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Flash radiography technology is commonly used in detonation physics experiments and nondestructive testing, in which an X-ray diode is an integral part of flash radiography equipment. Its function is to convert the electric energy stored in the front power supply into X-rays through the bremsstrahlung effect. Rod-pinch diode is one of the most commonly used X-ray diodes in 1–4 MV. It has the characteristics of a small focal spot and high imaging resolution. The anode ions of the rod pinch diode come from the anode plasma, and the anode plasma electrons are generated at the same time as the anode plasma ions. Before the establishment of the bipolar current between the anode and cathode of the rod pinch diode, these electrons are mainly absorbed by the anode; however, after the formation of the bipolar current, due to the zero electric field on the anode surface, plasma electrons will accumulate near the anode surface and will not be absorbed. Given the theoretical derivation of bipolar current in the gap between anode and cathode of rod pinch diode in the early stage, it is necessary to study the electrons in anode plasma. The simulation of the rod-pinch diode is an essential tool for improving the performance of the rod-pinch diode. To improve simulation accuracy, it is necessary to study the emission mechanism of cathode and anode particles and continuously optimize the simulation model. In this paper, PIC and Monte Carlo simulation are used. An anode plasma model is proposed in this work based on the anode ion emission model of the rod-pinch diode and the characteristics of space charge bipolar flow, that is, when the anode plasma environment is fully established, the electric field on the anode surface is zero, and ions and electrons will accumulate on the anode surface. The new model is analyzed in detail and compared with the anode ion emission model in rod-pinch diode current, electromagnetic field distribution between cathode and anode, electron energy spectrum, motion state of electron incident anode rod, dose, and spot size. The results show that the calculation results from the new model are closer to the experimental results, which shows that the role of electrons accumulated near the anode in the plasma cannot be ignored in the numerical calculation of the rod-pinch diode anode rod surface plasma. -
Keywords:
- rod-pinch diode /
- flash X-ray radiography /
- Monte Carlo Simulation /
- particle in cell simulation
[1] 刘军 2008 博士学位论文 (北京: 中国工程物理研究院)
Liu J 2008 Ph. D. Dissertation (Beijing: China Academy of Engineering Physics) (in Chinese)
[2] 张寿云 1985 爆炸与冲击 5 89
Zhang S Y 1985 Explos. Shock Waves 5 89
[3] Duff R E, Knight H T 1956 J. Chem. Phys. 25 1301
[4] 耿力东, 何泱, 袁建强, 王敏华, 曹龙博, 谢卫平 2018 强激光与粒子束 30 115003
Google Scholar
Geng L D, He Y, Yuan J Q, Wang M H, Cao L B, Xie W P 2018 High Power Laser Part. Beams 30 115003
Google Scholar
[5] Commisso R J, Cooperstein G, Hinshelwood D D, Mosher D, Young F C 2002 IEEE Trans. Plasma Sci. 30 338
Google Scholar
[6] 陈林, 姜巍, 谢卫平, 邓建军 2007 强激光与粒子束 19 1747
Chen L, Jiang W, Xie W P, Deng J J 2007 High Power Laser Part. Beams 19 1747
[7] 高屹, 邱爱慈, 吕敏, 杨海亮, 张众, 张鹏飞 2010 核技术 33 5
Gao Y, Qiu A C, Lü M, Yang H L, Zhang Z, Zhang P F 2010 Nucl. Tech. 33 5
[8] Hinshelwood D D, Cooperstein G, Mosher D, Ottinger P F, Schumer J W, Stephanakis S J, Swanekamp S B, Weber B V, Young F C 2002 Am. Inst. Phys. Conf. Proc. 650 203
[9] 孙剑锋, 孙江, 邱爱慈, 张鹏飞, 杨海亮, 李静雅, 尹佳辉, 胡杨, 金亮 2014 强激光与粒子束 26 276
Google Scholar
Sun J F, Sun J, Qiu A C, Zhang P F, Yang H L, Li J Y, Yin J H, Hu Y, Jin L 2014 High Power Laser Part. Beams 26 276
Google Scholar
[10] 孙江, 孙剑锋, 杨海亮, 张鹏飞, 苏兆锋, 周军 2013 现代应用物理 1 18
Google Scholar
Sun J, Sun J F, Yang H L, Zhang P F, Su Z F, Zhou J 2013 Mod. Appl. Phys. 1 18
