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In this work, a three-dimensional hybrid simulation program is used to investigate the process of the explosion and expansion of a large number of thermal debris ions in a low density background plasma. By quantitatively calculating the variation of the magnetic bubble and the bubble constraint in the motion of the debris cloud, studied are the influences of the background plasma charge density, the background ion atomic weight, and the charge-mass ratio of the fragment ion on the magnetic bubble. The results show that the background charge density has an important effect on the motion of the bubble and debris cloud. In the early stage of the debris cloud expansion, the background ion atomic weight has little effect on the bubble expansion, but it affects the movement of debris cloud at a later time. When the charge-mass ratio of the debris ion is small, the radius of the ion gyration is larger than the bubble radius, and the bubble radius is small so that it cannot restrain the debris cloud. When the charge-mass ratio of the debris ion is large, the radius of the ion gyration is smaller than the bubble radius. If the background charge density is low in this condition, the early expansion of the bubble and the debris cloud are slightly affected by the charge-mass ratio of the fragment ions, and only the subsequent evolution of the system is influenced. If the background charge density is large in this condition, the charge-mass ratio of the fragment ion has a prominent influence on the motion of the bubble and the debris cloud.
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Keywords:
- magnetic bubble /
- debris cloud /
- background charge density /
- background ion atomic weight /
- charge-mass ratio of fragment ion
[1] Gilbert J, Kappenman J, Radasky W, Savage E 2010 The Late-Time (E3) High-Altitude Electromagnetic Pulse (HEMP) and its Impact on the U. S. Power Grid (Oak Ridge National Laboratory: HEMP TAPS/HEMP-PC Audit Report) Meta-R-321
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Google Scholar
[3] Plechaty C, Presura R, Esaulov A A 2013 Phys. Rev. Lett. 111 185002
Google Scholar
[4] Siebert K, Witt E 2019 Nominal Waveforms for Late-Time High-Altitude Electromagnetic Pulse (Applied Research Associates Inc.) DTRA-TR-19-41
[5] 彭国良, 张俊杰 2021 物理学报 70 180703
Google Scholar
Peng G L, Zhang J J 2021 Acta Phys. Sin. 70 180703
Google Scholar
[6] Winske D, Huba J D, Niemann C, Le A 2019 Front. Astron. Space Sci. 5 51
Google Scholar
[7] Berezin Y A, Dudnikova G I, Fedoruk M P, Vshivkov V A 1998 Int. J. Comp. Fluid D 10 117
Google Scholar
[8] Ripin B H, Huba J D, McLean E A, Manka C K, Peyser T, Burris H R 1993 Phys. Fluids 5 3491
Google Scholar
[9] Gisler G, Lemons D S 1989 J. Geophys. Res. 94 10145
Google Scholar
[10] Winske D 1991 Simulations of HANE/VHANE Dynamics (Defense Nuclear Agency) AD-A243198
[11] Zakharov Y P 2003 IEEE Trans. Plasma Sci. 31 1243
Google Scholar
[12] Yamauchi K, Ohsawa Y 2007 Phys. Plasmas 14 053110
Google Scholar
[13] Winske D, Gary S P 2007 J. Geophys. Res. 112 A10303
Google Scholar
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Google Scholar
[16] Sergeivich B A 2015 Ph. D. Dissertation (Berkeley: University of California)
[17] Harned D S 1982 J. Comp. Phys. 47 452
Google Scholar
[18] Brecht S H, Thomas V A 1988 Comp. Phys. Commun. 48 135
Google Scholar
[19] Lipatov A S 2002 The Hybrid Multiscale Simulation Technology (Berlin Heidelberg: Springer)
[20] 傅竹风, 胡友秋 1994 空间等离子体数值模拟 (合肥: 安徽科学技术出版社) 第6页
Fu Z F, Hu Y Q 1994 Simulation of Space Plasma (Hefei: Anhui Science Press) p6 (in Chinese)
[21] 郑开春 2009 等离子体物理 (北京: 北京大学出版社) 第26页
Zheng K C 2009 Plasma Physics (Beijing: Peking University Press) p26 (in Chinese)
[22] Dedner A, Kemm F, Kroner D, Munz C. D, Schnitzer T, Wesenberg M 2002 J. Comp. Phys. 175 645
Google Scholar
[23] Christopher G C Jr 2007 Ph. D. Dissertation (Monterey, California: Naval Postgraduate School)
[24] Mignone A, Bodo G, Vaida B, Mattia G 2018 Astrophys. J. 859 13
Google Scholar
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图 1 磁场误差随时间的变化
Figure 1. Variation of magnet field variables error with time.
图 2 粒子速度误差随时间的变化
Figure 2. Variation of particles velocity error with time.
图 3 磁泡云图 (a) 垂直于背景磁场的截面; (b) 平行于背景磁场的截面
Figure 3. Magnetic bubbles contour: (a) Cross section perpendicular to background magnet; (b) cross section parallel to background magnet.
图 4 不同背景电荷数密度下磁泡半径随时间的演化
Figure 4. Magnetic bubbles radius vs. time under different background charge number density.
图 5 归一化磁泡半径和碎片云半径随时间的变化 (a) N = 1 × 1010 m–3; (b) N = 1 × 1012 m–3
Figure 5. Normalization debris radius and magnetic bubbles radius vs. time: (a) N = 1 × 1010 m–3; (b) N = 1 × 1012 m–3.
图 6 不同背景离子原子量下磁泡半径随时间的变化 (a) N = 1 × 1010 m–3; (b) N = 1 × 1012 m–3
Figure 6. Magnetic bubbles radius vs. time with different background ion atomic weight: (a) N = 1 × 1010 m–3; (b) N = 1 × 1012 m–3.
