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

doi:10.7498/aps.71.20221848

Abstract

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.

Keywords:

Authors and contacts

1.
School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China
2.
Graduate School, China Academy of Engineering Physics, Beijing 100088, China
3.
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
4.
Center for Applied Physics and Technology, Peking University, Beijing 100871, China

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).

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References

[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 1223 Google 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 145001 Google 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 13081 Google Scholar
[4]	Fiuza F, Fonseca R A, Tonge J, Mori W B, Silva L O 2012 Phys. Rev. Lett. 108 235004 Google Scholar
[5]	Caprioli D, Spitkovsky A 2013 Astrophys. J. 765 20 Google Scholar
[6]	Haines 1986 Can. J. Phys. 64 912 Google Scholar
[7]	Fox W, Matteucci J, Moissard C, Schaeffer D B, Bhattacharjee A, Germaschewski K, Hu S X 2018 Phys. Plasmas 25 102106 Google Scholar
[8]	Honda M 2000 Phys. Rev. Lett. 85 2128 Google Scholar
[9]	Jia Q, Cai H B, Wang W W, Zhu S P, Sheng Z M, He X T 2013 Phys. Plasmas 20 032113 Google Scholar
[10]	Courtois C, Ash A D, Chambers D M, Grundy R A D, Woolsey N C 2005 J. Appl. Phys. 98 054913 Google 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 115002 Google 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 083111 Google Scholar
[13]	Borghesi M 2001 Plasma Phys. Control. Fusion 43 A267 Google 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 1688 Google Scholar
[15]	Kugland N L, Ryutov D D, Plechaty C, Ross J S, Park H S 2012 Rev. Sci. Instrum. 83 101301 Google 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 8 542 Google 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 439 441 Google 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 114103 Google 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 114103 Google 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 012701 Google Scholar
[20]	杜报, 蔡洪波, 张文帅, 陈京, 邹士阳, 朱少平 2019 物理学报 68 185205 Google Scholar Du B, Cai H B, Zhang W S, Chen J, Zou S Y, Zhu S P 2019 Acta Phys. Sin. 68 185205 Google 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. 11 173 Google Scholar
[22]	Zhou S Y, Bai Y F, Tian Y, Sun H Y, Cao L H, Liu J S 2018 Phys. Rev. Lett. 121 255002 Google 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 135003 Google 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 215003 Google 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. 9 591 Google 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 905830614 Google Scholar
[27]	Li X F, Huang L, Huang Y 2007 Journal of Physics A:Mathematical and Theoretical 40 347 Google 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 29485 Google Scholar
[29]	Du B, Wang X F 2018 AIP Adv. 8 125328 Google 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 035903 Google 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 14479 Google Scholar

Cited By

图 1 质子照相示意图

Figure 1. Schematic diagram of the proton radiography.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 4 (a)反演磁场B_rec在r-z平面的投影; (b)预设磁场B_set、反演磁场B_rec及路径平均磁场B_avg的一维分布

Figure 4. (a) Projection of the inversion magnetic field B_recon the r-z plane; (b) the one-dimensional (1D) distributions of the preset magnetic field B_set, the inversion magnetic field B_rec and the path average magnetic field B_avg.

DownLoad: Full-Size Img PowerPoint

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B_rec和路径平均磁场B_avg的一维分布

Figure 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 B_rec and the path average magnetic field B_avg.

DownLoad: Full-Size Img PowerPoint

[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 1223 Google 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 145001 Google 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 13081 Google Scholar
[4]	Fiuza F, Fonseca R A, Tonge J, Mori W B, Silva L O 2012 Phys. Rev. Lett. 108 235004 Google Scholar
[5]	Caprioli D, Spitkovsky A 2013 Astrophys. J. 765 20 Google Scholar
[6]	Haines 1986 Can. J. Phys. 64 912 Google Scholar
[7]	Fox W, Matteucci J, Moissard C, Schaeffer D B, Bhattacharjee A, Germaschewski K, Hu S X 2018 Phys. Plasmas 25 102106 Google Scholar
[8]	Honda M 2000 Phys. Rev. Lett. 85 2128 Google Scholar
[9]	Jia Q, Cai H B, Wang W W, Zhu S P, Sheng Z M, He X T 2013 Phys. Plasmas 20 032113 Google Scholar
[10]	Courtois C, Ash A D, Chambers D M, Grundy R A D, Woolsey N C 2005 J. Appl. Phys. 98 054913 Google 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 115002 Google 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 083111 Google Scholar
[13]	Borghesi M 2001 Plasma Phys. Control. Fusion 43 A267 Google 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 1688 Google Scholar
[15]	Kugland N L, Ryutov D D, Plechaty C, Ross J S, Park H S 2012 Rev. Sci. Instrum. 83 101301 Google 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 8 542 Google 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 439 441 Google 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 114103 Google 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 114103 Google 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 012701 Google Scholar
[20]	杜报, 蔡洪波, 张文帅, 陈京, 邹士阳, 朱少平 2019 物理学报 68 185205 Google Scholar Du B, Cai H B, Zhang W S, Chen J, Zou S Y, Zhu S P 2019 Acta Phys. Sin. 68 185205 Google 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. 11 173 Google Scholar
[22]	Zhou S Y, Bai Y F, Tian Y, Sun H Y, Cao L H, Liu J S 2018 Phys. Rev. Lett. 121 255002 Google 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 135003 Google 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 215003 Google 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. 9 591 Google 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 905830614 Google Scholar
[27]	Li X F, Huang L, Huang Y 2007 Journal of Physics A:Mathematical and Theoretical 40 347 Google 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 29485 Google Scholar
[29]	Du B, Wang X F 2018 AIP Adv. 8 125328 Google 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 035903 Google 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 14479 Google Scholar

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