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

频率啁啾对强场下真空正负电子对产生的增强效应

谢柏松 李烈娟 麦丽开·麦提斯迪克 王莉

引用本文:
Citation:

频率啁啾对强场下真空正负电子对产生的增强效应

谢柏松, 李烈娟, 麦丽开·麦提斯迪克, 王莉

Enhancement effect of frequency chirp on vacuum electron-positron pair production in strong field

Xie Bai-Song, Li Lie-Juan, Melike Mohamedsedik, Wang Li
PDF
HTML
导出引用
  • 在强背景场下真空产生正反粒子对的研究中, 频率啁啾对增强粒子对的产生起着关键作用. 本文介绍了狄拉克-海森伯-维格纳(Dirac -Heisenberg-Wigner)、求解量子弗拉索夫方程(quantum Vlasov equation)和计算量子场论等方法, 并详细综述了它们如何应用到空间非均匀场、均匀含时场以及外部势场中正负电子对产生的研究. 通过研究各种不同的场得到了不同参数(如场强和基准频率)下产生的粒子动量谱和粒子对产额, 发现当频率啁啾形式或/和啁啾强度改变时结果受到显著影响. 在低频场下啁啾增强的数密度可提高2—3个数量级, 这主要是因为啁啾增加了场的高频成分, 从而低频强场和高频弱场相结合的动力学辅助机制起到了很大的作用. 一般来说在高频情况下数密度只有几倍的提高, 说明动力学辅助作用被大大地抑制了. 在有空间变化的场情形下, 对于小空间尺度变化的场, 无啁啾时本身的数密度不高, 但啁啾可以对数密度有数量级的提高; 对于大空间尺度变化的场, 数密度逐渐趋于空间均匀的结果, 啁啾也能对数密度有几倍的提高. 通过Wentzel-Kramer-Brillouin近似和转变点结构的物理分析和讨论可以对相关的数值结果进行理解. 最后简要地给出了频率啁啾对粒子对产生增强效应可能的应用前景与展望.
    In this review article, we show an important aspect of electron-positron pair production from vacuum under strong background field where the frequency chirping plays a key role in enhancing the pair production. A series of researches on the enhancement effect of frequency chirp on electron-positron pair production in strong field is summarized. Three approaches are introduced, i.e. the Dirac-Heisenberg-Wigner formalism used to treat the spatial inhomogeneous field or/and multidimensional homogeneous time-dependent field, quantum Vlasov equation to cope with the one-dimensional homogeneous time-dependent field, and the computation quantum field theory employed to study the problem with external potential. Some interesting results about the momentum spectrum structure of created particle and the yielding of pair numbers are demonstrated for various different field parameters such as field strength and central frequency, in particular their significant influence on results when the frequency chirping form or/and strength are changed. In general, the number density can be improved by 2-3 orders of magnitude with the strengthening of frequency chirping in comparison with that without chirping for low frequency field, which is attributed to the effect that the dynamically assisted mechanism plays a significant role since the chirping expands the frequency spectrum of field. For high frequency field, however, this effect is suppressed so that the number density is enhanced by about a few times. For spatially inhomogeneous field, field changing on a small scale does not make the number density so high and the frequency chirping can enhance the yield in the order of magnitude, while the field changing on a large scale makes the number density to approach to that of homogeneous field and the chirping increases the yield by a few times. These numerical results can be understood by the Wentzel-Kramer-Brillouin (WKB) approximation and the structure of turning points. Finally the possible applicable prospects of the electron-positron pair production by the frequency chirping are presented briefly.
      通信作者: 谢柏松, bsxie@bnu.edu.cn ; 王莉, wangli@brc.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 11875007, 11935008)资助的课题.
      Corresponding author: Xie Bai-Song, bsxie@bnu.edu.cn ; Wang Li, wangli@brc.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11875007, 11935008)
    [1]

    Dirac P A M 1928 Proc. R. Soc. A 118 351

    [2]

    Anderson C D 1933 Phys. Rev. 43 491Google Scholar

    [3]

    Sauter F 1931 Z. Phys. 69 742Google Scholar

    [4]

    Heisenberg W, Euler H 1936 Z. Phys. 98 714Google Scholar

    [5]

    Schwinger J 1951 Phys. Rev. 82 664Google Scholar

    [6]

    Ritus V I 1985 J. Sov. Laser Res. 6 497Google Scholar

    [7]

    Piazza A D 2011 Rev. Mod. Phys. 84 1177

    [8]

    Gelis F, Tanji N 2016 Prog. Part. Nucl. Phys. 87 1Google Scholar

    [9]

    Strickland D, Mourou G 1985 Opt. Commun. 55 447Google Scholar

    [10]

    Ringwald A 2001 Phys. Lett. B 510 107Google Scholar

    [11]

    Yanovsky V P, Chvykov V, Kalinchenko G, Rousseau P, Krushelnick K 2008 Opt. Express 16 2109Google Scholar