图 7 N = 1 × 1010 m–3时不同背景离子原子量的碎片云半径随时间的变化 (a) Ravg; (b) Rd
Figure 7. Debris radius vs. time at N = 1 × 1010 m–3 under different background ion atomic weight: (a) Ravg; (b) Rd.
图 8 N = 1 × 1012 m–3时碎片离子半径随时间的变化 (a) Ravg; (b) Rd
Figure 8. Debris radius vs. time at N = 1 × 1012 m–3 under different background ion atomic weight: (a) Ravg; (b) Rd.
图 9 不同碎片离子原子量下磁泡半径随时间的变化 (a) N = 1 × 1010 m–3; (b) N = 1 × 1012 m–3
Figure 9. Magnetic bubbles radius vs. time under different debris ion atomic weight: (a) N = 1 × 1010 m–3; (b) N = 1 × 1012 m–3.
图 10 N = 1010 m–3时不同碎片离子原子量下碎片云半径随时间的变化 (a) Ravg; (b) Rd
Figure 10. Debris radius vs. time at N = 1010 m–3 under different debris ion atomic weight: (a) Ravg; (b) Rd.
图 11 N = 1 × 1012 m–3时不同碎片离子原子量下碎片云半径随时间的变化 (a) Ravg; (b) Rd
Figure 11. Debris radius vs. time at N = 1 × 1012 m–3 under different debris ion atomic weight: (a) Ravg; (b) Rd.
图 12 不同碎片离子原子量下归一化碎片云半径和磁泡半径随时间的变化 (a) N = 1 × 1010 m–3; (b) N = 1 × 1012 m–3
Figure 12. Normalization debris radius and magnetic bubbles radius vs. time under different debris ion atomic weight: (a) N = 1 × 1010 m–3; (b) N = 1 × 1012 m–3.
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[1] Gilbert J, Kappenman J, Radasky W, Savage E 2010 The Late-Time (E3) High-Altitude Electromagnetic Pulse (HEMP) and its Impact on the U. S. Power Grid (Oak Ridge National Laboratory: HEMP TAPS/HEMP-PC Audit Report) Meta-R-321
[2] Valenzuela A, Haerendel G, Föppl H, Melzner F, Neuss H, Rieger E, Stöcker J, Bauer O, Höfner H, Loidl J 1986 Nature 320 700
Google Scholar
[3] Plechaty C, Presura R, Esaulov A A 2013 Phys. Rev. Lett. 111 185002
Google Scholar
[4] Siebert K, Witt E 2019 Nominal Waveforms for Late-Time High-Altitude Electromagnetic Pulse (Applied Research Associates Inc.) DTRA-TR-19-41
[5] 彭国良, 张俊杰 2021 物理学报 70 180703
Google Scholar
Peng G L, Zhang J J 2021 Acta Phys. Sin. 70 180703
Google Scholar
[6] Winske D, Huba J D, Niemann C, Le A 2019 Front. Astron. Space Sci. 5 51
Google Scholar
[7] Berezin Y A, Dudnikova G I, Fedoruk M P, Vshivkov V A 1998 Int. J. Comp. Fluid D 10 117
Google Scholar
[8] Ripin B H, Huba J D, McLean E A, Manka C K, Peyser T, Burris H R 1993 Phys. Fluids 5 3491
Google Scholar
[9] Gisler G, Lemons D S 1989 J. Geophys. Res. 94 10145
Google Scholar
[10] Winske D 1991 Simulations of HANE/VHANE Dynamics (Defense Nuclear Agency) AD-A243198
[11] Zakharov Y P 2003 IEEE Trans. Plasma Sci. 31 1243
Google Scholar
[12] Yamauchi K, Ohsawa Y 2007 Phys. Plasmas 14 053110
Google Scholar
[13] Winske D, Gary S P 2007 J. Geophys. Res. 112 A10303
Google Scholar
[14] Hewett D W, Brecht S H, Larson D J 2011 J. Geophys. Res. 116 A11310
[15] Peng G L, Zhang J J, Chen J N 2021 Phys. Fluids 33 076602
Google Scholar
[16] Sergeivich B A 2015 Ph. D. Dissertation (Berkeley: University of California)
[17] Harned D S 1982 J. Comp. Phys. 47 452
Google Scholar
[18] Brecht S H, Thomas V A 1988 Comp. Phys. Commun. 48 135
Google Scholar
[19] Lipatov A S 2002 The Hybrid Multiscale Simulation Technology (Berlin Heidelberg: Springer)
[20] 傅竹风, 胡友秋 1994 空间等离子体数值模拟 (合肥: 安徽科学技术出版社) 第6页
Fu Z F, Hu Y Q 1994 Simulation of Space Plasma (Hefei: Anhui Science Press) p6 (in Chinese)
[21] 郑开春 2009 等离子体物理 (北京: 北京大学出版社) 第26页
Zheng K C 2009 Plasma Physics (Beijing: Peking University Press) p26 (in Chinese)
[22] Dedner A, Kemm F, Kroner D, Munz C. D, Schnitzer T, Wesenberg M 2002 J. Comp. Phys. 175 645
Google Scholar
[23] Christopher G C Jr 2007 Ph. D. Dissertation (Monterey, California: Naval Postgraduate School)
[24] Mignone A, Bodo G, Vaida B, Mattia G 2018 Astrophys. J. 859 13
Google Scholar
[25] Mignone A 2014 J. Comp. Phys. 270 784
Google Scholar
[26] Toth G, Odstrcil D 1996 J. Comp. Phys. 128 82
Google Scholar
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