Free electron laser prepared high-intensity metastable helium and helium-like ions

Du Xiao-Jiao; Wei Long; Sun Yu; Hu Shui-Ming

doi:10.7498/aps.73.20240554

Abstract

In the precision spectroscopy of few-electron atoms, the generation of high-intensity metastable helium atoms and helium-like ions is crucial for implementing experimental studies as well as a critical factor for improving the signal-to-noise ratio of experimental measurements. With the rapid development of free-electron laser (FEL) and technology, FEL wavelengths extend from hard X-rays to soft X-rays and even vacuum ultraviolet bands. Meanwhile, laser pulses with ultra-fast, ultra-intense and high repetition frequencies are realized, thus making it possible for FEL to prepare single-quantum state atoms/ions with high efficiency. In this work, we propose an experimental method for obtaining high-intensity single-quantum state helium atoms and helium-like ions by using FEL. The preparation efficiency can be calculated by solving the master equation of light-atom interaction. Considering the experimental parameters involved in this work, we predict that the efficiencies of preparing metastable 2³S He, Li⁺ and Be²⁺ are about 3%, 6% and 2%, respectively. Compared with the common preparation methods such as gas discharge and electron bombardment, a state-of-the-art laser excitation method can not only increase the preparation efficiency, but also reduce the effects of high-energy stray particles such as electrons, ions, and photons generated during discharge. Furthermore, combined with the laser preparation technique, the sophisticated ion confinement technique, which can ensure a long interaction time between the ions and laser, increases the efficiency of metastable Li⁺ and Be²⁺ by several orders of magnitude. Therefore, the preparation of high-intensity metastable helium and helium-like ions can improve the measurement accuracy of precision spectroscopy of atoms and ions. A new experimental method, based on FEL, to study the fine structure energy levels 2³P of helium, has the potential to obtain the results with an accuracy exceeding the sub-kHz level. Thus, the high-precision fine structure constants can be determined with the development of high-order quantum electrodynamics theory. In order to measure energy levels with higher accuracy, a new detection technique, which can reduce or even avoid more systematic effects, must be developed. For example, the quantum interference effect, which has been proposed in recent years, seriously affects the accuracy of fine-structure energy levels. If the interference phenomenon of spontaneous radiation between different excited states can be avoided in the detection process, the measurement accuracy will not be affected by this quantum interference effect. High-intensity metastable atoms or ions in chemical reaction dynamics studies also have better chances to investigate reaction mechanisms. In summary, the FEL preparation of high-intensity metastable helium atoms and helium-like ions proposed in this work will lay an important foundation for developing cold atom physics and chemical reaction dynamics.

Keywords:

metastable helium and helium-like ions /
precision spectroscopy /
free electron laser /
signal-to-noise ratio /
preparation effciency

Authors and contacts

1.
Institute of Advanced Science Facilities, Shenzhen 518107, China
2.
Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Sun Yu, sunyu@mail.iasf.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12304291, 22241301, 91736101, 12393822) and the Science Foundation for Postdoctoral Research of the Ministry of Science and Technology of China (Grant No. 2022M723062).

