1934 Phys. Rev. 46 1087 [7] Yu J Q, Lu H Y, Takahashi T, Hu R H, Gong Z, Ma W J, Huang Y S, Chen C E, Yan X Q 2019 Phys. Rev. Lett. 122 014802 [8] 周美林, 颜学庆 2015 物理 44 281 Zhou M L, Yan X Q 2015 Physics 44 281 [9] Brady C S, Ridgers C, Arber T, Bell A R 2013 Plasma. Phys. Controlled Fusion 55 124016 [10] Yu J Q, Hu R H, Gong Z, Ting A, Najmudin Z, Wu D, Lu H Y, Ma W J, Yan X Q 2018 Appl. Phys. Lett. 112 204103 [11] Yu T P, Pukhov A, Sheng Z M, Liu F, Shvets G 2013 Phys. Rev. Lett. 110 045001 [12] Stark D J, Toncian T, Arefiev A V 2016 Phys. Rev. Lett. 116 185003 [13] Capdessus R, Humieres E, Tikhonchuk V T 2013 Phys. Rev. Lett. 110 215003 [14] Brady C S, Ridgers C P, Arber T D, Bell A R, Kirk J G 2012 Phys. Rev. Lett. 109 245006 [15] Nakamura T, Koga J K, Esirkepov T Z, Kando M, Korn G, Bulanov S V 2012 Phys. Rev. Lett. 108 195001 [16] Yi L, Pukhov A, Thanh P L, Shen B 2016 Phys. Rev. Lett. 116 115001 [17] Ji L L, Snyder J, Pukhov A, Freeman R R, Akli K U 2016 Sci. Rep. 6 23256 [18] Zhu X L, Yu T P, Sheng Z M, Yin Y, Turcu I C E, Pukhov A 2016 Nat. Commun. 7 13686 [19] Liu J X, Ma Y Y, Yu T P, Zhao J, Yang X H, Zou D B, Zhang G B, Zhao Y, Yang J K, Li H Z, Zhuo H B, Shao F Q, Kawata S 2017 Chin. Phys. B 26 035202 [20] Geng P F, Lv W J, Li X L, Tang R A, Xue J K 2018 Chin. Phys. B 27 035201 [21] Zhang G B, Hafz N A M, Ma Y Y, Qian L J, Shao F Q, Sheng Z M 2016 Chin. Phys. Lett. 33 095202 [22] Zhu X L, Yin Y, Yu T P, Shao F Q, Ge Z Y, Wang W Q, Liu J J 2015 New J. Phys. 17 053039 [23] Liu J J, Yu T P, Yin Y, Zhu X L, Shao F Q 2016 Opt. Express 24 14 [24] Yu T P, Hu L X, Yin Y, Shao F Q, Zhuo H B, Ma Y Y, Yang X H, Luo W, Pukhov A 2014 Appl. Phys. Lett. 105 114101 [25] Luo W, Zhu Y B, Zhuo H B, Ma Y Y, Song Y M, Zhu Z C, Wang X D, Li X H, Turcu I, Chen M 2015 Phys. Plasmas 22 063112 [26] Luo W, Wu S D, Liu W Y, Ma Y Y, Li F Y, Yuan T, Yu J Y, Chen M, Sheng Z M 2018 Plasma Phys. Controlled Fusion 60 095006 [27] Chen L M, Yan W C, Li D Z, Hu Z D, Zhang L, Wang W M, Hafz N, Mao J Y, Huang K, Ma Y, Zhao J R, Ma J L, Li Y T, Lu X, Sheng Z M, Wei Z Y, Gao J, Zhang J 2013 Sci. Rep. 3 1912 [28] Wang W M, Sheng Z M, Gibbon P, Chen L M, Li Y T, Zhang J 2018 Proc. Natl. Acad. Sci. U.S.A. 115 9911 [29] Wang W M, Gibbon P, Sheng Z M, Li Y T, Zhang J 2017 Phys. Rev. E 96 013201 [30] Chen M, Luo J, Li F Y, Liu F, Sheng Z M, Zhang J 2016 Light-Sci. Appl. 5 e16015 [31] Liu J B, Yu J Q, Shou Y R, Wang D H, Hu R H, Tang Y H, Wang P J, Cao Z X, Mei Z S, Lin C, Lu H Y, Zhao Y Y, Zhu K, Yan X Q, Ma W J 2019 Phys. Plasmas 26 033109 [32] Gong Z, Hu R H, Lu H Y, Yu J Q, Wang D H, Fu E G, Chen C E, He X T, Yan X Q 2018 Plasma Phys. Controlled Fusion 60 044004 [33] H X Chang, B Qiao, Y X Zhang, Z Xu, W P Yao, C T Zhou, X T He 2017 Phys. Plasmas 24 043111 [34] Cristoforetti G, Londrillo P, Singh P K et al. 2017 Phys. Plasmas 7 1479 [35] Huang T, Zhou C, Zhang H, Wu S, Qiao B, He X, Ruan S 2017 Appl. Phys. Lett. 110 021102 [36] Shen B, Bu Z, Xu J, Xu T, Ji L, Li R, Xu Z 2018 Plasma Phys. Controlled Fuison 60 044002 [37] Ribeyre X, d’Humieres E, Jansen O, Jequier S, Tikhonchuk V T, Lobet M 2016 Phys. Rev. E 93 013201 [38] Jansen O, d’Humieres E, Ribeyre X, Jequier S, Tikhonchuk V T 2018 J. Comput. Phys. 355 582 [39] Pike O J, Mackenroth F, Hill E G, Rose S J 2014 Nat. Photonics 8 434 [40] Ribeyre X, d’Humieres E, Jansen O, Jequier S, Tikhonchuk V T 2017 Plasma Phys. Controlled Fusion 59 014024

