搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

在质子照相中利用Abel逆变换反演等离子体自生磁场结构

邓娈 杜报 蔡洪波 康洞国 朱少平

引用本文:
Citation:

在质子照相中利用Abel逆变换反演等离子体自生磁场结构

邓娈, 杜报, 蔡洪波, 康洞国, 朱少平

Self-generated magnetic field in plasma reconstructed by using inverse Abel transformation in proton radiography

Deng Luan, Du Bao, Cai Hong-Bo, Kang Dong-Guo, Zhu Shao-Ping
PDF
HTML
导出引用
  • 质子照相是观测等离子体中自生磁场的常用实验诊断技术, 对质子照相实验结果的有效解读依赖于反演方法的可靠性和可用性. 传统质子照相反演方法往往只能提供自生磁场的一维或二维结构. 本研究发现, 在对具有柱对称结构的磁场进行侧向质子照相时, 偏转速度与磁场之间满足Abel变换关系, 这使得从质子照相结果中反演重建出磁场的三维结构成为可能. 通过数值模拟验证了该方法的可行性, 并基于该反演方法, 重新分析了Li等(2016 Nat. Commun. 7 13081)有关等离子体喷流自生磁场的质子照相实验结果, 给出的最大磁场强度约为传统反演结果的1.9倍. 本研究有助于对激光聚变和实验室天体物理相关的自生电磁场形成及其时空演化行为的认识更加清晰.
    The magnetic fields generated in plasmas have extensive influences on many processes of the inertial confinement fusion and the astrophysics. Therefore, the quantitative diagnosis of the magnetic field is quite essential. Proton radiography is a widely used experimental technique to diagnose the electric field or magnetic field in high-energy-density plasma. The effective explanation of the results of proton radiography depends on the reliability and availability of the inversion method. Traditional inversion methods can only provide one- or two-dimensional structure of the self-generated magnetic field. In this study, it is found that there is an Abel transformation relationship between the deflection velocity and the magnetic field with column symmetry, which allows us to reconstruct the three-dimensional structure of the magnetic field for the first time. We theoretically deduce the process of reconstructing the cylindrical magnetic field through proton radiography with the Abel inversion algorithm. The feasibility of this method is verified by numerical simulation as well. Based on this inversion method, we reanalyze the proton radiography experimental results of Li et al. (2016 Nat. Commun. 7 13081) on the self-generated magnetic field of plasma jets. The inversion results show that the maximum magnetic field intensity is about 1.9 times the traditional inversion results. We discuss a new proton radiography inversion method for the existence of magnetic fields with cylindrical symmetry in thiswork, which will contributes to an intensive understanding of the self-generated electromagnetic field and its spatiotemporal evolution related to the laser fusion and the laboratory astrophysics.
      通信作者: 杜报, dubao89@mail.ustc.edu.cn ; 蔡洪波, cai_hongbo@iapcm.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 11975055)和国家自然科学基金青年科学基金(批准号: 12105023)资助的课题.
      Corresponding author: Du Bao, dubao89@mail.ustc.edu.cn ; Cai Hong-Bo, cai_hongbo@iapcm.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11975055) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 12105023).
    [1]

    Rygg J R, Seguin F H, Li C K, Frenje J A, Manuel M J, Petrasso R D, Betti R, Delettrez J A, Gotchev O V, Knauer J P, Meyerhofer D D, Marshall F J, Stoeckl C, Theobald W 2008 Science 319 1223Google Scholar

    [2]

    Campbell P T, Walsh C A, Russell B K, Chittenden J P, Crilly A, Fiksel G, Nilson P M, Thomas A G R, Krushelnick K, Willingale L 2020 Phys. Rev. Lett. 125 145001Google Scholar

    [3]

    Li C K, Tzeferacos P, Lamb D, Gregori G, Norreys P A, Rosenberg M J, Follett R K, Froula D H, Koenig M, Seguin F H, Frenje J A, Rinderknecht H G, Sio H, Zylstra A B, Petrasso R D, Amendt P A, Park H S, Remington B A, Ryutov D D, Wilks S C, Betti R, Frank A, Hu S X, Sangster T C, Hartigan P, Drake R P, Kuranz C C, Lebedev S V, Woolsey N C 2016 Nat. Commun. 7 13081Google Scholar

