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基于激光尾场加速的全光汤姆孙散射能够提供高质量X射线束并大大减小装置的尺寸. 与分光式相比, 自反射式的构架可以降低实验的时空同步难度, 但是由于激光尾场电子加速和汤姆孙散射过程耦合, X射线优化难度大, 目前缺乏参数优化的相关报道. 本文用数值模拟修正解析理论的方法, 定量分析了激光尾场电子加速和汤姆孙散射过程中激光和电子束的焦斑、脉宽、能量等参数变化情况, 并给出了激光在等离子体镜上的反射率, 从而实现了用解析公式计算而非数值模拟跟踪参数变化, 在保证精度的同时节约了计算时间. 另外, 利用修正后的公式优化了给定激光条件下的自反射式全光汤姆孙散射X射线, 通过改变等离子体密度和等离子体镜位置这两个参数给出了最优X射线亮度和光子产额, 该方法为将来结合人工智能优化控制全光汤姆孙散射光源提供了理论基础.All-laser-driven Thomson scattering based on laser wakefield acceleration can provide high quality X-ray and greatly reduce the source size. Compared with two-pulse setting, the self-reflecting setting can reduce the requirement for temporal and spatial synchronization in experiment. However, it is difficult to optimize X-ray because Thomson scattering is coupled with laser wakefield acceleration in this process. In this paper, we correct theory formula through numerical simulation, and analyze the parameters quantitatively in laser wakefield acceleration and Thomson scattering, such as spot size, duration and energy of laser and electron beam, and reflectivity of plasma mirror. Then we can trace the parameters by using the modified formula rather than the numerical simulation with similar accuracy and less time. The modified formula is also used to optimize the self-reflecting all-laser-driven Thomson scattering X-ray under the given laser conditions. The optimal X-ray luminance and photon number can be obtained by changing the plasma density and the position of the plasma mirror.
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Keywords:
- laser wakefield acceleration /
- Thomson scattering /
- self-reflecting /
- X-ray
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图 1 自反射全光汤姆孙散射示意图
Fig. 1. Schematic of self-reflecting all-laser-driven Thomson scattering.
图 2 LWFA中激光的参量的变化 (a) 焦斑; (b) 脉宽; (c) 能量(图中能量低于能量截止线时包含激光能量和尾场能量); (d) 激光能量衰减长度
Fig. 2. Evolution of laser parameters in LWFA: (a) Laser spot size; (b) laser duration; (c) laser energy (energy in figure contains laser parts and wakefield parts when it is below dashed line); (d) pump depletion length.
图 3 LWFA中电子的参量变化 (a)电子平均能量; (b)失相长度; (c) 0.5 mm处轴线上的纵向尾场分布; (d)电子电荷量; (e)密度为4 × 1018 cm–3时电子束焦斑和脉宽; (f) 密度为4 × 1018 cm–3时电子束发散角
Fig. 3. Evolution of electron parameters in LWFA: (a) Average energy; (b) dephasing length; (c) longitudinal electric field on axis when d = 0.5 mm; (d) charge; (e) spot size and duration when np = 4 × 1018 cm–3; (f) divergence angle when np = 4 × 1018 cm–3.
图 5 汤姆孙散射X射线参数 (a) 能谱; (b) 角分布
Fig. 5. X-ray from Thomson sacttering: (a) Energy spectrum; (b) angle divergence distribution.
图 6 X射线优化结果 (a) 亮度; (b) 光子数; (c) 光子能量
Fig. 6. Optimization results of X-ray: (a) Brightness; (b) photon number; (c) photon energy.
表 1 等离子体密度4 × 1018 cm–3, PM位置2.5 mm时修正后的公式计算和数值模拟的部分参数比较
Table 1. Comparison of modified formula calculation and numerical simulation when plasma density is 4 × 1018 cm–3 and PM position is 2.5 mm away.
方法 经过LWFA的激光 电子束 X射线 焦斑/μm 脉宽/fs 能量损失/(%·mm–1) 能量/MeV 焦斑/μm 发散角/mrad 光子数/107 亮度/(1018photons·s–1·
mm–2·mrad–2·
(0.1%BW)–1)修正公式 10 7 17 460 2.0 18 4.1 1.3 数值模拟 10 6 17 450 1.8 16 4.0 1.6 
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[1] Albert F, Thomas A G R 2016 Plasma Phys. Controlled Fusion 58 103001
Google Scholar
[2] Corde S, Ta Phuoc K, Lambert G, Fitour R, Malka V, Rousse A, Beck A, Lefebvre E 2013 Rev. Mod. Phys. 85 1
Google Scholar
[3] Esarey E, Schroeder C B, Leemans W P 2009 Rev. Mod. Phys. 81 1229
Google Scholar
[4] Gonsalves A J, Nakamura K, Daniels J, Benedetti C, Pieronek C, de Raadt T C H, Steinke S, Bin J H, Bulanov S S, van Tilborg J, Geddes C G R, Schroeder C B, Toth C, Esarey E, Swanson K, Fan-Chiang L, Bagdasarov G, Bobrova N, Gasilov V, Korn G, Sasorov P, Leemans W P 2019 Phys. Rev. Lett. 122 084801
Google Scholar
[5] Wang W T, Li W T, Liu J S, Zhang Z J, Qi R, Yu C H, Liu J Q, Fang M, Qin Z Y, Wang C, Xu Y, Wu F X, Leng Y X, Li R X, Xu Z Z 2016 Phys. Rev. Lett. 117 124801