#### Cited By

• 图 1  单能光子180°对撞时　(a)电子动量分布; (b)正电子动量分布

Figure 1.  (a) Electron momentum distribution; (b) positron momentum distribution of 180° collision of single-energy photons.

图 2  单能光子60°对撞时　(a)电子动量分布; (b)正电子动量分布

Figure 2.  (a) Electron momentum distribution; (b) positron momentum distribution from 60° collision of single-energy photons.

图 3  粒子模拟程序得到的光子束角-谱分布[7,10]

Figure 3.  Angle-spectral distribution of photon beams from particle simulator[7,10].

图 4  106光子170°对撞电子动量极角分布　(a)区块分法一; (b)区块分法二

Figure 4.  Polar angular distribution of electron momentum from 170° collision of 106 photons: (a) the first block division; (b) the second block division.

图 5  电子产额随光子束对撞角的变化趋势

Figure 5.  The trend of electronic yield with the collision angle of photon beam.

图 6  电子产额随光子束偏移量的变化趋势

Figure 6.  The trend of electronic yield with the offset of photon beam.

•  [1] Marklund M, Shukla P K 2006 Rev. Mod. Phys. 78 591 [2] Ehlotzky F, Krajewska K, Kamiński J 2009 Rep. Prog. Phys. 72 046401 [3] Piazza A D, Müller C, Hatsagortsyan K Z, Keitel C H 2012 Rev. Mod. Phys. 84 1177 [4] 黄金书, 罗鹏晖, 鲁公儒 2009 物理学报 58 12 Huang J S, Luo P H, Lu G R 2009 Acta Phys. Sin. 58 12 [5] Burke D L, Field R C, Smith G H, Spencer J E, Walz D 1997 Phys. Rev. Lett. 79 1626 [6] Breit G, Wheeler J A 1934 Phys. Rev. 46 1087 [7] Yu J Q, Lu H Y, Takahashi T, Hu R H, Gong Z, Ma W J, Huang Y S, Chen C E, Yan X Q 2019 Phys. Rev. Lett. 122 014802 [8] 周美林, 颜学庆 2015 物理 44 281 Zhou M L, Yan X Q 2015 Physics 44 281 [9] Brady C S, Ridgers C, Arber T, Bell A R 2013 Plasma. Phys. Controlled Fusion 55 124016 [10] Yu J Q, Hu R H, Gong Z, Ting A, Najmudin Z, Wu D, Lu H Y, Ma W J, Yan X Q 2018 Appl. Phys. Lett. 112 204103 [11] Yu T P, Pukhov A, Sheng Z M, Liu F, Shvets G 2013 Phys. Rev. Lett. 110 045001 [12] Stark D J, Toncian T, Arefiev A V 2016 Phys. Rev. Lett. 116 185003 [13] Capdessus R, Humieres E, Tikhonchuk V T 2013 Phys. Rev. Lett. 110 215003 [14] Brady C S, Ridgers C P, Arber T D, Bell A R, Kirk J G 2012 Phys. Rev. Lett. 109 245006 [15] Nakamura T, Koga J K, Esirkepov T Z, Kando M, Korn G, Bulanov S V 2012 Phys. Rev. Lett. 108 195001 [16] Yi L, Pukhov A, Thanh P L, Shen B 2016 Phys. Rev. Lett. 116 115001 [17] Ji L L, Snyder J, Pukhov A, Freeman R R, Akli K U 2016 Sci. Rep. 6 23256 [18] Zhu X L, Yu T P, Sheng Z M, Yin Y, Turcu I C E, Pukhov A 2016 Nat. Commun. 