Generation of collisionless electrostatic shock waves in interaction between strong intense laser and near-critical-density plasma

Yue Dong-Ning; Dong Quan-Li; Chen Min; Zhao Yao; Geng Pan-Fei; Yuan Xiao-Hui; Sheng Zheng-Ming; Zhang Jie

doi:10.7498/aps.72.20230271

Abstract

Weak and strong collisionless electrostatic shock wave (CESW) generated in the interaction between strong intense laser and near-critical-density plasma are studied by the one-dimensional particle-in-cell simulation in this work. And the effects of the ranges of plasma density profiles, non-relativistic and relativistic laser intensities on the generation of CESWs are also investigated. The non-relativistic weakly driven laser generates the weak CESW in the interaction between the laser and near-critical-density plasma. The electron spectra show double-temperature distribution because the non-relativistic driven laser cannot heat the electrons sufficiently. The low-temperature electrons have an important influence on the generation of weak CESW, and they can also cause the protons to be accelerated and reflected from the CESWs. The spectra of the weak CESW protons show a continuously distributed profile. When the range of plasma density up-ramp is large, the process can be observed that the post-soliton structure evolves into the ion acoustic wave and further into the weak collisionless electrostatic shock wave. When the driven laser intensity is relativistic, the electrons are heated sufficiently to a single relativistic temperature. The effect of the range of plasma density profile on the generation of CESW is further analyzed and it is found that 1) when the range of plasma density up-ramp is large, the potential barrier of ion acoustic wave is shielded by the hot electrons; 2) when the range of plasma density up-ramp is small, the effective distance (i.e. the Debye length) of accelerating field is larger and the endurance time is longer than when the range of plasma density up-ramp is large. This makes the ion acoustic wave structure more stable in its forward propagation process. When the difference in velocity between the ion acoustic wave accelerating protons and the target normal sheath accelerating protons satisfies the proton reflection condition of CESW, the ion acoustic wave further evolves into the strong CESW, the monoenergetic protons generated at the same time.

Keywords:

strong intense laser /
collisionless electrostatic shock waves /
electron temperature /
ion acoustic wave

Authors and contacts

1.
School of Science, Harbin Institute of Technology (Weihai), Weihai 264209, China
2.
Key Laboratory for Laser Plasmas (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
3.
Collaborative Innovation Center of IFSA, Shanghai Jiao Tong University, Shanghai 200240, China
4.
School of Science, Shenzhen Campus of Sun Yat-sen University, Shenzhen 518107, China

Corresponding author: Dong Quan-Li, qldong@aphy.iphy.ac.cn

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 12204131), the Strategic Priority Research Program of the Chinese Academy of Sciences, China (Grant Nos. XDA25030300, XDA25010100), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019ZD44), and the Basic and Applied Basic Research Foundation of Guangdong, China (Grant No. 2023A1515011695).

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References

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[9]	Romagnani L, Bulanov S V, Borghesi M, Audebert P, Gauthier J C, Löwenbrück K, Mackinnon A J, Patel P, Pretzler G, Toncian T, Willi O 2008 Phys. Rev. Lett. 101 025004 Google Scholar
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[12]	Chen M, Sheng Z M, Dong Q L, He M Q, Li Y T, Bari M A, Zhang J 2007 Phys. Plasmas 14 053102 Google Scholar
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Cited By

图 1 初始激光等离子体条件设置, 驱动激光分为弱光强(a₀ = 0.5)和强光强(a₀ = 3.0)两种. 近临界密度分布分为10 μm和40 μm线性上升沿两种情况, 峰值密度均为1.5n_c, 下降沿均为指数分布, 特征长度为8 μm

Figure 1. The setup of initial laser-plasma conditions, the drive intense lasers are divided as the weak intensity and the strong intensity corresponding to the normalized amplitude as a₀ = 0.5 and a₀ = 3.0. The density profiles are set up as 10 μm and 40 μm linear density up-ramp respectively. The peak densities both are 1.5n_c. The density down-ramps both are exponentially distributed which the characteristic scale is 8 μm.