    [4]

    Fiuza F, Fonseca R A, Tonge J, Mori W B, Silva L O 2012 Phys. Rev. Lett. 108 235004Google Scholar

    [5]

    Caprioli D, Spitkovsky A 2013 Astrophys. J. 765 20Google Scholar

    [6]

    Haines 1986 Can. J. Phys. 64 912Google Scholar

    [7]

    Fox W, Matteucci J, Moissard C, Schaeffer D B, Bhattacharjee A, Germaschewski K, Hu S X 2018 Phys. Plasmas 25 102106Google Scholar

    [8]

    Honda M 2000 Phys. Rev. Lett. 85 2128Google Scholar

    [9]

    Jia Q, Cai H B, Wang W W, Zhu S P, Sheng Z M, He X T 2013 Phys. Plasmas 20 032113Google Scholar

    [10]

    Courtois C, Ash A D, Chambers D M, Grundy R A D, Woolsey N C 2005 J. Appl. Phys. 98 054913Google Scholar

    [11]

    Kaluza M C, Schlenvoigt H P, Mangles S P, Thomas A G, Dangor A E, Schwoerer H, Mori W B, Najmudin Z, Krushelnick K M 2010 Phys. Rev. Lett. 105 115002Google Scholar

    [12]

    Wang W, Cai H, Teng J, Chen J, He S, Shan L, Lu F, Wu Y, Zhang B, Hong W, Bi B, Zhang F, Liu D, Xue F, Li B, Liu H, He W, Jiao J, Dong K, Zhang F, He Y, Cui B, Xie N, Yuan Z, Tian C, Wang X, Zhou K, Deng Z, Zhang Z, Zhou W, Cao L, Zhang B, Zhu S, He X, Gu Y 2018 Phys. Plasmas 25 083111Google Scholar

    [13]

    Borghesi M 2001 Plasma Phys. Control. Fusion 43 A267Google Scholar

    [14]

    Borghesi M, Schiavi A, Campbell D H, Haines M G, Willi O, Mackinnon A J, Patel P, Galimberti M, Gizzi L A 2003 Rev. Sci. Instrum. 74 1688Google Scholar

    [15]

    Kugland N L, Ryutov D D, Plechaty C, Ross J S, Park H S 2012 Rev. Sci. Instrum. 83 101301Google Scholar

    [16]

    Wilks S C, Langdon A B, Cowan T E, Roth M, Singh M, Hatchett S, Key M H, Pennington D, MacKinnon A, Snavely R A 2001 Phys. Plasmas 8 542Google Scholar

    [17]

    Hegelich B M, Albright B J, Cobble J, Flippo K, Letzring S, Paffett M, Ruhl H, Schreiber J, Schulze R K, Fernandez J C 2006 Nature 439 441Google Scholar

    [18]

    滕建, 朱斌, 王剑, 洪伟, 闫永宏, 赵宗清, 曹磊峰, 谷渝秋 2013 物理学报 62 114103Google Scholar

    Teng J, Zhu B, Wang J, Hong W, Yan Y H, Zhao Z Q, Cao L F, Gu Y Q 2013 Acta Phys. Sin. 62 114103Google Scholar

    [19]

    Séguin F H, Li C K, Manuel M J E, Rinderknecht H G, Sinenian N, Frenje J A, Rygg J R, Hicks D G, Petrasso R D, Delettrez J, Betti R, Marshall F J, Smalyuk V A 2012 Phys. Plasmas 19 012701Google Scholar

    [20]

    杜报, 蔡洪波, 张文帅, 陈京, 邹士阳, 朱少平 2019 物理学报 68 185205Google Scholar

    Du B, Cai H B, Zhang W S, Chen J, Zou S Y, Zhu S P 2019 Acta Phys. Sin. 68 185205Google Scholar

    [21]

    Huntington C M, Fiuza F, Ross J S, Zylstra A B, Drake R P, Froula D H, Gregori G, Kugland N L, Kuranz C C, Levy M C, Li C K, Meinecke J, Morita T, Petrasso R, Plechaty C, Remington B A, Ryutov D D, Sakawa Y, Spitkovsky A, Takabe H, Park H S 2015 Nat. Phys. 11 173Google Scholar

