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The mechanism of photon acceleration driven by the near-forward scattering (NFS) in the interaction between an intense laser and under-dense plasmas is studied by particle-in-cell (PIC) simulation. This mechanism utilizes tunneling ionization effect to stimulate electron plasma waves when the intense laser pulse propagates in under-dense plasmas. The electron plasma density is inhomogeneous both in longitudinal and transverse direction. In the longitudinal direction, a steep ionized electron density front is generated by incident laser ionizing the helium gas. Around the ionization front, the incident laser interacts with electron plasma waves, thus generating the first kind of NFS waves. Compared with the frequency of laser, the frequency of NFS wave increases. This is the first characteristic peak in the frequency spectrum. In the transverse direction, the electron plasma waves have different phase velocities, which makes the incident laser pulse undergo NFS process and upshift its frequency. This is the second characteristic peak in the frequency spectrum. Owing to the fact that the electron density inhomogeneity is much larger than the electron density perturbation of electron plasma wave, the scattering model and dispersion relationships, which are based on perturbation theory like stimulated Raman scattering, are no longer applicable to this case. Our further study shows that the incident laser, electron density plasma waves and NFS waves still satisfy the energy conservation and momentum conservation that is, they still satisfy the three-wave coupling relationship of momentum and energy conservation under the condition of heterogeneous density, thus explaining the appearance of two characteristic peaks in the frequency spectrum and their growth in the wave-vector space. This study has significant reference to the spectrum evolution when the intense laser pulse propagates in under-dense plasma.
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Keywords:
- intense laser /
- electron plasma wave /
- near-forward scattering /
- photon acceleration
[1] Strickland D, Mourou G 1985 Opt. Commun. 55 447
Google Scholar
[2] Tajima T, Dawson J M 1979 Phys. Rev. Lett. 43 267
Google Scholar
[3] Esarey E, Schroeder C B, Leemans W P 2009 Rev. Mod. Phys. 81 1229
Google Scholar
[4] 陈民, 刘峰, 李博原, 翁苏明, 陈黎明, 盛政明, 张杰 2020 强激光与粒子束 32 092001
Google Scholar
Chen M, Liu F, Li B Y, Weng S M, Chen L M, Sheng Z M, Zhang J 2020 High Power Laser Part. Beams 32 092001
Google Scholar
[5] Ke L T, Feng K, Wang W T, Qin Z Y, Yu C H, Wu Y, Chen Y, Qi R, Zhang Z J, Xu Y, Yang X J, Leng Y X, Liu J S, Li R X, Xu Z Z 2021 Phys. Rev. Lett. 126 214801
Google Scholar
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Google Scholar
[8] 吴学志, 寿寅任, 弓正, 赵研英, 朱昆, 杨根, 卢海洋, 林晨, 马文君, 陈佳洱, 颜学庆 2020 强激光与粒子束 32 092002
Google Scholar
Wu X Z, Shou Y R, Gong Z, Zhao Y Y, Zhu K, Yang G, Lu H Y, Lin C, Ma W J, Chen J E, Yan X Q 2020 High Power Laser Part. Beams 32 092002
Google Scholar
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Google Scholar
[10] Chen M, Pukhov A, Yu T, Sheng Z M 2009 Phys. Rev. Lett. 103 024801
Google Scholar
[11] Pukhov A 2001 Phys. Rev. Lett. 86 3562
Google Scholar
[12] Wilks S, Langdon A, Cowan T, Roth M, Singh M, Hatchett S, Key M H, Pennington D, MacKinnon A, Snavely R A 2001 Phys. Plasmas 8 542
Google Scholar
[13] 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
[14] 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
[15] 马文君, 刘志鹏, 王鹏杰, 赵家瑞, 颜学庆 2021 70 084102
Google Scholar
Ma W J, Liu Z P, Wang P J, Zhao J R, Yan X Q 2021 Acta Phys. Sin. 70 084102
Google Scholar
[16] Bulanov S V, Dylov D V, Esirkepov T Z, Kamenets F F, Sokolov D V 2005 Plasma Phys. Rep. 31 369
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[21] Dias J M, Stenz C, Lopes N, Badiche X, Blasco F, Santos A D, Silva L O, Mysyrowicz A, Antonetti A, Mendonça J T 1997 Phys. Rev. Lett. 78 4773
Google Scholar
[22] Murphy C D, Trines R, Vieira J, Reitsma A J W, Bingham R, Collier J L, Divall E J, Foster P S, Hooker C J, Langley A J, Norreys P A, Fonseca R A, Fiuza F, Silva L O, Mendonça J T, Mori W B, Gallacher J G, Viskup R, Jaroszynski D A, Mangles S P D, Thomas A G R, Krushelnick K, Najmudin Z 2006 Phys. Plasmas 13 033108
Google Scholar
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Google Scholar
[24] Zhao Y, Zheng J, Chen M, Yu L L, Weng S M, Ren C, Liu C S, Sheng Z M 2014 Phys. Plasmas 21 112114
Google Scholar
[25] 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
[26] Ammosov M V, Delone N B, Krainov V P 1986 Proc. SPIE 664 138
Google Scholar
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Google Scholar
Yü S H, Li X F, Weng S M, Zhao Y, Ma H H, Chen M, Sheng Z M 2021 High Power Laser Part. Beams 33 012006
Google Scholar
[28] Montgomery D S 2016 Phys. Plasmas 23 055601
Google Scholar
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图 1 (a) 强激光在亚临界密度气体中传输时利用近前向散射驱动光子加速的原理示意图; (b), (c)激光与电子等离子体波相互作用的三波耦合关系, 其中(b)第1类近前向散射, (c)第2类近前向散射
Figure 1. (a) Schematics of photon acceleration driven by the near-forward scattering when intense laser pulse propagates in under-dense gas. The three-wave matching conditions for the laser pulse and electron plasma waves: (b) The first kind of NFS; (c) the second kind of NFS.