DownLoad: Full-Size Img PowerPoint

图 2 t = 150T₀, t = 350T₀, t = 500T₀时刻, 弱驱动光强下, 质子密度n_p (a), (c) 和纵向加速电场E_x (b), (d) 的分布　(a), (b) 第1种等离子体密度分布; (c), (d) 第2种等离子体密度分布, T₀为对应波长1.0 μm的归一化激光周期

Figure 2. Distributions of (a), (c) the proton density n_pand (b), (d) the longitudinal electric field E_x with the weak drive laser intensity at t = 150T₀, t = 350T₀, t = 500T₀: (a), (b) plasma density profile 1; (c), (d) plasma density profile 2, T₀ is the normalized laser period which is corresponding to 1.0 μm wavelength.

DownLoad: Full-Size Img PowerPoint

图 3 (a) 图2(a)中A点(蓝线)和图2(c)中B点(红线)处激光电场E_z随时间的分布, (b)对应的频谱分布, ω₀为入射激光角频率

Figure 3. (a) Distributions of the laser electric field E_z of point A in Fig.2(a) (blue line) and point B in Fig.2(c) (red line); (b) the corresponding frequency spectrum, ω₀ is the angular frequency of incident laser.

DownLoad: Full-Size Img PowerPoint

图 4 t = 500T₀时刻, 弱驱动光强下, 质子在相空间(x, p_x)中的分布　(a) 第1种等离子体密度分布; (b) 第2种等离子体密度分布; (c) 对应的动量p_x > 0的质子能谱分布

Figure 4. Protons distributions in phase-space (x, p_x) with the weak drive laser intensity at t = 500T₀: (a) Plasma density profile 1; (b) plasma density profile 2; (c) the corresponding energy spectra for protons with proton momenta p_x > 0 at t = 500T₀.

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图 5 t = 500T₀时刻, 弱驱动光强下, 电子能谱和拟合电子温度T_e分布(低温T_eL和高温T_eH)　(a) 第1种等离子体密度分布; (b) 第2种等离子体密度分布

Figure 5. Distributions of the electron energy spectrum and fitted electron temperature T_e (low temperature T_eL and high temperature T_eH) with the weak drive laser intensity at t = 500T₀: (a) Plasma density profile 1, (b) plasma density profile 2.

DownLoad: Full-Size Img PowerPoint

图 6 　t = 100T₀, t = 150T₀, t = 200T₀时刻, 强驱动光强下, 质子密度n_p(a), (c)和纵向加速电场E_x (b), (d)的分布　(a), (b) 第1种等离子体密度分布; (c), (d) 第2种等离子体密度分布.

Figure 6. Distributions of the proton density n_p(a), (c) and the longitudinal electric field E_x(b), (d) with the strong drive laser intensity at t = 100T₀, t = 150T₀, t = 200T₀: (a), (b) Plasma density profile 1; (c), (d) plasma density profile 2.

DownLoad: Full-Size Img PowerPoint

图 7 t = 300T₀, t = 350T₀, t = 400T₀时刻, 强驱动光强下, 质子密度n_p(a), (c)和纵向加速电场E_x (b), (d)的分布　(a), (b) 第1种等离子体密度分布; (c), (d) 第2种等离子体密度分布

Figure 7. Distributions of the proton density n_p(a), (c) and the longitudinal electric field E_x(b), (d) with the strong drive laser intensity at t = 300T₀, t = 350T₀, t = 400T₀: (a), (b) Plasma density profile 1; (c), (d) plasma density profile 2.

DownLoad: Full-Size Img PowerPoint

图 8 t = 300T₀, t = 350T₀, t = 400T₀时刻, 强驱动光强下, 质子在相空间(x, p_x)中的分布　(a) 第1种等离子体密度分布; (b) 第2种等离子体密度分布; (c) t = 400T₀时刻, 对应的动量p_x > 0的质子能谱分布

Figure 8. Protons distributions in phase-space (x, p_x) with the strong drive laser intensity at t = 300T₀, t = 350T₀ and t = 400T₀: (a) Plasma density profile 1; (b) plasma density profile 2; (c) the corresponding energy spectra for protons with proton momenta p_x > 0 at t = 400T₀.