    [22]

    Zhou S Y, Bai Y F, Tian Y, Sun H Y, Cao L H, Liu J S 2018 Phys. Rev. Lett. 121 255002Google Scholar

    [23]

    Li C K, Seguin F H, Frenje J A, Rygg J R, Petrasso R D, Town R P, Amendt P A, Hatchett S P, Landen O L, Mackinnon A J, Patel P K, Smalyuk V A, Sangster T C, Knauer J P 2006 Phys. Rev. Lett. 97 135003Google Scholar

    [24]

    Gao L, Nilson P M, Igumenshchev I V, Haines M G, Froula D H, Betti R, Meyerhofer D D 2015 Phys. Rev. Lett. 114 215003Google Scholar

    [25]

    Tzeferacos P, Rigby A, Bott A F A, Bell A R, Bingham R, Casner A, Cattaneo F, Churazov E M, Emig J, Fiuza F, Forest C B, Foster J, Graziani C, Katz J, Koenig M, Li C K, Meinecke J, Petrasso R, Park H S, Remington B A, Ross J S, Ryu D, Ryutov D, White T G, Reville B, Miniati F, Schekochihin A A, Lamb D Q, Froula D H, Gregori G 2018 Nat. Commun. 9 591Google Scholar

    [26]

    Bott A F A, Graziani C, Tzeferacos P, White T G, Lamb D Q, Gregori G, Schekochihin A A 2017 J. Plasma Phys. 83 905830614Google Scholar

    [27]

    Li X F, Huang L, Huang Y 2007 Journal of Physics A:Mathematical and Theoretical 40 347Google Scholar

    [28]

    Zhang C J, Hua J F, Xu X L, Li F, Pai C H, Wan Y, Wu Y P, Gu Y Q, Mori W B, Joshi C, Lu A W 2016 Sci. Rep. 6 29485Google Scholar

    [29]

    Du B, Wang X F 2018 AIP Adv. 8 125328Google Scholar

    [30]

    Du B, Cai H B, Zhang W S, Wang X F, Kang D G, Deng L, Zhang E H, Yao P L, Yan X X, Zou S Y, Zhu S P 2021 Matter Radiat. at Extremes 6 035903Google Scholar

    [31]

    Chen L, Li R Z, Chen J, Zhu P F, Liu F, Cao J M, Sheng Z M, Zhang J 2015 Proc. Natl. Acad. Sci. USA 112 14479Google Scholar

  • 图 1  质子照相示意图

    Fig. 1.  Schematic diagram of the proton radiography.

    图 2  (a)预设磁场Bx = 50 μm平面上的分布; (b)探测面上的质子通量密度扰动

    Fig. 2.  (a) Distributions of the preset magnetic field at x = 50 μm; (b) the flux density perturbations of the protons in the detection plane.

    图 3  (a)质子偏转速度的反演结果; (b)质子的模拟偏转速度和反演偏转速度在z = 50 μm时的径向分布

    Fig. 3.  (a) Reconstruction of the protons deflection velocities; (b) the radial distributions of the protons inversion deflection velocities and simulated deflection velocities at z = 50 μm.

    图 4  (a)反演磁场Brecr-z平面的投影; (b)预设磁场Bset、反演磁场Brec及路径平均磁场Bavg的一维分布

    Fig. 4.  (a) Projection of the inversion magnetic field Brec on the r-z plane; (b) the one-dimensional (1D) distributions of the preset magnetic field Bset, the inversion magnetic field Brec and the path average magnetic field Bavg.

    图 5  (a)等离子体喷流的质子照相实验原图[3]; (b)局部的质子通量密度扰动; (c)反演磁场Brec和路径平均磁场Bavg的一维分布

    Fig. 5.  (a) Original proton radiographic image of the plasma jet; (b) the flux density perturbations of the protons at the local area; (c) the 1D distributions of the inversion magnetic field Brec and the path average magnetic field Bavg.