FullText HTML : translate this paragraph

References

[1]	Heydarizadmotlagh F, Skinner T D G, Kato K, George M C, Hessels E A 2024 Phys. Rev. Lett. 132 163001 Google Scholar
[2]	Wen J L, Tang J D, Dong J F, Du X J, Hu S M, Sun Y R 2023 Phys. Rev. A 107 042811 Google Scholar
[3]	Henson B, Ross J, Thomas K, et al. 2022 Science 376 199 Google Scholar
[4]	Tiesinga E, Mohr P J, Newell D B, Taylor B N 2021 J. Phys. Chem. Ref. Data 50 033105 Google Scholar
[5]	Sun Y R, Hu S M 2020 Natl. Sci. Rev. 7 1818 Google Scholar
[6]	Chen J J, Sun Y, Wen J L, Hu S M 2020 Phys. Rev. A 101 053824 Google Scholar
[7]	Kato K, Skinner T, Hessels E 2018 Phys. Rev. Lett. 121 143002 Google Scholar
[8]	郑昕, 孙羽, 陈娇娇, 胡水明 2018 物理学报 67 164203 Google Scholar Zheng X, Sun Y R, Chen J J, Hu S M 2018 Acta Phys. Sin. 67 164203 Google Scholar
[9]	Zheng X, Sun Y, Chen J J, Jiang W, Pachucki K, Hu S M 2017 Phys. Rev. Lett. 119 263002 Google Scholar
[10]	Feng G P, Zheng X, Sun Y R, Hu S M 2015 Phys. Rev. A 91 030502 Google Scholar
[11]	Zheng X, Sun Y, Chen J J, Jiang W, Pachucki K, Hu S M 2017 Phys. Rev. Lett. 118 063001 Google Scholar
[12]	Vutha A C, Hessels E A 2015 Phys. Rev. A 92 052504 Google Scholar
[13]	Pastor P C, Consolino L, Giusfredi G, De Natale P, Inguscio M, Yerokhin V, Pachucki K 2012 Phys. Rev. Lett. 108 143001 Google Scholar
[14]	Smiciklas M, Shiner D 2010 Phys. Rev. Lett. 105 123001 Google Scholar
[15]	Borbely J, George M, Lombardi L, Weel M, Fitzakerley D, Hessels E 2009 Phys. Rev. A 79 060503 Google Scholar
[16]	Giusfredi G, Pastor P C, Natale P D, Mazzotti D, Mauro C d, Fallani L, Hagel G, Krachmalnicoff V, Inguscio M 2005 Can. J. Phys. 83 301 Google Scholar
[17]	Zelevinsky T, Farkas D, Gabrielse G 2005 Phys. Rev. Lett. 95 203001 Google Scholar
[18]	George M, Lombardi L, Hessels E 2001 Phys. Rev. Lett. 87 173002 Google Scholar
[19]	Sun W, Zhang P P, Zhou P P, Chen S L, Zhou Z Q, Huang Y, Qi X Q, Yan Z C, Shi T Y, Drake G W F, Zhong Z X, Guan H, Gao K L 2023 Phys. Rev. Lett. 131 103002 Google Scholar
[20]	Scholl T J, Cameron R, Rosner S D, Zhang L, Holt R A, Sansonetti C J, Gillaspy J D 1993 Phys. Rev. Lett. 71 2188 Google Scholar
[21]	Schwartz C 1964 Phys. Rev. 134 A1181 Google Scholar
[22]	Paliwal P, Deb N, Reich D M, van der Avoird A, Koch C P, Narevicius E 2021 Nat. Chem. 13 94 Google Scholar