7 13686 [19] Liu J X, Ma Y Y, Yu T P, Zhao J, Yang X H, Zou D B, Zhang G B, Zhao Y, Yang J K, Li H Z, Zhuo H B, Shao F Q, Kawata S 2017 Chin. Phys. B 26 035202 [20] Geng P F, Lv W J, Li X L, Tang R A, Xue J K 2018 Chin. Phys. B 27 035201 [21] Zhang G B, Hafz N A M, Ma Y Y, Qian L J, Shao F Q, Sheng Z M 2016 Chin. Phys. Lett. 33 095202 [22] Zhu X L, Yin Y, Yu T P, Shao F Q, Ge Z Y, Wang W Q, Liu J J 2015 New J. Phys. 17 053039 [23] Liu J J, Yu T P, Yin Y, Zhu X L, Shao F Q 2016 Opt. Express 24 14 [24] Yu T P, Hu L X, Yin Y, Shao F Q, Zhuo H B, Ma Y Y, Yang X H, Luo W, Pukhov A 2014 Appl. Phys. Lett. 105 114101 [25] Luo W, Zhu Y B, Zhuo H B, Ma Y Y, Song Y M, Zhu Z C, Wang X D, Li X H, Turcu I, Chen M 2015 Phys. Plasmas 22 063112 [26] Luo W, Wu S D, Liu W Y, Ma Y Y, Li F Y, Yuan T, Yu J Y, Chen M, Sheng Z M 2018 Plasma Phys. Controlled Fusion 60 095006 [27] Chen L M, Yan W C, Li D Z, Hu Z D, Zhang L, Wang W M, Hafz N, Mao J Y, Huang K, Ma Y, Zhao J R, Ma J L, Li Y T, Lu X, Sheng Z M, Wei Z Y, Gao J, Zhang J 2013 Sci. Rep. 3 1912 [28] Wang W M, Sheng Z M, Gibbon P, Chen L M, Li Y T, Zhang J 2018 Proc. Natl. Acad. Sci. U.S.A. 115 9911 [29] Wang W M, Gibbon P, Sheng Z M, Li Y T, Zhang J 2017 Phys. Rev. E 96 013201 [30] Chen M, Luo J, Li F Y, Liu F, Sheng Z M, Zhang J 2016 Light-Sci. Appl. 5 e16015 [31] Liu J B, Yu J Q, Shou Y R, Wang D H, Hu R H, Tang Y H, Wang P J, Cao Z X, Mei Z S, Lin C, Lu H Y, Zhao Y Y, Zhu K, Yan X Q, Ma W J 2019 Phys. Plasmas 26 033109 [32] Gong Z, Hu R H, Lu H Y, Yu J Q, Wang D H, Fu E G, Chen C E, He X T, Yan X Q 2018 Plasma Phys. Controlled Fusion 60 044004 [33] H X Chang, B Qiao, Y X Zhang, Z Xu, W P Yao, C T Zhou, X T He 2017 Phys. Plasmas 24 043111 [34] Cristoforetti G, Londrillo P, Singh P K et al. 2017 Phys. Plasmas 7 1479 [35] Huang T, Zhou C, Zhang H, Wu S, Qiao B, He X, Ruan S 2017 Appl. Phys. Lett. 110 021102 [36] Shen B, Bu Z, Xu J, Xu T, Ji L, Li R, Xu Z 2018 Plasma Phys. Controlled Fuison 60 044002 [37] Ribeyre X, d’Humieres E, Jansen O, Jequier S, Tikhonchuk V T, Lobet M 2016 Phys. Rev. E 93 013201 [38] Jansen O, d’Humieres E, Ribeyre X, Jequier S, Tikhonchuk V T 2018 J. Comput. Phys. 355 582 [39] Pike O J, Mackenroth F, Hill E G, Rose S J 2014 Nat. Photonics 8 434 [40] Ribeyre X, d’Humieres E, Jansen O, Jequier S, Tikhonchuk V T 2017 Plasma Phys. Controlled Fusion 59 014024
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•  Citation:
##### Metrics
• Abstract views:  107
• Cited By: 0
##### Publishing process
• Received Date:  14 May 2019
• Accepted Date:  18 October 2019
• Available Online:  07 December 2019
• Published Online:  01 January 2020