  • [1]

    Rygg J R, Seguin F H, Li C K, Frenje J A, Manuel M J, Petrasso R D, Betti R, Delettrez J A, Gotchev O V, Knauer J P, Meyerhofer D D, Marshall F J, Stoeckl C, Theobald W 2008 Science 319 1223Google Scholar

    [2]

    Campbell P T, Walsh C A, Russell B K, Chittenden J P, Crilly A, Fiksel G, Nilson P M, Thomas A G R, Krushelnick K, Willingale L 2020 Phys. Rev. Lett. 125 145001Google Scholar

    [3]

    Li C K, Tzeferacos P, Lamb D, Gregori G, Norreys P A, Rosenberg M J, Follett R K, Froula D H, Koenig M, Seguin F H, Frenje J A, Rinderknecht H G, Sio H, Zylstra A B, Petrasso R D, Amendt P A, Park H S, Remington B A, Ryutov D D, Wilks S C, Betti R, Frank A, Hu S X, Sangster T C, Hartigan P, Drake R P, Kuranz C C, Lebedev S V, Woolsey N C 2016 Nat. Commun. 7 13081Google Scholar

    [4]

    Fiuza F, Fonseca R A, Tonge J, Mori W B, Silva L O 2012 Phys. Rev. Lett. 108 235004Google Scholar

    [5]

    Caprioli D, Spitkovsky A 2013 Astrophys. J. 765 20Google Scholar

    [6]

    Haines 1986 Can. J. Phys. 64 912Google Scholar

    [7]

    Fox W, Matteucci J, Moissard C, Schaeffer D B, Bhattacharjee A, Germaschewski K, Hu S X 2018 Phys. Plasmas 25 102106Google Scholar

    [8]

    Honda M 2000 Phys. Rev. Lett. 85 2128Google Scholar

    [9]

    Jia Q, Cai H B, Wang W W, Zhu S P, Sheng Z M, He X T 2013 Phys. Plasmas 20 032113Google Scholar

    [10]

    Courtois C, Ash A D, Chambers D M, Grundy R A D, Woolsey N C 2005 J. Appl. Phys. 98 054913Google Scholar

    [11]

    Kaluza M C, Schlenvoigt H P, Mangles S P, Thomas A G, Dangor A E, Schwoerer H, Mori W B, Najmudin Z, Krushelnick K M 2010 Phys. Rev. Lett. 105 115002Google Scholar

    [12]

    Wang W, Cai H, Teng J, Chen J, He S, Shan L, Lu F, Wu Y, Zhang B, Hong W, Bi B, Zhang F, Liu D, Xue F, Li B, Liu H, He W, Jiao J, Dong K, Zhang F, He Y, Cui B, Xie N, Yuan Z, Tian C, Wang X, Zhou K, Deng Z, Zhang Z, Zhou W, Cao L, Zhang B, Zhu S, He X, Gu Y 2018 Phys. Plasmas 25 083111Google Scholar

    [13]

    Borghesi M 2001 Plasma Phys. Control. Fusion 43 A267Google Scholar

    [14]

    Borghesi M, Schiavi A, Campbell D H, Haines M G, Willi O, Mackinnon A J, Patel P, Galimberti M, Gizzi L A 2003 Rev. Sci. Instrum. 74 1688Google Scholar

    [15]

    Kugland N L, Ryutov D D, Plechaty C, Ross J S, Park H S 2012 Rev. Sci. Instrum. 83 101301Google Scholar

    [16]

    Wilks S C, Langdon A B, Cowan T E, Roth M, Singh M, Hatchett S, Key M H, Pennington D, MacKinnon A, Snavely R A 2001 Phys. Plasmas 8 542Google Scholar

    [17]

    Hegelich B M, Albright B J, Cobble J, Flippo K, Letzring S, Paffett M, Ruhl H, Schreiber J, Schulze R K, Fernandez J C 2006 Nature 439 441Google Scholar

    [18]

    滕建, 朱斌, 王剑, 洪伟, 闫永宏, 赵宗清, 曹磊峰, 谷渝秋 2013 物理学报 62 114103Google Scholar

    Teng J, Zhu B, Wang J, Hong W, Yan Y H, Zhao Z Q, Cao L F, Gu Y Q 2013 Acta Phys. Sin. 62 114103Google Scholar

    [19]

    Séguin F H, Li C K, Manuel M J E, Rinderknecht H G, Sinenian N, Frenje J A, Rygg J R, Hicks D G, Petrasso R D, Delettrez J, Betti R, Marshall F J, Smalyuk V A 2012 Phys. Plasmas 19 012701Google Scholar