[23]	Klein A, Shagam Y, Skomorowski W, Zuchowski P S, Pawlak M, Janssen L M, Moiseyev N, Meerakker S Y V D, Avoird A V D, Koch C P, Narevicius E 2017 Nat. Phys. 13 35 Google Scholar
[24]	Henson A B, Gersten S, Shagam Y, Narevicius J, Narevicius E 2012 Science 338 234 Google Scholar
[25]	Martin D W, Weiser C, Sperlein R F, Bernfeld D L, Siska P E 1989 J. Chem. Phys 90 1564 Google Scholar
[26]	Pachucki K, Yerokhin V A 2023 Phys. Rev. Lett. 130 053002 Google Scholar
[27]	Yerokhin V A, Patkóš V, Pachucki K 2023 Phys. Rev. A 107 012810 Google Scholar
[28]	Patkóš V, Yerokhin V A, Pachucki K 2021 Phys. Rev. A 103 042809 Google Scholar
[29]	Pachucki K, Yerokhin V A 2010 Phys. Rev. Lett. 104 070403 Google Scholar
[30]	Pachucki K, Patkóš V C V, Yerokhin V A 2023 Phys. Rev. A 108 052802 Google Scholar
[31]	Yerokhin V A, Patkóš V, Pachucki K 2022 Phys. Rev. A 106 022815 Google Scholar
[32]	Pachucki K 2022 Phys. Rev. A 106 022802 Google Scholar
[33]	Qi X Q, Zhang P P, Yan Z C, Shi T Y, Drake G W F, Chen A X, Zhong Z X 2023 Phys. Rev. A 107 L010802 Google Scholar
[34]	Qi X Q, Zhang P P, Yan Z C, Drake G W F, Zhong Z X, Shi T Y, Chen S L, Huang Y, Guan H, Gao K L 2020 Phys. Rev. Lett. 125 183002 Google Scholar
[35]	Johnson W R, Cheng K T, Plante D R 1997 Phys. Rev. A 55 2728 Google Scholar
[36]	Tang K T, Toennies J P 1984 J. Chem. Phys. 80 3726 Google Scholar
[37]	Cheng C F, Jiang W, Yang G M, Sun Y R, Pan H, Gao Y, Liu A W, Hu S M 2010 Rev. Sci. Instrum. 81 123106 Google Scholar
[38]	Kponou A, Hughes V W, Johnson C E, Lewis S A, Pichanick F M J 1981 Phys. Rev. A 24 264 Google Scholar
[39]	Scholl T J, Holt R A, Rosner S D 1989 Phys. Rev. A 39 1163 Google Scholar
[40]	Chen S L, Liang S Y, Sun W, Huang Y, Guan H, Gao K L 2019 Rev. Sci. Instrum. 90 043112 Google Scholar
[41]	Bergeson S D, Balakrishnan A, Baldwin K, Lucatorto T B, Marangos J, McIlrath T, O’Brian T R, Rolston S, Sansonetti C J, Wen J 1998 Phys. Rev. Lett. 80 3475 Google Scholar
[42]	Wang J S, Ritterbusch F, Dong X Z, Gao C, Li H, Jiang W, Liu S Y, Lu Z T, Wang W H, Yang G M, Zhang Y S, Zhang Z Y 2021 Phys. Rev. Lett. 127 023201 Google Scholar
[43]	Steck D A 2017 Quantum and Atom Optics (Eugene: University of Oregon
[44]	Baig M 2022 Atoms 10 39 Google Scholar
[45]	Chen S L, Zhou P P, Liang S Y, Sun W, Sun H Y, Huang Y, Guan H, Gao K L 2020 Chin. Phys. Lett. 37 073201 Google Scholar