Google Scholar
[11] Weber B V, Allen R, Comrmsso R J, Cooperstein G, Hinshelwood D D, Mosher D, Murphy D P, Ottinger PF, Phipps D G, Schumer J W 2007 IEEE 34th International Conference on Plasma Science (ICOPS) Albuquerque, NM, USA, June 17–22, 2007 p440
[12] Sorokin S A 2010 Tech. Phys. Lett. 36 379
Google Scholar
[13] Weber B V, Cooperstein G, Hinshelwood D D, Mosher D, Schumer J W, Stephanakis S J, Strasburg S B, Swanekamp S B, Young F C 2002 AIP Conf. Proc. 650 191
Google Scholar
[14] 徐启福 2012 博士学位论文 (长沙: 国防科学技术大学)
Xu Q F 2012 Ph. D. Dissertation (Chang Sha: National University of Defense Science and technology) (in Chinese)
[15] Poukey J W 1975 Appl. Phys. Lett. 26 145
Google Scholar
[16] 耿力东, 谢卫平, 袁建强, 王敏华, 曹龙博, 付佳斌, 赵小明, 何泱 2018 强激光与粒子束 30 085003
Google Scholar
Geng L D, Xie W P, Yuan J Q, Wang M H, Cao L B, Fu J B, Zhao X M, He Y 2018 High Power Laser Part. Beams 30 085003
Google Scholar
[17] Miller C L, Welch D R, Rose D V, Oliver B V 2010 IEEE Trans. Plasma Sci. 38 2507
Google Scholar
[18] 王宇, 李洪涛, 王文斗, 邓建军, 刘金峰, 马成刚 2015 强激光与粒子束 27 095005
Google Scholar
Wang Y, Li H T, Wang W D, Deng J J, Liu J F, Ma C G 2015 High Power Laser Part. Beams 27 095005
Google Scholar
[19] 耿力东, 谢卫平, 袁建强, 王敏华, 曹龙博, 张思群, 赵小明, 何泱 2018 原子能科学技术 52 1512
Google Scholar
Geng L D, Xie W P, Yuan J Q, Wang M H, Cao L B, Zhang S Q, Zhao X M, He Y 2018 At. Energy Sci. Technol. 52 1512
Google Scholar
[20] Xie W, Xia M, Guo F, Geng L, Zhao Y, Xu L, Feng S, Zhou L, Wei B, He A, Yuan J, Chen L, Li H, Han W, Jiang J, Li F, Wang Z, Li Y, Kang J, Zhang Y, Wu W, Wang M, Zou W 2021 Phys. Rev. Accel. Beams 24 110401
Google Scholar
[21] Zhou J, Liu D, Chen L, Li Z 2009 IEEE Trans. Plasma Sci. 37 2002
Google Scholar
[22] Perl J, Shin J, Schümann J, Faddegon B, Paganetti H 2012 Med. Phys. 39 6818
Google Scholar
[23] Allison J, Amako K, Apostolakis J, Araujo H, Dubois P A, Asai M, Barrand G, Capra R, Chauvie S, Chytracek R 2006 IEEE Trans. Nucl. Sci. 53 270
Google Scholar
[24] Allison J, Amako K, Apostolakis J, Arce P, Asai M, Aso T, Bagli E, Bagulya A, Banerjee S, Barrand G, Beck B R, Bogdanov A G, Brandt D, Brown J M C, Burkhardt H, Canal P, Cano-Ott D, Chauvie S, Cho K, Cirrone G A P, Cooperman G, Cortés-Giraldo M A, Cosmo G, Cuttone G, Depaola G, Desorgher L, Dong X, Dotti A, Elvira V D, Folger G, Francis Z, Galoyan A, Garnier L, Gayer M, Genser K L, Grichine V M, Guatelli S, Guèye P, Gumplinger P, Howard A S, Hřivnáčová I, Hwang S, Incerti S, Ivanchenko A, Ivanchenko V N, Jones F W, Jun S Y, Kaitaniemi P, Karakatsanis N, Karamitros M, Kelsey M, Kimura A, Koi T, Kurashige H, Lechner A, Lee S B, Longo F, Maire M, Mancusi D, Mantero A, Mendoza E, Morgan B, Murakami K, Nikitina T, Pandola L, Paprocki P, Perl J, Petrović I, Pia M G, Pokorski W, Quesada J M, Raine M, Reis M A, Ribon A, Ristić Fira A, Romano F, Russo G, Santin G, Sasaki T, Sawkey D, Shin J I, Strakovsky I I, Taborda A, Tanaka S, Tomé B, Toshito T, Tran H N, Truscott P R, Urban L, Uzhinsky V, Verbeke J M, Verderi M, Wendt B L, Wenzel H, Wright D H, Wright D M, Yamashita T, Yarba J, Yoshida H 2016 Nucl. Instrum. Methods Phys. Res. , Sect. A 835 186
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[25] Agostinelli S, Allison J, Amako K, Apostolakis J, Zschiesche D 2003 Nucl. Instrum. Methods Phys. Res. , Sect. A 506 250
Google Scholar
[26] 李成刚 2015 博士学位论文 (北京: 中国工程物理研究院)
Li C G 2015 Ph. D. Dissertation (Beijing: China Academy of Engineering Physics) (in Chinese)
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图 1 电子相空间分布 (a) 阴极电子爆炸发射的模型; (b) 阴极电子-阳极离子发射模型; (c) 阴极电子-阳极等离子体模型
Figure 1. Spatial distribution of electron phase: (a) Model of cathode electron explosion emission; (b) Cathode electron anode ion emission model; (c) Cathode electron anode plasma model.