图 2 初始激光等离子体条件设置, 即真空-氦气-真空分布. 插图为初始时刻激光电场强度分布
Figure 2. Setup of initial laser-plasma conditions, namely, vacuum-helium-gas-vacuum distribution. The inset is the initial distribution of laser electric field.
图 3 不同时刻, 激光电场Ez在(a), (c), (e), (g)空间(x, y)和(b), (d), (f), (h)波矢空间(kx, ky)中的分布((a)—(f)有电子等离子体, (g), (h)无电子等离子体; T0为激光周期) (a), (b) t = 62.5T0; (c), (d) t = 93.8T0; (e), (f), (g), (h) t = 125.0T0;
Figure 3. Distributions of laser electric field Ez in (a), (c), (e), (g) spatial space (x, y) and (b), (d), (f), (h) wave vector space (kx, ky) at (a), (b) t = 62.5T0; (c), (d) t = 93.8T0; (e)–(h) t = 125.0T0. Panels (a)–(f) are with electron plasma (EP); panels (g), (h) are without (w/o) electron plasma (EP). T0 is the laser period.
图 4 t = 93.8T0时刻, (a)激光电场Ez (绿线)和电子密度ne (红线); (b)纵向电场Ex (绿线)和电子等离子体波密度扰动δne = (ne – 0.05nc) (红线)在激光传输轴上的分布
Figure 4. Distributions of (a) laser electric field Ez (green line) and electron density ne (red line); (b) longitudinal electric field Ex (green line) and electron density perturbation of electron plasma wave δne = (ne – 0.05nc) (red line) on laser axis at t = 93.8T0.
图 5 t = 93.8T0时刻, (a)电子密度ne和(b)纵向电场Ex在空间(x, y)中的分布, (c) 纵向电场Ex在波矢空间(kx, ky)中的分布
Figure 5. Distributions of (a) electron density ne and (b) longitudinal electric field Ex in spatial space (x, y), (c) distribution of longitudinal electric field Ex in wave vector space (kx, ky) at t = 93.8T0.
图 6 t = 93.8T0时刻, (a)第1类散射波滤波之后的效果, (b)第1类散射波进行傅里叶逆变换后的结果, (c)第2类散射波滤波之后的效果, (d)第2类散射波进行傅里叶逆变换后的结果
Figure 6. (a) Filter result of the first kind of NFS, (b) the result of the first kind of NFS after inverse fast Fourier transform, (c) the filter result of the second kind of NFS, (d) the result of the second kind of NFS after inverse fast Fourier transform at t = 93.8T0.
图 7 (a) 图2中A点处电场的频谱分布; (b) 两类近前向散射波的波矢强度
$ {I}_{{\rm{s}}1} $ 和$ {I}_{{\rm{s}}2} $ 随时间的演化; (c)$x=110\;{\text{μm}}$ 处得到的两类散射波的相对强度$ {I}_{{\rm{s}}1}/{I}_{0} $ 和$ {I}_{{\rm{s}}2}/{I}_{0} $ 随散射角$ \theta $ 的演化, 其中,$ {I}_{0} $ 为激光频率$ {\omega }_{0} $ 对应的强度Figure 7. (a) Frequency spectrum at A point in Fig. 2; (b) the intensity of two kinds of NFS waves,
$ {I}_{{\rm{s}}1} $ and$ {I}_{{\rm{s}}2} $ , evolve with simulation time; (c) the relativistic intensity of two kinds of NFS waves,$ {I}_{{\rm{s}}1}/{I}_{0} $ and$ {I}_{{\rm{s}}2}/{I}_{0} $ , change with the scattering angle$ \theta $ at$x=110\;{\text{μm}}$ , where$ {I}_{0} $ is the intensity corresponding to the laser frequency$ {\omega }_{0} $ . -
[1] Strickland D, Mourou G 1985 Opt. Commun. 55 447
Google Scholar
[2] Tajima T, Dawson J M 1979 Phys. Rev. Lett. 43 267
Google Scholar
[3] Esarey E, Schroeder C B, Leemans W P 2009 Rev. Mod. Phys. 81 1229
Google Scholar
[4] 陈民, 刘峰, 李博原, 翁苏明, 陈黎明, 盛政明, 张杰 2020 强激光与粒子束 32 092001
Google Scholar
Chen M, Liu F, Li B Y, Weng S M, Chen L M, Sheng Z M, Zhang J 2020 High Power Laser Part. Beams 32 092001
Google Scholar
[5] Ke L T, Feng K, Wang W T, Qin Z Y, Yu C H, Wu Y, Chen Y, Qi R, Zhang Z J, Xu Y, Yang X J, Leng Y X, Liu J S, Li R X, Xu Z Z 2021 Phys. Rev. Lett. 126 214801
Google Scholar
