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The interaction of a high-intensity laser with a solid target generates a large number of superthermal electrons. When these superthermal electrons are transported in the target material, X-rays, including Kα line and bremsstrahlung emissions are produced. The contrast of Kα line emission, i.e. the intensity of Kα line relative to the intensity of bremsstrahlung continua around the Kα line, depends on the anisotropy of the bremsstrahlung emission and is related to the energy and transportation of the superthermal electrons. In the past, some researchers used axial or annular magnetic fields to collimate superthermal electrons, but whether these magnetic fields can enhance the contrast of Kα emission has not been studied. In the present work, the effect of an axially uniform magnetic field or an annular magnetic field with a Gaussian distribution on the contrast of Cu Kα emission is investigated by Monte Carlo simulations. The simulation results and analysis show that the axially uniform magnetic field cannot strengthen the anisotropy of the bremsstrahlung emission, so it cannot enhance the contrast of Kα emission efficiently. For the annular magnetic field with a Gaussian distribution, when an electron beam with a Boltzmann energy distribution is incident, due to the weak anisotropy of bremsstrahlung emission by low-energy electrons in the electron beam, the increase of Kα emission contrast is small. When an electron beam with a Boltzmann energy distribution, in which the low-energy part is cut off, or a mono-energetic electron beam is incident, the annular magnetic field with a Gaussian distribution significantly enhances the contrast of Kα emission in the back direction of the electron beam incidence. For an incident electron beam with an energy value in a range of 200–1000 keV, an annular magnetic field with a Gaussian distribution and a peak value of approximately 100 T is optimal for enhancing the contrast of Kα emission. Considering the existing experiments on generating annular magnetic fields and non-Boltzmann energy distribution superthermal electrons, it is possible to generate higher contrast Kα emissions with the enhancement of magnetic field in future experiments.
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Keywords:
- contrast of Kα emission /
- bremsstrahlung emission /
- magnetic field /
- Monte Carlo simulation
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图 1 模拟中坐标系和角度定义
Figure 1. The coordinate and detection angle defined in the simulation.
图 2 $ {T_{\text{h}}} = 600{\text{ keV}} $的玻尔兹曼能量分布电子束入射产生的X射线谱
Figure 2. X-ray spectra produced by Boltzmann distribution electron incidence with $ {T_{\text{h}}} = 600{\text{ keV}} $.
图 3 靶中无磁场(WOB)或存在$ {{\boldsymbol{B}}_{\boldsymbol{z}}} = 100{\text{ T}} $时的Kα辐射对比度 (a) $ {T_{\text{h}}} = 600{\text{ keV}} $的玻尔兹曼能量分布电子束入射; (b) $ {E_{\text{k}}} = 600{\text{ keV}} $的单能电子束入射
Figure 3. Contrasts of Kα emission without a magnetic field (WOB) or with $ {{\boldsymbol{B}}_{\boldsymbol{z}}} = 100{\text{ T}} $ in the target: (a) Boltzmann distribution electron incidence with $ {T_{\text{h}}} = 600{\text{ keV}} $; (b) mono-energetic electron incidence with $ {E_{\text{k}}} = 600{\text{ keV}} $.
图 4 电子在z方向匀强磁场中运动示意图
Figure 4. Schematic diagram of the motion of an electron in a z-direction uniform magnetic field.
图 5 (a) 高斯分布的环形磁场的示意图; (b) 环形磁场在x-y平面内的分布; (c) 磁场准直电子的示意图
Figure 5. (a) Schematic diagram of an annular magnetic field with a Gaussian distribution; (b) distribution of the annular magnetic field in the x-y plane; (c) schematic diagram of the collimation of electrons by the magnetic field.
图 6 玻尔兹曼能量分布电子束入射的模拟结果 (a) $ {T_{\text{h}}} = 200{\text{ keV}} $和$ 600{\text{ keV}} $时不同方向的$ {C_{{{{\mathrm{K}}\alpha }}}} $; (b) $ \theta = {135^ \circ } $的$ {C_{{{{\mathrm{K}}\alpha }}}} $与$ {T_{\text{h}}} $的关系
Figure 6. Simulation results of Boltzmann distribution electron incidences: (a) $ {C_{{{{\mathrm{K}}\alpha }}}} $ in different directions for $ {T_{\text{h}}} = 200{\text{ keV}} $ and 600 keV, respectively; (b) the dependence of $ {C_{{{{\mathrm{K}}\alpha }}}} $ at $ \theta = {135^ \circ } $ on $ {T_{\text{h}}} $.