Google Scholar
[6] Umstadter D P 2015 Contemp. Phys. 56 417
Google Scholar
[7] Chen S, Powers N D, Ghebregziabher I, Maharjan C M, Liu C, Golovin G, Banerjee S, Zhang J, Cunningham N, Moorti A, Clarke S, Pozzi S, Umstadter D P 2013 Phys. Rev. Lett. 110 155003
Google Scholar
[8] Liu C, Golovin G, Chen S, Zhang J, Zhao B, Haden D, Banerjee S, Silano J, Karwowski H, Umstadter D 2014 Opt. Lett. 39 4132
Google Scholar
[9] Powers N D, Ghebregziabher I, Golovin G, Liu C, Chen S, Banerjee S, Zhang J, Umstadter D P 2014 Nat. Photonics 8 28
Google Scholar
[10] Yan W, Fruhling C, Golovin G, Haden D, Luo J, Zhang P, Zhao B, Zhang J, Liu C, Chen M, Chen S, Banerjee S, Umstadter D 2017 Nat. Photonics 11 514
Google Scholar
[11] Sarri G, Corvan D J, Schumaker W, Cole J, Piazza A Di, Ahmed H, Harvey C, Keitel C H, Krushelnick K, Mangles S P D, Najmudin Z, Symes D, Thomas A G R, Yeung M, Zhao Z, Zepf M 2014 Phys. Rev. Lett. 113 224801
Google Scholar
[12] Ta Phuoc K, Corde S, Thaury C, Malka V, Tafzi A, Goddet J P, Shah R C, Sebban S, Rousse A 2012 Nat. Photonics 6 308
Google Scholar
[13] Shaw J M, Bernstein A C, Zgadzaj R, Hannasch A, LaBerge M, Chang Y Y, Weichman K, Welch J, Henderson W, Tsai H E, Fazel N, Wang X, Ditmire T, Donovan M, Dyer G, Gaul E, Gordon J, Martinez M, Spinks M, Toncian T, Wagner C, Downer M C 2017 arXiv: 1705.08637 vl[physics.acc-ph]
[14] Tsai H E, Wang X M, Shaw J M, Li Z Y, Arefiev A V, Zhang X, Zgadzaj R, Henderson W, Khudik V, Shvets G, Downer M C 2015 Phys. Plasmas 22 023106
Google Scholar
[15] Bruemmer T, Debus A, Pausch R, Osterhoff J, Gruener F 2020 Phys. Rev. Accel. Beams 23 031601
Google Scholar
[16] Fonseca R 2002 Proceedings of the Second International Conference on Computational Science—ICCS Amsterdam, Netherlands, April 21–24, 2002 p342
[17] Lu W 2006 Ph. D. Dissertation (Los Angeles: University of California)
[18] Chen P, Hortonsmith G, Ohgaki T 1995 Nucl. Instrum. Methods Phys. Res., Sect. A 335 107
Google Scholar
[19] 王广辉, 王晓方, 董克攻 2012 物理学报 61 165201
Google Scholar
Wang G H, Wang X F, Dong K G 2012 Acta Phys. Sin. 61 165201
Google Scholar
[20] Decker C D, Mori W B, Tzeng K C, Katsouleas T 1996 Phys. Plasmas 3 2047
Google Scholar
[21] Li G, Ain Q, Li S, Saeed M, Papp D, Kamperidis C, Hafz N A M 2020 Plasma Phys. Controlled Fusion 62 055004
Google Scholar
[22] Gotzfried J, Dopp A, Gilljohann M, Foerster M, Ding H, Schindler S, Schilling G, Buck A, Veisz L, Karsch S 2020 Phys. Rev. X 10 041015
Google Scholar
[23] Couperus J P, Pausch R, Kohler A, Zarini O, Kramer J M, Garten M, Huebl A, Gebhardt R, Helbig U, Bock S, Zeil K, Debus A, Bussmann M, Schramm U, Irman A 2017 Nat. Commun. 8 487
Google Scholar
[24] Modena Z N A, Dangor A E, Clayton C E, Marsh K A, Joshi C, MalkaV, Darrow C B, Danson C N, Neely D, Walsh F N 1995 Nature 377 606
Google Scholar
[25] Amorim L D, Najafabadi N V 2018 Advanced Accelerator Concepts Breckenridge, Colorado, USA, August 12–17, 2018 p345
[26] Pollock B B, Clayton C E, Ralph J E, Albert F, Davidson A, Divol L, Filip C, Glenzer S H, Herpoldt K, Lu W, Marsh K A, Meinecke J, Mori W B, Pak A, Rensink T C, Ross J S, Shaw J, Tynan G R, Joshi C, Froula D H 2011 Phys. Rev. Lett. 107 045001
Google Scholar
[27] Gonsalves A J, Nakamura K, Lin C, Panasenko D, Shiraishi S, Sokollik T, Benedetti C, Schroeder C B, Geddes C G R, Tilborg J V, Osterhoff J, Esarey E, Toth C, Leemans W P 2011 Nat. Phys. 7 862
Google Scholar
[28] Swanson K K, Tsai H E, Barber S K, Lehe R, Mao H S, Steinke S, van Tilborg J, Nakamura K, Geddes C G R, Schroeder C B, Esarey E, Leemans W P 2017 Phys. Rev. Accel. Beams 20 051301
Google Scholar
[29] Thaury F Q C, Anna L, Tiberio C 2007 Nat. Phys. 3 424
Google Scholar
[30] Esarey E, Ride S K, Sprangle P 1993 Phys. Rev. E 48 3003
Google Scholar
[31] Ride S K, Esarey E, Baine M 1995 Phys. Rev. E 52 5425
Google Scholar
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