    [20]

    杜报, 蔡洪波, 张文帅, 陈京, 邹士阳, 朱少平 2019 物理学报 68 185205Google Scholar

    Du B, Cai H B, Zhang W S, Chen J, Zou S Y, Zhu S P 2019 Acta Phys. Sin. 68 185205Google Scholar

    [21]

    Huntington C M, Fiuza F, Ross J S, Zylstra A B, Drake R P, Froula D H, Gregori G, Kugland N L, Kuranz C C, Levy M C, Li C K, Meinecke J, Morita T, Petrasso R, Plechaty C, Remington B A, Ryutov D D, Sakawa Y, Spitkovsky A, Takabe H, Park H S 2015 Nat. Phys. 11 173Google Scholar

    [22]

    Zhou S Y, Bai Y F, Tian Y, Sun H Y, Cao L H, Liu J S 2018 Phys. Rev. Lett. 121 255002Google Scholar

    [23]

    Li C K, Seguin F H, Frenje J A, Rygg J R, Petrasso R D, Town R P, Amendt P A, Hatchett S P, Landen O L, Mackinnon A J, Patel P K, Smalyuk V A, Sangster T C, Knauer J P 2006 Phys. Rev. Lett. 97 135003Google Scholar

    [24]

    Gao L, Nilson P M, Igumenshchev I V, Haines M G, Froula D H, Betti R, Meyerhofer D D 2015 Phys. Rev. Lett. 114 215003Google Scholar

    [25]

    Tzeferacos P, Rigby A, Bott A F A, Bell A R, Bingham R, Casner A, Cattaneo F, Churazov E M, Emig J, Fiuza F, Forest C B, Foster J, Graziani C, Katz J, Koenig M, Li C K, Meinecke J, Petrasso R, Park H S, Remington B A, Ross J S, Ryu D, Ryutov D, White T G, Reville B, Miniati F, Schekochihin A A, Lamb D Q, Froula D H, Gregori G 2018 Nat. Commun. 9 591Google Scholar

    [26]

    Bott A F A, Graziani C, Tzeferacos P, White T G, Lamb D Q, Gregori G, Schekochihin A A 2017 J. Plasma Phys. 83 905830614Google Scholar

    [27]

    Li X F, Huang L, Huang Y 2007 Journal of Physics A:Mathematical and Theoretical 40 347Google Scholar

    [28]

    Zhang C J, Hua J F, Xu X L, Li F, Pai C H, Wan Y, Wu Y P, Gu Y Q, Mori W B, Joshi C, Lu A W 2016 Sci. Rep. 6 29485Google Scholar

    [29]

    Du B, Wang X F 2018 AIP Adv. 8 125328Google Scholar

    [30]

    Du B, Cai H B, Zhang W S, Wang X F, Kang D G, Deng L, Zhang E H, Yao P L, Yan X X, Zou S Y, Zhu S P 2021 Matter Radiat. at Extremes 6 035903Google Scholar

    [31]

    Chen L, Li R Z, Chen J, Zhu P F, Liu F, Cao J M, Sheng Z M, Zhang J 2015 Proc. Natl. Acad. Sci. USA 112 14479Google Scholar