图 7 单能电子束入射时的模拟结果 (a) $ {E_{\text{k}}} = 200{\text{ keV}} $和$ 600{\text{ keV}} $不同方向的$ {C_{{{{\mathrm{K}}\alpha }}}} $; (b) $ \theta = {135^ \circ } $的$ {C_{{{{\mathrm{K}}\alpha }}}} $和$ {R_{{\text{in}}}} $与$ {E_{\text{k}}} $的关系
Figure 7. Simulation results of mono-energetic electron incidences: (a) $ {C_{{{{\mathrm{K}}\alpha }}}} $ of $ {E_{\text{k}}} = 200{\text{ keV}} $ and $ 600{\text{ keV}} $ in different directions; (b) dependence of $ {C_{{{{\mathrm{K}}\alpha }}}} $ and $ {R_{{\text{in}}}} $at $ \theta = {135^ \circ } $ on $ {E_{\text{k}}} $.
图 8 $ {T_{\text{h}}} = 600{\text{ keV}} $的玻尔兹曼能量分布的电子中能量大于500 keV的电子入射时不同探测角度的$ {C_{{{{\mathrm{K}}\alpha }}}} $
Figure 8. $ {C_{{{{\mathrm{K}}\alpha }}}} $ at different detection angles for Boltzmann distribution electron incidence with $ {T_{\text{h}}} = 600{\text{ keV}} $ and electron energy higher than 500 keV.
图 9 单能电子束入射时, 无磁场和存在磁场$ {{\boldsymbol{B}}_\phi } $条件下的模拟结果 (a) $ {E_{\text{k}}} = 600{\text{ keV}} $时靶后表面的电子数密度分布; (b) 电子数密度分布的半高全宽与$ {E_{\text{k}}} $的关系
Figure 9. Simulation results for mono-energetic electron incidence without a magnetic field and with $ {{\boldsymbol{B}}_\phi } $: (a) Distribution of the electron number density on the rear surface of the target for $ {E_{\text{k}}} = 600{\text{ keV}} $; (b) dependence of full width at half maximum of the distribution of the electron number density on $ {E_{\text{k}}} $.
图 10 存在不同$ {B_0} $和$ {\sigma _{\text{f}}} $的环形磁场时$ \theta = {135^ \circ } $的Kα辐射的对比度$ {C_{{{{\mathrm{K}}\alpha }}}} $ (a) $ {\sigma _{\text{f}}} = 20{\text{ μm}} $时$ {C_{{{{\mathrm{K}}\alpha }}}} $与$ {B_0} $的关系; (b) $ {B_0} = 100{\text{ T}} $时$ {C_{{{{\mathrm{K}}\alpha }}}} $与$ {\sigma _{\text{f}}} $的关系
Figure 10. Contrasts of Kα emission at $ \theta = {135^ \circ } $ versus $ {B_0} $ and $ {\sigma _{\text{f}}} $ of annular magnetic fields: (a) The dependence of $ {C_{{{{\mathrm{K}}\alpha }}}} $ on $ {B_0} $ with $ {\sigma _{\text{f}}} = 20{\text{ μm}} $; (b) the dependence of $ {C_{{{{\mathrm{K}}\alpha }}}} $ on $ {\sigma _{\text{f}}} $ with $ {B_0} = 100{\text{ T}} $.
图 11 不同环形磁场下的电子轨迹
Figure 11. Trajectories of electrons in different annular magnetic fields.
图 12 能量为600 keV的单能电子束入射不同厚度的铜平面靶时$ \theta = {135^ \circ } $的Kα辐射对比度
Figure 12. Contrasts of Kα emission at $ \theta = {135^ \circ } $ for 600 keV mono-energetic electron incidence versus planar target thickness.