DownLoad: Full-Size Img PowerPoint

图 9 t = 400T₀时刻, 强驱动光强下, 电子能谱和拟合电子温度T_e分布　(a) 第1种等离子体密度分布; (b) 第2种等离子体密度分布

Figure 9. Distributions of the electron energy spectrum and fitted electron temperature T_e with the strong drive laser intensity at t = 400T₀: (a) Plasma density profile 1; (b) plasma density profile 2.

DownLoad: Full-Size Img PowerPoint

[1]	Moiseev S S, Sagdeev R Z 1963 J. Nucl. Energy, Part C Plasma Phys. 5 43 Google Scholar
[2]	Taylor R J, Baker D R, Ikezi H 1970 Phys. Rev. Lett. 24 206 Google Scholar
[3]	Ghavamian P, Schwartz S J, Mitchell J, Masters A, Laming J M 2013 Space Sci. Rev. 178 633 Google Scholar
[4]	Waxman E 2006 Plasma Phys. Control. Fusion 48 B137 Google Scholar
[5]	Nishikawa K -I, Hardee P, Richardson G, Preece R, Sol H, Fishman G J 2003 Astrophys. J. 595 555 Google Scholar
[6]	Huang J, Weng S M, Wang X, Zhong J Y, Zhu X L, Li X F, Chen M, Masakatsu M, Sheng Z M 2022 Astrophys. J. 931 36 Google Scholar
[7]	Drake R P 2000 Phys. Plasmas 7 4690 Google Scholar
[8]	Courtois C, Grundy R A D, Ash A D, Chambers D M, Woolsey N C, Dendy R O, McClements K G 2004 Phys. Plasmas 11 3386 Google Scholar
[9]	Romagnani L, Bulanov S V, Borghesi M, Audebert P, Gauthier J C, Löwenbrück K, Mackinnon A J, Patel P, Pretzler G, Toncian T, Willi O 2008 Phys. Rev. Lett. 101 025004 Google Scholar
[10]	Denavit J 1992 Phys. Rev. Lett. 69 3052 Google Scholar
[11]	Silva L O, Marti M, Davies J R, Fonseca R A, Ren C, Tsung F S, Mori W B 2004 Phys. Rev. Lett. 92 015002 Google Scholar
[12]	Chen M, Sheng Z M, Dong Q L, He M Q, Li Y T, Bari M A, Zhang J 2007 Phys. Plasmas 14 053102 Google Scholar
[13]	Liu M, Weng S M, Li Y T, Yuan D W, Chen M, Mulser P, Sheng Z M, Murakami M, Yu L L, Zheng X L, Zhang J 2016 Phys. Plasmas 23 113103 Google Scholar
[14]	Fiuza F, Stockem A, Boella E, Fonseca R A, Silva L O, Haberberger D, Tochitsky S, Gong C, Mori W B, Joshi C 2012 Phys. Rev. Lett. 109 215001 Google Scholar
[15]	Zhang W L, Qiao B, Huang T W, X. F. Shen, W. Y. You, X. Q. Yan, S. Z. Wu, Zhou C T, He X T 2016 Phys. Plasmas 23 073118 Google Scholar
[16]	Zhang W L, Qiao B, Shen X F, You W Y, Huang T W, Yan X Q, Wu S Z, Zhou C T, He X T 2016 New J. Phys. 18 093029 Google Scholar
[17]	Haberberger D, Tochitsky S, Fiuza F, Gong C, Fonseca R A, Silva L O, Mori W B, Joshi C 2012 Nat. Phys. 8 95 Google Scholar
[18]	Zhang H, Shen B F, Wang W P, Zhai S H, Li S S, Lu X M, Li J F, Xu R J, Wang X L, Liang X Y, Leng Y X, Li R X, Xu Z Z 2017 Phys. Rev. Lett. 119 164801 Google Scholar
[19]	Dover N P, Cook N, Tresca O, Ettlinger O, Maharjan C, Polyanskiy M N, Shkolnikov P, Pogorelsky I, Najmudin Z 2016 J. Plasma Phys. 82 415820101 Google Scholar