Cited By

图 1 (a)制备亚稳态氦原子的相关能级; (b)制备亚稳态氦原子/类氦离子的装置示意图

Figure 1. (a) Energy levels for the preparation of metastable helium; (b) schematic of designed apparatus for the preparation of metastable helium/helium-like ions.

DownLoad: Full-Size Img PowerPoint

图 2 单脉冲作用时单个氦原子不同能级布居数的时间演化结果

Figure 2. Time evolution for different energy levels of helium by single-pulse excitation.

DownLoad: Full-Size Img PowerPoint

图 3 激光制备亚稳态氦原子的效率随光斑大小的模拟结果

Figure 3. Simulation results of preparation efficiency of metastable helium with respect to spot size.

DownLoad: Full-Size Img PowerPoint

图 4 激发效率随同步辐射光通量的变化

Figure 4. Excitation efficiency as a function of the photon flux for synchrotron radiation sources.

DownLoad: Full-Size Img PowerPoint

图 5 制备亚稳态$ {\rm{Li^{+}}} $和$ {\rm{Be^{2+}}} $的相关能级示意图

Figure 5. Energy levels of metastable $ {\rm{Li^{+}}} $ and $ {\rm{Be^{2+}}} $.

DownLoad: Full-Size Img PowerPoint

DownLoad: Full-Size Img PowerPoint

[1]	Heydarizadmotlagh F, Skinner T D G, Kato K, George M C, Hessels E A 2024 Phys. Rev. Lett. 132 163001 Google Scholar
[2]	Wen J L, Tang J D, Dong J F, Du X J, Hu S M, Sun Y R 2023 Phys. Rev. A 107 042811 Google Scholar
[3]	Henson B, Ross J, Thomas K, et al. 2022 Science 376 199 Google Scholar
[4]	Tiesinga E, Mohr P J, Newell D B, Taylor B N 2021 J. Phys. Chem. Ref. Data 50 033105 Google Scholar
[5]	Sun Y R, Hu S M 2020 Natl. Sci. Rev. 7 1818 Google Scholar
[6]	Chen J J, Sun Y, Wen J L, Hu S M 2020 Phys. Rev. A 101 053824 Google Scholar
[7]	Kato K, Skinner T, Hessels E 2018 Phys. Rev. Lett. 121 143002 Google Scholar
[8]	郑昕, 孙羽, 陈娇娇, 胡水明 2018 物理学报 67 164203 Google Scholar Zheng X, Sun Y R, Chen J J, Hu S M 2018 Acta Phys. Sin. 67 164203 Google Scholar
[9]	Zheng X, Sun Y, Chen J J, Jiang W, Pachucki K, Hu S M 2017 Phys. Rev. Lett. 119 263002 Google Scholar
[10]	Feng G P, Zheng X, Sun Y R, Hu S M 2015 Phys. Rev. A 91 030502 Google Scholar
[11]	Zheng X, Sun Y, Chen J J, Jiang W, Pachucki K, Hu S M 2017 Phys. Rev. Lett. 118 063001 Google Scholar
[12]	Vutha A C, Hessels E A 2015 Phys. Rev. A 92 052504 Google Scholar
[13]	Pastor P C, Consolino L, Giusfredi G, De Natale P, Inguscio M, Yerokhin V, Pachucki K 2012 Phys. Rev. Lett. 108 143001 Google Scholar
[14]	Smiciklas M, Shiner D 2010 Phys. Rev. Lett. 105 123001 Google Scholar
[15]	Borbely J, George M, Lombardi L, Weel M, Fitzakerley D, Hessels E 2009 Phys. Rev. A 79 060503 Google Scholar
[16]	Giusfredi G, Pastor P C, Natale P D, Mazzotti D, Mauro C d, Fallani L, Hagel G, Krachmalnicoff V, Inguscio M 2005 Can. J. Phys. 83 301 Google Scholar
[17]	Zelevinsky T, Farkas D, Gabrielse G 2005 Phys. Rev. Lett. 95 203001 Google Scholar
[18]	George M, Lombardi L, Hessels E 2001 Phys. Rev. Lett. 87 173002 Google Scholar