图 2 研究流程图
Figure 2. Research flow chart.
图 3 杆箍缩二极管电压、电流位置示意图(a)与D-dot探头标定结果(b)
Figure 3. Schematic diagram of D-dot, B-dot position of Rod-pinch diode (a) and D-dot calibration results (b).
图 4 4—54发实验在50 ns各物理量空间分布图 (a) A模型电子空间分布; (b) B模型电子空间分布; (c) A模型Bphi空间分布; (d) B模型Bphi空间分布; (e) A模型Er空间分布; (f) B模型Er空间分布; (g) A模型Ez空间分布; (h) B模型Ez空间分布(图中白色部分为超量程值)
Figure 4. 4–54 Experiments in 50 ns each physical quantity spatial distribution diagram: (a) A model electronic spatial distribution; (b) B model electronic spatial distribution; (c) A model Bphi spatial distribution; (d) B model Bphi spatial distribution; (E) A model Er spatial distribution; (f) B model Er spatial distribution; (g) A model EZ spatial distribution; (H) B model EZ spatial distribution (The white part in the Figure is the over range value).
图 5 1—4 MV杆箍缩二极管阳极入射电子能谱 (a) 1 MV; (b) 2 MV; (c) 3 MV; (d) 4 MV
Figure 5. Incident electron spectrum of 1–4 MV rod-pinch diode anode: (a) 1 MV; (b) 2 MV; (c) 3 MV; (d) 4 MV.
图 6 1—4 MV杆箍缩二极管阳极入射电子位置 (a) 1 MV; (b) 2 MV; (c) 3 MV; (d) 4 MV
Figure 6. 1–4 MV rod-pinch diode anode incident electron position: (a) 1 MV; (b) 2 MV; (c) 3 MV; (d) 4 MV.
图 7 入射角示意图
Figure 7. Schematic diagram of incident angle.
图 8 1—4 MV杆箍缩二极管阳极侧面入射电子角度分布 (a) 1 MV; (b) 2 MV; (c) 3 MV; (d) 4 MV
Figure 8. Angle distribution of incident electrons on the anode side of 1–4 MV rod pinch diode: (a) 1 MV; (b) 2 MV; (c) 3 MV; (d) 4 MV.
图 9 1—4 MV杆箍缩二极管阳极端面入射电子角度分布 (a) 1 MV; (b) 2 MV; (c) 3 MV; (d) 4 MV
Figure 9. Angle distribution of incident electrons on the anode end face of 1–4 MV rod pinch diode: (a) 1 MV; (b) 2 MV; (c) 3 MV; (d) 4 MV.
图 10 针孔成像法焦斑计算示意图
Figure 10. Schematic diagram of focal spot calculation of pinhole imaging method.
图 11 模型焦斑图像 (a) 等离子体模型焦斑图像; (b) 离子模型焦斑图像
Figure 11. Model focal spot images: (a) Plasma model focal spot image; (b) Ion model focal spot image.
图 12 (a) 等离子体模型焦斑高斯拟合曲线; (b) 离子模型焦斑高斯拟合曲线
Figure 12. (a) Gaussian fitting curve of plasma model; (b) Gaussian fitting curve of ion model.
表 1 杆箍缩二极管1—4 MV实验结果
Table 1. Results of Rod-pinch diode 1–4 MV experiment.
发次/No. 电压/MV 电流/kA 剂量/rad rC/mm L/mm 1—6 1.42 57.00 1.23 6.00 10.00 4—54 2.06 58.80 3.60 7.00 10.00 4—62 3.13 73.70 9.50 9.00 10.00 4—81 4.10 98.50 16.60 9.00 16.00 
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表 2 杆箍缩二极管电流实验与模拟结果
Table 2. Experimental and simulation results of rod-pinch diode current.