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[1] 温贤伦, 洪伟, 谷渝秋, 何颖玲, 唐翠明, 王剑 2007 强激光与粒子束 19 1373
Wen X L, Hong W, Gu Y Q, He Y L, Tang C M, Wang J 2007 High Power Laser and Particle Beams 19 1373
[2] Gambari M, Clady R, Stolidi A, Utéza O, Sentis M, Ferré A 2020 Sci. Rep. 10 6766
Google Scholar
[3] Ivanov K A, Gavrilin I M, Volkov R V, Gavrilov S A, Savel Ev A B 2021 Laser Phys. Lett. 18 075401
Google Scholar
[4] Sawada H, Lee S, Shiroto T, Nagatomo H, Arikawa Y, Nishimura H, Ueda T, Shigemori K, Sunahara A, Ohnishi N, Beg F N, Theobald W, Pérez F, Patel P K, Fujioka S 2016 Appl. Phys. Lett. 108 254101
Google Scholar
[5] Park H S, Chambers D M, Chung H K, Clarke R J, Eagleton R, Giraldez E, Goldsack T, Heathcote R, Izumi N, Key M H, King J A, Koch J A, Landen O L, Nikroo A, Patel P K, Price D F, Remington B A, Robey H F, Snavely R A, Steinman D A, Stephens R B, Stoeckl C, Storm M, Tabak M, Theobald W, Town R P J, Wickersham J E, Zhang B B 2006 Phys. Plasmas 13 056309
Google Scholar
[6] Kritcher A L, Neumayer P, Castor J, Döppner T, Falcone R W, Landen O L, Lee H J, Lee R W, Holst B, Redmer R, Morse E C, Ng A, Pollaine S, Price D, Glenzer S H 2009 Phys. Plasmas 16 056308
Google Scholar
[7] Westover B, MacPhee A, Chen C, Hey D, Ma T, Maddox B, Park H S, Remington B, Beg F N 2010 Phys. Plasmas 17 082703
Google Scholar
[8] Chen L M, Kando M, Xu M H, Li Y T, Koga J, Chen M, Xu H, Yuan X H, Dong Q L, Sheng Z M, Bulanov S V, Kato Y, Zhang J, Tajima T 2008 Phys. Rev. Lett. 100 045004
Google Scholar
[9] 蔡涓涓, 黄文忠, 谷渝秋, 董克攻, 吴玉迟, 朱斌, 王晓方 2011 强激光与粒子束 23 1082
Google Scholar
Cai J J, Huang W Z, Gu Y Q, Dong K G, Wu Y C, Zhu B, Wang X F 2011 High Power Laser Part. Beams 23 1082
Google Scholar
[10] Azamoum Y, Tcheremiskine V, Clady R, Ferré A, Charmasson L, Utéza O, Sentis M 2018 Sci. Rep. 8 4119
Google Scholar
[11] Tillman C, Mercer I, Svanberg S, Herrlin K 1996 J. Opt. Soc. Am. B 13 209
Google Scholar
[12] 陆中伟, 王晓方 2019 物理学报 68 035202
Google Scholar
Lu Z W, Wang X F 2019 Acta Phys. Sin. 68 035202
Google Scholar
[13] Lévy A, Dorchies F, Audebert P, Chalupský J, Hájková V, Juha L, Kaempfer T, Sinn H, Uschmann I, Vyšín L, Gaudin J 2010 Appl. Phys. Lett. 96 151114
Google Scholar
[14] Wang R R, An H H, Xie Z Y, Wang W 2018 Phys. Plasmas 25 053303
Google Scholar
[15] 王瑞荣, 陈伟民, 董佳钦, 熊俊, 傅思祖 2008 光学学报 28 1220
Google Scholar
Wang R R, Chen W M, Dong J Q, Xiong J, Fu S Z 2008 Acta Opt. Sin. 28 1220
Google Scholar
[16] Zhao J C, Zheng J H, Cao L H, Zhao Z Q, Li S, Gu Y Q, Liu J 2016 Phys. Plasmas 23 093102
Google Scholar
[17] Yoshioka A, Yamaguchi Y, Tamura K, Shimizu R 2004 Surf. Interface Anal. 36 1417
Google Scholar
[18] 徐妙华, 梁天骄, 张杰 2006 物理学报 55 2357
