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超声分子束的膨胀和输运过程是一个较为复杂的分子动力学问题, 相关的参数较难准确计算. 本文基于麦克风测量方法研究了多种气体(H2, D2, N2, Ar, He, CH4)超声分子束在自由膨胀过程中的平均速度及其沿出射方向在远域空间(喷射距离/喷嘴直径>310)的演变情况, 获得了较大范围内分子束平均速度分布随气体种类、温度、气压和膨胀距离的变化规律. 结果表明, H2, D2, He分子束的速度分别只占各自理论极限速度的54%, 60%和68%, 且在远域空间速度下降较快. 而CH4, N2和Ar分子束的速度与其各自的极限速度十分接近, 占比分别为85%, 92%和99%, 且在远域空间速度下降较缓.The expansion and transportation of supersonic molecular beams is a complex process of molecular dynamics, and the related parameters are difficult to calculate accurately. Currently there is no rigorous theory to accurately predict the beam expansion process under specific valve conditions, and current researches are less concerned with the spatial evolution of supersonic molecular beam characteristics over long distance. In addition, time-of-flight mass spectrometry is not well suitable for supersonic molecular beam injection in the field of magnetic confinement fusion. Therefore, based on microphone measurements, the average velocities of several supersonic molecular beams (H2, D2, N2, Ar, He, CH4) in the process of free expansion and their evolutions in the far-field space (flight distance/nozzle diameter > 310) are studied in this work. The variations of velocity distribution with gas type, temperature, pressure and expansion distance are obtained. The results show that the velocities of H2, D2 and He beams account for only 54%, 60% and 68% of their ideal limit velocities, respectively, and their velocities decrease rapidly in the far-field space. The velocities of CH4, N2 and Ar beams are very close to their limit velocities, accounting for 85%, 92% and 99% respectively, and their velocities decrease slowly in the far-field space. And the results show that the velocities of the H2 and D2 beams increase with the source pressure, while the velocities of the other four molecular beams decrease slightly with the source pressure. And it is found that the velocity of supersonic beam without skimmer is negatively correlated with the square root of the molecular mass. For the effect of temperature on velocity, the results show that the velocities of H2 and D2 beams increase with the source temperature but are smaller than their limit velocities at given temperature, and the difference is larger for higher temperature. The results of this experiment provide basic data for controlling the parameters of the supersonic molecular beam by adjusting the temperature and pressure of the gas source, which will contribute to the application of supersonic molecular beams in fusion reactor fueling technology. And this study will contribute to further exploration of the evolution of supersonic molecular beam properties in the far-field space.
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Keywords:
- microphone /
- supersonic molecular beam /
- free expansion /
- velocity distribution
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Yao L H, Feng B B, Chen C Y, Feng Z, Li W, Jiao Y M 2008 Acta Phys. Sin. 57 4159
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Zhao D W 2009 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China) (in Chinese)
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图 1 超声分子束速度测量装置示意图
Fig. 1. Schematic diagram of supersonic molecular beam velocity measuring device.
图 2 多次测量定时误差 (a)和频率分布直方图(b)
Fig. 2. Timing error (a) and frequency distribution histogram (b) of multiple measurements
图 3 压强P0为50 bar时, 超声分子束速度随轴向距离的变化规律 (a) H2, D2和He的速度结果; (b) N2, Ar和CH4的速度结果
Fig. 3. The velocity of the supersonic molecular beam varies with the axial distance when the pressure P0 was 50 bar: (a) The velocity results of H2,D2 and He; (b) the velocity results of N2,Ar and CH4.
图 4 H2, D2和He分子束(a), 以及N2, Ar和CH4分子束(b)的飞行速度随源压强的变化曲线
Fig. 4. The curves of the velocities of H2, D2 and He molecular beams (a) and N2, Ar and CH4 molecular beams (b) with pressure.
图 5 六种超声分子束的速度与分子量之间的关系 实心方形■代表在50 bar源压强下速度的测量结果, 空心圆○代表估算的极限速度结果
Fig. 5. The relationship between the velocities of the six supersonic molecular beams and their molecular weights. The solid square ■ represents the measured velocity at 50 bar source pressure, and the hollow circle ○ represents the estimated limit velocity.
图 6 H2(a), D2(b)超声束速度随温度的变化结果
Fig. 6. The variation of supersonic H2(a) and D2(b) beam velocity with temperature.
表 1 H2, D2, N2, Ar, He和CH4的实验拟合速度和各自极限速度的对比
Table 1. Comparison of the experimental fitting velocities and the limit velocities of H2, D2, N2, Ar, He and CH4.