发次/No. 实验测量电流/kA A模型模拟电流/kA A模型电流百分差/% B模型模拟电流/kA B模型电流百分差/% 1—6 57.00 36.30 36.32 54.80 3.86 4—54 58.80 47.80 18.71 63.89 8.66 4—62 73.70 63.50 13.84 83.60 13.43 4—81 98.50 84.00 14.72 104.60 6.19
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表 3 杆箍缩二极管1 m处剂量实验与模拟结果
Table 3. Experimental and simulation results of dose at 1 m of rod pinch diode.
发次/No. 实验测量剂量/Rad A模型模拟剂量/Rad A模型剂量百分差/% B模型模拟剂量/Rad B模型剂量百分差/% 1—6 1.23 0.86 29.83 1.25 1.63 4—54 3.60 3.36 6.67 3.76 4.44 4—62 9.50 5.41 43.09 8.73 8.11 4—81 16.60 13.12 20.96 17.18 3.49
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表 4 焦斑计算结果
Table 4. Focal spot calculation results.
模型 FWHM成像屏/mm FWHM光源/mm A模型 4.66 ± 0.38 2.33 ± 0.20 B模型 2.40 ± 0.16 1.20 ± 0.08
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[1] 刘军 2008 博士学位论文 (北京: 中国工程物理研究院)
Liu J 2008 Ph. D. Dissertation (Beijing: China Academy of Engineering Physics) (in Chinese)
[2] 张寿云 1985 爆炸与冲击 5 89
Zhang S Y 1985 Explos. Shock Waves 5 89
[3] Duff R E, Knight H T 1956 J. Chem. Phys. 25 1301
[4] 耿力东, 何泱, 袁建强, 王敏华, 曹龙博, 谢卫平 2018 强激光与粒子束 30 115003
Google Scholar
Geng L D, He Y, Yuan J Q, Wang M H, Cao L B, Xie W P 2018 High Power Laser Part. Beams 30 115003
Google Scholar
[5] Commisso R J, Cooperstein G, Hinshelwood D D, Mosher D, Young F C 2002 IEEE Trans. Plasma Sci. 30 338
Google Scholar
[6] 陈林, 姜巍, 谢卫平, 邓建军 2007 强激光与粒子束 19 1747
Chen L, Jiang W, Xie W P, Deng J J 2007 High Power Laser Part. Beams 19 1747
[7] 高屹, 邱爱慈, 吕敏, 杨海亮, 张众, 张鹏飞 2010 核技术 33 5
Gao Y, Qiu A C, Lü M, Yang H L, Zhang Z, Zhang P F 2010 Nucl. Tech. 33 5
[8] Hinshelwood D D, Cooperstein G, Mosher D, Ottinger P F, Schumer J W, Stephanakis S J, Swanekamp S B, Weber B V, Young F C 2002 Am. Inst. Phys. Conf. Proc. 650 203
[9] 孙剑锋, 孙江, 邱爱慈, 张鹏飞, 杨海亮, 李静雅, 尹佳辉, 胡杨, 金亮 2014 强激光与粒子束 26 276
Google Scholar
Sun J F, Sun J, Qiu A C, Zhang P F, Yang H L, Li J Y, Yin J H, Hu Y, Jin L 2014 High Power Laser Part. Beams 26 276
Google Scholar
[10] 孙江, 孙剑锋, 杨海亮, 张鹏飞, 苏兆锋, 周军 2013 现代应用物理 1 18
Google Scholar
Sun J, Sun J F, Yang H L, Zhang P F, Su Z F, Zhou J 2013 Mod. Appl. Phys. 1 18
Google Scholar
[11] Weber B V, Allen R, Comrmsso R J, Cooperstein G, Hinshelwood D D, Mosher D, Murphy D P, Ottinger PF, Phipps D G, Schumer J W 2007 IEEE 34th International Conference on Plasma Science (ICOPS) Albuquerque, NM, USA, June 17–22, 2007 p440
[12] Sorokin S A 2010 Tech. Phys. Lett. 36 379
Google Scholar
[13] Weber B V, Cooperstein G, Hinshelwood D D, Mosher D, Schumer J W, Stephanakis S J, Strasburg S B, Swanekamp S B, Young F C 2002 AIP Conf. Proc. 650 191
Google Scholar
[14] 徐启福 2012 博士学位论文 (长沙: 国防科学技术大学)
Xu Q F 2012 Ph. D. Dissertation (Chang Sha: National University of Defense Science and technology) (in Chinese)
[15] Poukey J W 1975 Appl. Phys. Lett. 26 145
Google Scholar