[19]	Sun W, Zhang P P, Zhou P P, Chen S L, Zhou Z Q, Huang Y, Qi X Q, Yan Z C, Shi T Y, Drake G W F, Zhong Z X, Guan H, Gao K L 2023 Phys. Rev. Lett. 131 103002 Google Scholar
[20]	Scholl T J, Cameron R, Rosner S D, Zhang L, Holt R A, Sansonetti C J, Gillaspy J D 1993 Phys. Rev. Lett. 71 2188 Google Scholar
[21]	Schwartz C 1964 Phys. Rev. 134 A1181 Google Scholar
[22]	Paliwal P, Deb N, Reich D M, van der Avoird A, Koch C P, Narevicius E 2021 Nat. Chem. 13 94 Google Scholar
[23]	Klein A, Shagam Y, Skomorowski W, Zuchowski P S, Pawlak M, Janssen L M, Moiseyev N, Meerakker S Y V D, Avoird A V D, Koch C P, Narevicius E 2017 Nat. Phys. 13 35 Google Scholar
[24]	Henson A B, Gersten S, Shagam Y, Narevicius J, Narevicius E 2012 Science 338 234 Google Scholar
[25]	Martin D W, Weiser C, Sperlein R F, Bernfeld D L, Siska P E 1989 J. Chem. Phys 90 1564 Google Scholar
[26]	Pachucki K, Yerokhin V A 2023 Phys. Rev. Lett. 130 053002 Google Scholar
[27]	Yerokhin V A, Patkóš V, Pachucki K 2023 Phys. Rev. A 107 012810 Google Scholar
[28]	Patkóš V, Yerokhin V A, Pachucki K 2021 Phys. Rev. A 103 042809 Google Scholar
[29]	Pachucki K, Yerokhin V A 2010 Phys. Rev. Lett. 104 070403 Google Scholar
[30]	Pachucki K, Patkóš V C V, Yerokhin V A 2023 Phys. Rev. A 108 052802 Google Scholar
[31]	Yerokhin V A, Patkóš V, Pachucki K 2022 Phys. Rev. A 106 022815 Google Scholar
[32]	Pachucki K 2022 Phys. Rev. A 106 022802 Google Scholar
[33]	Qi X Q, Zhang P P, Yan Z C, Shi T Y, Drake G W F, Chen A X, Zhong Z X 2023 Phys. Rev. A 107 L010802 Google Scholar
[34]	Qi X Q, Zhang P P, Yan Z C, Drake G W F, Zhong Z X, Shi T Y, Chen S L, Huang Y, Guan H, Gao K L 2020 Phys. Rev. Lett. 125 183002 Google Scholar
[35]	Johnson W R, Cheng K T, Plante D R 1997 Phys. Rev. A 55 2728 Google Scholar
[36]	Tang K T, Toennies J P 1984 J. Chem. Phys. 80 3726 Google Scholar
[37]	Cheng C F, Jiang W, Yang G M, Sun Y R, Pan H, Gao Y, Liu A W, Hu S M 2010 Rev. Sci. Instrum. 81 123106 Google Scholar
[38]	Kponou A, Hughes V W, Johnson C E, Lewis S A, Pichanick F M J 1981 Phys. Rev. A 24 264 Google Scholar
[39]	Scholl T J, Holt R A, Rosner S D 1989 Phys. Rev. A 39 1163 Google Scholar
[40]	Chen S L, Liang S Y, Sun W, Huang Y, Guan H, Gao K L 2019 Rev. Sci. Instrum. 90 043112 Google Scholar
[41]	Bergeson S D, Balakrishnan A, Baldwin K, Lucatorto T B, Marangos J, McIlrath T, O’Brian T R, Rolston S, Sansonetti C J, Wen J 1998 Phys. Rev. Lett. 80 3475 Google Scholar
[42]	Wang J S, Ritterbusch F, Dong X Z, Gao C, Li H, Jiang W, Liu S Y, Lu Z T, Wang W H, Yang G M, Zhang Y S, Zhang Z Y 2021 Phys. Rev. Lett. 127 023201 Google Scholar
[43]	Steck D A 2017 Quantum and Atom Optics (Eugene: University of Oregon
[44]	Baig M 2022 Atoms 10 39 Google Scholar
[45]	Chen S L, Zhou P P, Liang S Y, Sun W, Sun H Y, Huang Y, Guan H, Gao K L 2020 Chin. Phys. Lett. 37 073201 Google Scholar