[6] Wang W T, Feng K, Ke L T, Yu C H, Xu Y, Qi R, Chen Y, Qin Z Y, Zhang Z J, Fang M, Liu J Q, Jiang K N, Wang H, Wang C, Yang X J, Wu F X, Leng Y X, Liu J S, Li R X, Xu Z Z 2021 Nature 595 516
Google Scholar
[7] Macchi A, Borghesi M, Passoni M 2013 Rev. Mod. Phys. 85 751
Google Scholar
[8] 吴学志, 寿寅任, 弓正, 赵研英, 朱昆, 杨根, 卢海洋, 林晨, 马文君, 陈佳洱, 颜学庆 2020 强激光与粒子束 32 092002
Google Scholar
Wu X Z, Shou Y R, Gong Z, Zhao Y Y, Zhu K, Yang G, Lu H Y, Lin C, Ma W J, Chen J E, Yan X Q 2020 High Power Laser Part. Beams 32 092002
Google Scholar
[9] Esirkepov T, Borghesi M, Bulanov S, Mourou G, Tajima T 2004 Phys. Rev. Lett. 92 175003
Google Scholar
[10] Chen M, Pukhov A, Yu T, Sheng Z M 2009 Phys. Rev. Lett. 103 024801
Google Scholar
[11] Pukhov A 2001 Phys. Rev. Lett. 86 3562
Google Scholar
[12] Wilks S, Langdon A, Cowan T, Roth M, Singh M, Hatchett S, Key M H, Pennington D, MacKinnon A, Snavely R A 2001 Phys. Plasmas 8 542
Google Scholar
[13] 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
[14] 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
[15] 马文君, 刘志鹏, 王鹏杰, 赵家瑞, 颜学庆 2021 70 084102
Google Scholar
Ma W J, Liu Z P, Wang P J, Zhao J R, Yan X Q 2021 Acta Phys. Sin. 70 084102
Google Scholar
[16] Bulanov S V, Dylov D V, Esirkepov T Z, Kamenets F F, Sokolov D V 2005 Plasma Phys. Rep. 31 369
Google Scholar
[17] Park J, Bulanov S S, Bin J, Ji Q, Steinke S, Vay J L, Geddes C G R, Schroeder C B, Leemans W P, Schenkel T, Esarey E 2019 Phys. Plasmas 26 103108
Google Scholar
[18] Liu B, Meyer-Ter-Vehn J, Bamberg K U, Ma W J, Liu J, He X T, Yan X Q, Ruhl H 2016 Phys. Rev. Accel. Beams 19 073401
Google Scholar
[19] Liu B, Meyer-Ter-Vehn J, Ruhl H 2018 Phys. Plasmas 25 103117
Google Scholar
[20] Savage Jr R L, Joshi C, Mori W B 1992 Phys. Rev. Lett. 68 946
Google Scholar
[21] Dias J M, Stenz C, Lopes N, Badiche X, Blasco F, Santos A D, Silva L O, Mysyrowicz A, Antonetti A, Mendonça J T 1997 Phys. Rev. Lett. 78 4773
Google Scholar
[22] Murphy C D, Trines R, Vieira J, Reitsma A J W, Bingham R, Collier J L, Divall E J, Foster P S, Hooker C J, Langley A J, Norreys P A, Fonseca R A, Fiuza F, Silva L O, Mendonça J T, Mori W B, Gallacher J G, Viskup R, Jaroszynski D A, Mangles S P D, Thomas A G R, Krushelnick K, Najmudin Z 2006 Phys. Plasmas 13 033108
Google Scholar
[23] Trines R M G M, Murphy C D, Lancaster K L, Chekhlov O, Norreys P A, Bingham R, Mendonça J T, Silva L O, Mangles S P D, Kamperidis C, Thomas A, Krushelnick K, Najmudin Z 2009 Plasma Phys. Control. Fusion 51 024008
Google Scholar
[24] Zhao Y, Zheng J, Chen M, Yu L L, Weng S M, Ren C, Liu C S, Sheng Z M 2014 Phys. Plasmas 21 112114
Google Scholar
[25] 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
[26] Ammosov M V, Delone N B, Krainov V P 1986 Proc. SPIE 664 138
Google Scholar
[27] 余诗瀚, 李晓峰, 翁苏明, 赵耀, 马行行, 陈民, 盛政明 2021 强激光与粒子束 33 012006
Google Scholar
Yü S H, Li X F, Weng S M, Zhao Y, Ma H H, Chen M, Sheng Z M 2021 High Power Laser Part. Beams 33 012006
Google Scholar
[28] Montgomery D S 2016 Phys. Plasmas 23 055601
Google Scholar
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