  • [1] 黄华, 李江涛, 王倩男, 孟令彪, 齐伟, 洪伟, 张智猛, 张博, 贺书凯, 崔波, 伍艺通, 张航, 吉亮亮, 周维民, 胡建波. 星光III装置上材料动态压缩过程的激光质子照相实验研究. 物理学报, 2022, 71(19): 195202. doi: 10.7498/aps.71.20220919
    [2] 陈锋, 郝建红, 许海波. 考虑磁透镜边缘场的质子成像系统优化设计. 物理学报, 2021, 70(2): 022901. doi: 10.7498/aps.70.20201141
    [3] 周彦玲, 范军, 王斌. 塑料类高分子聚合物材料水中目标声学参数反演. 物理学报, 2019, 68(21): 214301. doi: 10.7498/aps.68.20190991
    [4] 徐敏, 申晋, 黄钰, 徐亚南, 朱新军, 王雅静, 刘伟, 高明亮. 基于颗粒粒度信息分布特征的动态光散射加权反演. 物理学报, 2018, 67(13): 134201. doi: 10.7498/aps.67.20172377
    [5] 陈洁, 张淳民, 王鼎益, 张兴赢, 王舒鹏, 栗彦芬, 刘冬冬, 荣飘. 地表反照率对短波红外探测大气CO2的影响. 物理学报, 2015, 64(23): 239201. doi: 10.7498/aps.64.239201
    [6] 段晓亮, 王一博, 杨慧珠. 基于逆散射理论的地震波速度正则化反演. 物理学报, 2015, 64(7): 078901. doi: 10.7498/aps.64.078901
    [7] 李伦, 吴雄斌. 高频地波雷达多站浅海水深与海流反演. 物理学报, 2014, 63(11): 118404. doi: 10.7498/aps.63.118404
    [8] 李伦, 吴雄斌, 徐兴安. 基于优化理论的高频地波雷达海浪参数反演. 物理学报, 2014, 63(3): 038403. doi: 10.7498/aps.63.038403
    [9] 韩月琪, 钟中, 王云峰, 杜华栋. 梯度计算的集合变分方案及其在大气Ekman层湍流系数反演中的应用. 物理学报, 2013, 62(4): 049201. doi: 10.7498/aps.62.049201
    [10] 滕建, 朱斌, 王剑, 洪伟, 闫永宏, 赵宗清, 曹磊峰, 谷渝秋. 激光加速质子束对电磁孤立子的照相模拟研究. 物理学报, 2013, 62(11): 114103. doi: 10.7498/aps.62.114103
    [11] 李海燕, 胡云安, 任建存, 朱敏, 刘亮. 非匹配不确定交叉严反馈超混沌系统神经网络反演同步. 物理学报, 2012, 61(14): 140502. doi: 10.7498/aps.61.140502
    [12] 何然, 黄思训, 周晨腾, 姜祝辉. 遗传算法结合正则化方法反演海洋大气波导. 物理学报, 2012, 61(4): 049201. doi: 10.7498/aps.61.049201
    [13] 董建军, 曹柱荣, 陈伯伦, 黄天暄, 缪文勇, 张继彦, 刘慎业, 江少恩, 丁永坤, 谷渝秋, 单连强. 基于Abel逆变换的辐射驱动内爆壳层密度分布研究. 物理学报, 2012, 61(11): 115206. doi: 10.7498/aps.61.115206
    [14] 丁世敬, 葛德彪, 申宁. 复合介质等效电磁参数的数值研究. 物理学报, 2010, 59(2): 943-948. doi: 10.7498/aps.59.943
    [15] 杨坤德, 马远良. 利用海底反射信号进行地声参数反演的方法. 物理学报, 2009, 58(3): 1798-1805. doi: 10.7498/aps.58.1798
    [16] 滕建, 洪伟, 赵宗清, 巫顺超, 秦孝尊, 何颖玲, 谷渝秋, 丁永坤. 激光质子照相特性模拟研究. 物理学报, 2009, 58(3): 1635-1641. doi: 10.7498/aps.58.1635
    [17] 张宏超, 陆建, 倪晓武. 干涉法诊断由纳秒激光诱导产生的大气等离子体的电子密度. 物理学报, 2009, 58(6): 4034-4040. doi: 10.7498/aps.58.4034
    [18] 孙贤明, 哈恒旭. 基于反射太阳光反演气溶胶光学厚度和有效半径. 物理学报, 2008, 57(9): 5565-5570. doi: 10.7498/aps.57.5565
    [19] 张新明, 刘家琦, 刘克安. 一维双相介质孔隙率的小波多尺度反演. 物理学报, 2008, 57(2): 654-660. doi: 10.7498/aps.57.654
    [20] 魏 兵, 葛德彪. 各向异性有耗介质板介电系数和电导率的反演. 物理学报, 2005, 54(2): 648-652. doi: 10.7498/aps.54.648
计量
  • 文章访问数:  3445
  • PDF下载量:  170
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-09-22
  • 修回日期:  2022-10-14
  • 上网日期:  2022-11-16
  • 刊出日期:  2022-12-24

/

返回文章
返回