[16] 耿力东, 谢卫平, 袁建强, 王敏华, 曹龙博, 付佳斌, 赵小明, 何泱 2018 强激光与粒子束 30 085003
Google Scholar
Geng L D, Xie W P, Yuan J Q, Wang M H, Cao L B, Fu J B, Zhao X M, He Y 2018 High Power Laser Part. Beams 30 085003
Google Scholar
[17] Miller C L, Welch D R, Rose D V, Oliver B V 2010 IEEE Trans. Plasma Sci. 38 2507
Google Scholar
[18] 王宇, 李洪涛, 王文斗, 邓建军, 刘金峰, 马成刚 2015 强激光与粒子束 27 095005
Google Scholar
Wang Y, Li H T, Wang W D, Deng J J, Liu J F, Ma C G 2015 High Power Laser Part. Beams 27 095005
Google Scholar
[19] 耿力东, 谢卫平, 袁建强, 王敏华, 曹龙博, 张思群, 赵小明, 何泱 2018 原子能科学技术 52 1512
Google Scholar
Geng L D, Xie W P, Yuan J Q, Wang M H, Cao L B, Zhang S Q, Zhao X M, He Y 2018 At. Energy Sci. Technol. 52 1512
Google Scholar
[20] Xie W, Xia M, Guo F, Geng L, Zhao Y, Xu L, Feng S, Zhou L, Wei B, He A, Yuan J, Chen L, Li H, Han W, Jiang J, Li F, Wang Z, Li Y, Kang J, Zhang Y, Wu W, Wang M, Zou W 2021 Phys. Rev. Accel. Beams 24 110401
Google Scholar
[21] Zhou J, Liu D, Chen L, Li Z 2009 IEEE Trans. Plasma Sci. 37 2002
Google Scholar
[22] Perl J, Shin J, Schümann J, Faddegon B, Paganetti H 2012 Med. Phys. 39 6818
Google Scholar
[23] Allison J, Amako K, Apostolakis J, Araujo H, Dubois P A, Asai M, Barrand G, Capra R, Chauvie S, Chytracek R 2006 IEEE Trans. Nucl. Sci. 53 270
Google Scholar
[24] Allison J, Amako K, Apostolakis J, Arce P, Asai M, Aso T, Bagli E, Bagulya A, Banerjee S, Barrand G, Beck B R, Bogdanov A G, Brandt D, Brown J M C, Burkhardt H, Canal P, Cano-Ott D, Chauvie S, Cho K, Cirrone G A P, Cooperman G, Cortés-Giraldo M A, Cosmo G, Cuttone G, Depaola G, Desorgher L, Dong X, Dotti A, Elvira V D, Folger G, Francis Z, Galoyan A, Garnier L, Gayer M, Genser K L, Grichine V M, Guatelli S, Guèye P, Gumplinger P, Howard A S, Hřivnáčová I, Hwang S, Incerti S, Ivanchenko A, Ivanchenko V N, Jones F W, Jun S Y, Kaitaniemi P, Karakatsanis N, Karamitros M, Kelsey M, Kimura A, Koi T, Kurashige H, Lechner A, Lee S B, Longo F, Maire M, Mancusi D, Mantero A, Mendoza E, Morgan B, Murakami K, Nikitina T, Pandola L, Paprocki P, Perl J, Petrović I, Pia M G, Pokorski W, Quesada J M, Raine M, Reis M A, Ribon A, Ristić Fira A, Romano F, Russo G, Santin G, Sasaki T, Sawkey D, Shin J I, Strakovsky I I, Taborda A, Tanaka S, Tomé B, Toshito T, Tran H N, Truscott P R, Urban L, Uzhinsky V, Verbeke J M, Verderi M, Wendt B L, Wenzel H, Wright D H, Wright D M, Yamashita T, Yarba J, Yoshida H 2016 Nucl. Instrum. Methods Phys. Res. , Sect. A 835 186
Google Scholar
[25] Agostinelli S, Allison J, Amako K, Apostolakis J, Zschiesche D 2003 Nucl. Instrum. Methods Phys. Res. , Sect. A 506 250
Google Scholar
[26] 李成刚 2015 博士学位论文 (北京: 中国工程物理研究院)
Li C G 2015 Ph. D. Dissertation (Beijing: China Academy of Engineering Physics) (in Chinese)
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