[1]	Zhang Qian-Yu, Bai Wen-Li, Ao Zhi-Yuan, Ding Yan-Hao, Peng Wen-Cui, He Sheng-Guo, Tong Xin. Precision measurement based on rovibrational spectrum of cold molecular hydrogen ion. Acta Physica Sinica, 2024, 73(20): 203301. doi: 10.7498/aps.73.20241064
[2]	Xiao Zheng-Rong, Zhang Heng-Zhi, Hua Lin-Qiang, Tang Li-Yan, Liu Xiao-Jun. Precision spectroscopic measurements of few-electron atomic systems in extreme ultraviolet region. Acta Physica Sinica, 2024, 73(20): 204205. doi: 10.7498/aps.73.20241231
[3]	Li Hui, Tan Fang-Rui, Yin Hao-Yu, Ma Yue-Yang, Wu Xiao-Bin. Simulation study of decoherence and light intensity uniformization for extreme ultraviolet of uniform light pipe. Acta Physica Sinica, 2024, 73(11): 114201. doi: 10.7498/aps.73.20240335
[4]	Zhong Yin-Peng, Yang Xia. Advances in free-electron-laser based scattering techniques and spectroscopic methods. Acta Physica Sinica, 2024, 73(19): 194101. doi: 10.7498/aps.73.20240930
[5]	Guan Hua, Qi Xiao-Qiu, Chen Shao-Long, Shi Ting-Yun, Gao Ke-Lin. Precision spectroscopy and nuclear structure information of Li⁺ ions. Acta Physica Sinica, 2024, 73(20): 204203. doi: 10.7498/aps.73.20241128
[6]	Liu Xin, Zhou Xiao-Peng, Wen Wei-Qiang, Lu Qi-Feng, Yan Cheng-Long, Xu Guo-Qin, Xiao Jun, Huang Zhong-Kui, Wang Han-Bing, Chen Dong-Yang, Shao Lin, Yuan Yang, Wang Shu-Xing, Ma Wan-Lu, Ma Xin-Wen. Spectral calibration for electron beam ion trap and precision measurement of M1 transition wavelength in Ar¹³⁺. Acta Physica Sinica, 2022, 71(3): 033201. doi: 10.7498/aps.71.20211663
[7]	. Spectral Calibration for Electron Beam Ion Trap and Precision Measurement of M1 Transition Wavelength in Ar13+. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20211663
[8]	Li Ming, Yang Xing-Fan, Xu Zhou, Shu Xiao-Jian, Lu Xiang-Yang, Huang Wen-Hui, Wang Han-Bin, Dou Yu-Huan, Shen Xu-Ming, Shan Li-Jun, Deng De-Rong, Xu Yong, Bai Wei, Feng Di-Chao, Wu Dai, Xiao De-Xin, Wang Jian-Xin, Luo Xing, Zhou Kui, Lao Cheng-Long, Yan Long-Gang, Lin Si-Fen, Zhang Peng, Zhang Hao, He Tian-Hui, Pan Qing, Li Xiang-Kun, Li Peng, Liu Yu, Yang Lin-De, Liu Jie, Zhang De-Min, Li Kai, Chen Ya-Nan. Experimental study on the stimulated saturation of terahertz free electron laser. Acta Physica Sinica, 2018, 67(8): 084102. doi: 10.7498/aps.67.20172413
[9]	Guo Jing, Guo Fu-Ming, Chen Ji-Gen, Yang Yu-Jun. Pulse duration effect on photoelectron spectrum of atom irradiated by strong high frequency laser. Acta Physica Sinica, 2018, 67(7): 073202. doi: 10.7498/aps.67.20172440
[10]	Song Wen-Juan, Guo Fu-Ming, Chen Ji-Gen, Yang Yu-Jun. Theoretical investigation of atomic low-order harmonics under irradiation of two high frequency laser pulses. Acta Physica Sinica, 2018, 67(3): 033201. doi: 10.7498/aps.67.20172129
[11]	Zheng Xin, Sun Yu, Chen Jiao-Jiao, Hu Shui-Ming. Precision spectroscopy on the 2 3S-2 3P transition of atomic helium. Acta Physica Sinica, 2018, 67(16): 164203. doi: 10.7498/aps.67.20180914
[12]	Feng Gao-Ping, Sun Yu, Zheng Xin, Hu Shui-Ming. Design and measurement of a magnetic field for precision spectroscopy of helium. Acta Physica Sinica, 2014, 63(12): 123201. doi: 10.7498/aps.63.123201
[13]	Sun Yu, Feng Gao-Ping, Cheng Cun-Feng, Tu Le-Yi, Pan Hu, Yang Guo-Min, Hu Shui-Ming. Precision spectroscopy of helium using a laser-cooled atomic beam. Acta Physica Sinica, 2012, 61(17): 170601. doi: 10.7498/aps.61.170601
[14]	Yang Ning-Xuan, Jiang Jun, Xie Lu-You, Dong Chen-Zhong. The effects of the Breit interaction on electron impact excitation cross sections of the 1s2s3S1 metastable level of He-like ions. Acta Physica Sinica, 2008, 57(5): 2888-2894. doi: 10.7498/aps.57.2888
[15]	Yang Zhi-Hu, Zhang Xiao-An, Zhao Yong-Tao, Yin Wei-Wei, Li Ning-Xi. Precision measurement of excited spectra of oxygen ions. Acta Physica Sinica, 2006, 55(9): 4520-4527. doi: 10.7498/aps.55.4520
[16]	Wang Qian, Xu Jin-Qiang, Wu Jin, Li Yong-Gui. The imaging of chemical samples with a scanning near-field infrared microscope. Acta Physica Sinica, 2003, 52(2): 298-301. doi: 10.7498/aps.52.298
[17]	HU SU-XING, FU EN-SHENG, XU ZHI-ZHAN. EFFICIENCY ENHANCEMENT OF FAR INFRARED FREE ELECTRON LASER BY USING A REVERSE TAPERING WAVEGUIDE. Acta Physica Sinica, 1996, 45(8): 1326-1330. doi: 10.7498/aps.45.1326
[18]	ZHU SHI-TONG, SHEN WEN-DA, GUO QI-ZHI. WAVE FUNCTION OF FREE ELECTRON IN A STRONG LASER PLASMA. Acta Physica Sinica, 1993, 42(9): 1471-1478. doi: 10.7498/aps.42.1471
[19]	ZHANG SHI-CHANG. EFFECT OF SPACE-CHARGE WAVE IN RAMAN FREE-ELEC-TRON LASERS. Acta Physica Sinica, 1991, 40(2): 219-225. doi: 10.7498/aps.40.219
[20]	ZHANG ZHONG, ZHANG SHI-CHANG. EFFECT OF DC SPACE-CHARGE FIELDS ON EQUILIBRIUM ORBITS OF ELECTRONS IN FREE-ELECTRON LASERS. Acta Physica Sinica, 1989, 38(2): 285-289. doi: 10.7498/aps.38.285

Catalog

Vol. 73, Issue 15 - 2024-08-05

Metrics

Abstract views: 2514
PDF Downloads: 160
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板