## Numerical method of electron-positron pairs generation in photon-photon collider

###### Corresponding author: Yu Jin-Qing, jinqing.yu@hnu.edu.cn;
• 1. College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
• 2. State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China

Abstract: The creation of positron and electron pairs through photon-photon collision, named Breit-Wheeler process, has been well understood in the theories of quantum electrodynamics for nearly 100 years. The photon-photon collision, which is one of the most basic processes of matter generation in the universe, has not been observed yet. The study on photon-photon collision can promote the development of two-photon physics, quantum electrodynamics theories and high energy physics. To observe photon-photon collision in the laboratory, one needs to collimate a huge number of energetic γ-ray photons into a very small spot. Recently, the development of highly collomated source generated by 10 PW laser makes photon-photon collider much more possible than before. In photon-photon collider, the study of numerical simulation plays a critical role since no experiment has achieved such a process. In this paper, a new numerical method is developed to handle the two-photon Breit-Wheeler process. This method is based on the exact two-photon collision dynamic principle, including energy threshold condition, cross-section condition, Lorentz transformation, etc. In the method, the photons are divided into quantitative photon blocks based on the spatial coordinates. Firstly, one needs to find the collision blocks according to the spatial motion law. Secondly, the ergodic method is used to look up the photons that satisfy the energy threshold condition and the cross-section condition from the blocks. Then, one can calculate the electron yield of the photon collision, and the kinetic parameters of the positrons and electrons. This method rigorously follows the physical principle so it has high precision. On the other hand, this method determines the collision of the block in advance, which can reduce the computational requirement a lot. A series of tests is carried out to confirm the accuracy and feasibility of this numerical method by calculating the collision between mono-energetic photon beams. In the tests, the collision angle is assumed to 180° and 60° separately, the results of pair momentum distribution are discussed. We also simulate the collision of the γ-ray beams generated through the interaction between ultra-intense laser and narrow tube targets. In the simulations, the collision angle is changed from 170° to 30° to see its effect on pair production. It is found that the yield of electron-positron pairs decreases with collision angle increasing, which has also been reported in previous work. Therefore, this numerical method can be efficiently used for modeling photon-photon collider, and provide theoretical reference and suggestion to the future experimental design of γ-ray collision.

Reference (40)

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