Gas H2 D2 N2 Ar He CH4 T/℃ 22 26 24 26 24 24 vfit/m·s–1 1392—1572 1083—1234 609—727 497—556 1048—1174 847—984 vlim/m·s–1 2931 2086 786 557 1757 1157 
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[1] Dunning F B, Hulet R G 1996 Atomic, Molecular, and Optical Physics: Atoms and Molecules (London: Academic Press) Volume 29B, p435
[2] 赵健华, 刘晓敏, 刘培启, 胡大鹏 2015 化工机械 42 59
Zhao J H, Liu X M, Liu P Q, Hu D P 2015 Chem. Mach. 42 59
[3] Farias D, Rieder K 1998 Rep. Prog. Phys. 61 1575
Google Scholar
[4] Smalley R E, Ramakrishna B L, Levy D H, Wharton L 1974 J. Chem. Phys. 61 4363
Google Scholar
[5] 姚良骅, 冯北滨, 冯震, 董贾福, 郦文忠, 徐德明, 洪文玉 2002 51 596
Yao L H, Feng B B, Feng Z, Dong J F, Li W Z, Xu D M, Hong W Y 2002 Acta Phys. Sin. 51 596
[6] 姚良骅, 冯北滨, 陈程远, 冯震, 李伟, 焦一鸣 2008 57 4159
Yao L H, Feng B B, Chen C Y, Feng Z, Li W, Jiao Y M 2008 Acta Phys. Sin. 57 4159
[7] Soukhanovskii V A, Kugel H W, Kaita R, Majeski R, Roquemore A L 2004 Rev. Sci. Instrum. 75 4320
Google Scholar
[8] Ekinci Y, Knuth E L, Toennies J P 2006 J. Chem. Phys. 125 133409
Google Scholar
[9] Christen W, Krause T, Rademann K 2007 Rev. Sci. Instrum. 78 73106
Google Scholar
[10] 吴雪科, 孙小琴, 刘殷学, 李会东, 周雨林, 王占辉, 冯灏 2017 66 195201
Wu X K, Sun X Q, Liu Y X, Li H D, Zhou Y L, Wang Z H, Feng H 2017 Acta Phys. Sin. 66 195201
[11] 董贾福, 唐年益, 李伟, 罗俊林, 郭干诚, 钟云泽, 刘仪, 傅炳忠, 姚良骅, 冯北滨, 秦运文 2002 51 2074
Dong J F, Tang N Y, Li W, Luo J L, Guo G C, Zhong Y Z, Liu Y, Fu B Z, Yao L H, Feng B B, Qin Y W 2002 Acta Phys. Sin. 51 2074
[12] Wang Z H, Xu X Q, Xia T Y, Rognlien T D 2014 Nucl. Fusion 54 43019
Google Scholar
[13] Zhou Y L, Wang Z H, Xu M, Wang Q, Nie L 2016 Chin. Phys. B 25 106601
[14] Zhou Y L, Wang Z H, Xu X Q, Li H D, Feng H, Sun W G 2015 Phys. Plasmas 22 12503
Google Scholar
[15] Hagena O F, Varma A K 1968 Rev. Sci. Instrum. 39 47
Google Scholar
[16] Haberland H, Buck U, Tolle M 1985 Rev. Sci. Instrum. 56 1712
Google Scholar
[17] Christen W, Krause T, Kobin B, Rademann K 2011 J. Phys. Chem. A 115 6997
Google Scholar
[18] Christen W 2013 J. Chem. Phys. 139 24202
Google Scholar
[19] Irie T, Asunobu T Y, Kashimura H 2003 J. Therm. Sci. 12 132
Google Scholar
[20] Tejeda G, Mate B, Fernandez-Sanchez J M, Montero S 1996 Phys. Rev. Lett. 76 34
Google Scholar
[21] Teshima K, Sommerfeld M 1987 Exp. Fluids 5 197
Google Scholar
[22] Belan M A D P 2004 Astrophys. Space Sci. 293 225
Google Scholar
[23] Even U 2014 Adv. Chem. 2014 636042
[24] Wei G, Zhu R, Cheng T, Zhao F 2016 J. Iron Steel Res. Int. 23 997
Google Scholar
[25] Christen W, Rademann K, Even U 2010 J. Phys. Chem. A 114 11189
Google Scholar
[26] Kornilov O, Toennies J P 2009 Int. J. Mass Spectrom. 280 209
Google Scholar
[27] Reisinger T, Greve M M, Eder S D, Bracco G, Holst B 2012 Phys. Rev. A 86 043804
Google Scholar
[28] Christen W, Rademann K 2009 Phys. Scripta 80 48127
Google Scholar
[29] He L, Yi S, Zhao Y, Tian L, Chen Z 2011 Sci. China: Phys. Mech. Astron. 54 1702
Google Scholar
[30] Kerhervé F, Jordan P, Gervais Y, Valière J C, Braud P 2004 Exp. Fluids 37 419
Google Scholar
[31] Liu D, Han J F, Chen Z Y, Bai L X, Zhou J X 2016 Rev. Sci. Instrum. 87 123504
Google Scholar
[32] Chen Z, Li M, Zhou M, Liu D, Qu G, Wang Y, Han J 2019 J. Fusion Energ. 38 228
[33] Han J, Yang C, Miao J, Fu P, Luo X, Shi M 2010 J. Appl. Phys. 108 64327
Google Scholar
[34] Liepmann H W, Roshko A 2001 Elements of Gasdynamics ( New York: Courier Corporation)
[35] 赵大为 2009 硕士学位论文(成都: 电子科技大学)
Zhao D W 2009 M. S. Thesis (Chengdu: University of Electronic Science and Technology of China) (in Chinese)
[36] Eder S D, Salvador Palau A, Kaltenbacher T, Bracco G, Holst B 2018 Rev. Sci. Instrum. 89 113301
Google Scholar
[37] Hagena O F, Obert W 1972 J. Chem. Phys. 56 1793
Google Scholar
[38] Smith R A, Ditmire T, Tisch J W G 1998 Rev. Sci. Instrum. 69 3798
Google Scholar
[39] Akiyoshi M, Junichi M, Tsuchiya H 2010 J. Plasma Fusion Res. SERIES 9 79
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