Google Scholar
Xu M H, Liang T J, Zhang J 2006 Acta Phys. Sin. 55 2357
Google Scholar
[19] Xiao Y Y, Wang X F 2024 Phys. Plasmas 31 073302
Google Scholar
[20] 蔡达锋, 王利娟, 王剑, 郑志坚 2009 原子与分子物理学报 26 535
Cai D F, Wang L J, Wang J, Zheng Z J 2009 J. At. Mol. Phys. 26 535
[21] Bailly-Grandvaux M, Santos J J, Bellei C, Forestier-Colleoni P, Fujioka S, Giuffrida L, Honrubia J J, Batani D, Bouillaud R, Chevrot M, Cross J E, Crowston R, Dorard S, Dubois J L, Ehret M, Gregori G, Hulin S, Kojima S, Loyez E, Marquès J R, Morace A, Nicolaï P, Roth M, Sakata S, Schaumann G, Serres F, Servel J, Tikhonchuk V T, Woolsey N, Zhang Z 2018 Nat. Commun. 9 102
Google Scholar
[22] Malko S, Vaisseau X, Perez F, Batani D, Curcio A, Ehret M, Honrubia J, Jakubowska K, Morace A, Santos J J, Volpe L 2019 Sci. Rep. 9 14061
Google Scholar
[23] Xu H, Yang X H, Sheng Z M, McKenna P, Ma Y Y, Zhuo H B, Yin Y, Ren C, Zhang J 2019 Nucl. Fusion 59 126024
Google Scholar
[24] Reich Ch, Gibbon P, Uschmann I, Förster E 2000 Phys. Rev. Lett. 84 4846
Google Scholar
[25] Šmíd M, Renner O, Colaitis A, Tikhonchuk V T, Schlegel T, Rosmej F B 2019 Nat. Commun. 10 4212
Google Scholar
[26] Khattak F Y, Garcia Saiz E, Gibbon P, Karmakar A, Dzelzainis T W J, Lewis C L S, Robinson A P L, Zepf M, Riley D 2012 Eur. Phys. J. D 66 298
Google Scholar
[27] Salvat F, Fernández-Varea J, Sempau J 2008 PENELOPE-2008, A Code System for Monte Carlo Simulation of Electron and Photon Transport (Issy-les-Moulineau: OECD/NEA Data Bank
[28] Li B Y, Tian C, Zhang Z M, Zhang F, Shan L Q, Zhang B, Zhou W M, Zhang B H, Gu Y Q 2016 Phys. Plasmas 23 093121
Google Scholar
[29] Green J S, Ovchinnikov V M, Evans R G, Akli K U, Azechi H, Beg F N, Bellei C, Freeman R R, Habara H, Heathcote R, Key M H, King J A, Lancaster K L, Lopes N C, Ma T, MacKinnon A J, Markey K, McPhee A, Najmudin Z, Nilson P, Onofrei R, Stephens R, Takeda K, Tanaka K A, Theobald W, Tanimoto T, Waugh J, Van Woerkom L, Woolsey N C, Zepf M, Davies J R, Norreys P A 2008 Phys. Rev. Lett. 100 015003
Google Scholar
[30] Salzmann D, Reich C, Uschmann I, Förster E, Gibbon P 2002 Phys. Rev. E 65 036402
Google Scholar
[31] Toncian T, Wang C, McCary E, Meadows A, Arefiev A V, Blakeney J, Serratto K, Kuk D, Chester C, Roycroft R, Gao L, Fu H, Yan X Q, Schreiber J, Pomerantz I, Bernstein A, Quevedo H, Dyer G, Ditmire T, Hegelich B M 2016 Matter Radiat. Extremes 1 82
Google Scholar
[32] Roet D, Ceballos C, Van Espen P 2006 Nucl. Instrum. Methods Phys. Res. B 251 317
Google Scholar
[33] Braenzel J, Andreev A A, Abicht F, Ehrentraut L, Platonov K, Schnurer M 2017 Phys. Rev. Lett. 118 014801
Google Scholar
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