[20]	Marquès J -R, Loiseau P, Bonvalet J, Tarisien M, d'Humières E, Domange J, Hannachi F, Lancia L, Larroche O, Nicolaï P, Puyuelo-Valdes P, Romagnani L, Santos J J, Tikhonchuk V 2021 Phys. Plasmas 28 023103 Google Scholar
[21]	Puyuelo-Valdes P, Henares J L, Hannachi F, Ceccotti T, Domange J, Ehret M, d'Humieres E, Lancia L, Marquès J -R, Ribeyre X, Santos J J, Tikhonchuk V, Tarisien M 2019 Phys. Plasmas 26 123109 Google Scholar
[22]	Helle M H, Gordon D F, Kaganovich D, Chen Y, Palastro J P, Ting A 2016 Phys. Rev. Lett. 117 165001 Google Scholar
[23]	Deng Y, Zhang Q, Yue D, Wei W, Feng L, Cui Y, Ma Y, Lu F, Yang Y, Huang Z, Wu Y, Zhou W, Weng S, Liu F, Chen M, Yuan X, Zhang J 2022 Phys. Plasmas 29 123103 Google Scholar
[24]	Deng Y Q, Yue D N, Luo M F, Zhao X, Li Y J, Ge X L, Liu F, Weng S M, Chen M, Yuan X H, Zhang J 2022 High Power Laser Sci. 10 e39 Google Scholar
[25]	Naumova N M, Bulanov S V, Esirkepov T Zh, Farina D, Nishihara K, Pegoraro F, Ruhl H, Sakharov A S 2001 Phys. Rev. Lett. 87 185004 Google Scholar
[26]	Borghesi M, Bulanov S, Campbell D H, Clarke R J, Esirkepov T Z, Galimberti M, Gizzi L A, MacKinnon A J, Naumova N M, Pegoraro F, Ruhl H, Schiavi A, Willi O 2002 Phys. Rev. Lett. 88 135002 Google Scholar
[27]	Liu Y, Klimo O, Esirkepov T Z, Bulanov S V, Gu Y, Weber S, Korn G 2015 Phys. Plasmas 22 112302 Google Scholar
[28]	Yue D N, Chen M, Zhao Y, Geng P F, Yuan X H, Dong Q L, Sheng Z M, Zhang J 2022 Chin. Phys. B 31 045205 Google Scholar
[29]	Yue D N, Chen M, Geng P F, Yuan X H, Weng S M, Bulanov S S, Bulanov S V, Mima K, Sheng Z M, Zhang J 2021 Phys. Plasmas 28 042303 Google Scholar
[30]	Yue D N, Chen M, Geng P F, Yuan X H, Sheng Z M, Zhang J, Dong Q L, Das A, Kumar G R 2021 Plasma Phys. Control. Fusion 63 075009 Google Scholar
[31]	Yi L Q, Pusztai I, Pukhov A, Shen B F and Fülöp T 2019 J. Plasma Phys. 85 905850403 Google Scholar
[32]	Yue D N, Chen M, Geng P F, Yuan X H, Dong Q L, Sheng Z M, Zhang J 2022 Plasma Phys. Control. Fusion 64 045025 Google Scholar
[33]	Fonseca R A, Silva L O, Tsung F S, Decyk V K, Lu W, Ren C, Mori W B, Deng S, Lee S, Katsouleas T, Adam J C 2002 Lect. Notes Comput. Sci. 2331 342
[34]	Yuan D W, Li Y T, Liu M, Zhong J Y, Zhu B J, Li Y F, Wei H G, Han B, Pei X X, Zhao J R, Li F, Zhang Z, Liang G Y, Wang F L, Weng S M, Li Y J, Jiang S E, Du K, Ding Y K, Zhu B Q, Zhu J Q, Zhao G, Zhang J 2017 Sci. Rep. 7 42915 Google Scholar
[35]	Chenais-Popovics C, Renaudin P, Rancu O, Gilleron F, Gauthier J C, Larroche O, Peyrusse O, Dirksmöller M, Sondhauss P, Missalla T, Uschmann I, Förster E, Renner O, Krousky E 1997 Phys. Plasmas 4 190 Google Scholar

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Vol. 72, Issue 11 - 2023-06-05

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