    [12]

    Heinzl T, Ilderton A 2009 Eur. Phys. J. D 55 359Google Scholar

    [13]

    Marklund M, Lundin J 2009 Eur. Phys. J. D 55 319Google Scholar

    [14]

    Dunne G V 2009 Eur. Phys. J. D 55 327Google Scholar

    [15]

    Pike O J, Mackenroth F, Hill E G, Rose S J 2014 Nat. Photonics 8 434Google Scholar

    [16]

    https://www.eli -beams .eu/. [2022-1-21]

    [17]

    Schuetzhold R, Gies H, Dunne G 2008 Phys. Rev. Lett. 101 130404Google Scholar

    [18]

    Bell A R, Kirk J G 2008 Phys. Rev. Lett. 101 2952

    [19]

    Dunne G V, Gies H, Schützhold R 2009 Phys. Rev. D 80 111301Google Scholar

    [20]

    Piazza A D, E Lötstedt, Milstein A I, Keitel C H 2009 Phys. Rev. Lett. 103 170403Google Scholar

    [21]

    Bulanov S S, Mur V D, Narozhny N B, Nees J, Popov V S 2010 Phys. Rev. Lett. 104 220404Google Scholar

    [22]

    https://xcels.iapras .ru /news .html[2022-1-21]

    [23]

    http://www.hibef.eu[2022-1-21]

    [24]

    Nikishov A I 1969 Sov. Phys. JETP 30 660

    [25]

    Brezin E, Itzykson C 1970 Phys. Rev. D 2 1191Google Scholar

    [26]

    Marinov M S, Popov V S 1977 Fortschr. Phys. 25 373Google Scholar

    [27]

    Nikishov A I 1985 J. Sov. Laser Res. 6 619Google Scholar

    [28]

    Gies H, Klingmüller K 2005 Phys. Rev. D 72 065001

    [29]

    Dunne G, Wang Q H, Gies H, Schubert C 2006 Phys. Rev. D 73 065028

    [30]

    Xie B S, Melike M, Sayipjamal D 2012 Chin. Phys. Lett. 29 021102Google Scholar

    [31]

    Schneider C, Schützhold R 2016 J. High Energy Phys. 02 164Google Scholar

    [32]

    Kluger Y, Eisenberg J M, Svetitsky B, Cooper F, Mottola E 1991 Phys. Rev. Lett. 67 2427Google Scholar

    [33]

    Alkofer R, Hecht M B, Roberts C D, Schmidt S M, Vinnik D V 2001 Phys. Rev. Lett. 87 193902Google Scholar

    [34]

    Abdukerim N, Li Z L, Xie B S 2017 Chin. Phys. B 26 020301Google Scholar

    [35]

    Krekora P, Cooley K, Su Q, Grobe R 2005 Phys. Rev. Lett. 95 070403Google Scholar

    [36]

    Lv Q Z, Liu Y, Li Y J, Grobe R, Su Q 2013 Phys. Rev. Lett. 111 183204Google Scholar

    [37]

    Wang L, Wu B B, Xie B S 2019 Phys. Rev. A 100 022127Google Scholar

    [38]

    Hebenstreit F, Alkofer R, Gies H 2011 Phys. Rev. Lett. 107 180403Google Scholar

    [39]

    Kohlfürst C 2015 Ph. D. Dissertation arXiv: 1512.06082

    [40]

    Xie B S, Li Z L, Tang S 2017 Matter Radiat. Extremes 2 225Google Scholar

    [41]

    Kohlfürst C, Alkofer R 2018 Phys. Rev. D 97 036026Google Scholar

    [42]

    Ababekri M, Dulat S, Xie B S, Zhang J 2020 Phys. Lett. B 810 135815Google Scholar

    [43]

    Kohlfürst C 2020 Phys. Rev. D 101 096003Google Scholar

    [44]

    Hebenstreit F, Alkofer R, Dunne G V, Gies H 2009 Phys. Rev. Lett. 102 150404Google Scholar

    [45]

    Dumlu C K 2010 Phys. Rev. D 82 045007Google Scholar

    [46]

    Olugh O, Li Z L, Xie B S, Alkofer R 2019 Phys. Rev. D 99 036003Google Scholar

    [47]

    Orthaber M, Hebenstreit F, Alkofer R 2011 Phys. Lett. B 698 80Google Scholar

    [48]

    Ababekri M, Xie B S, Zhang J 2019 Phys. Rev. D 100 016003Google Scholar

    [49]

    Olugh O, Li Z L, Xie B S 2020 Phys. Lett. B 802 135259Google Scholar

    [50]

    Gong C, Li Z L, Xie B S, Li Y J 2020 Phys. Rev. D 101 016008Google Scholar

    [51]

    Wang K, Hu X H, Dulat S, Xie B S 2021 Chin. Phys. B 30 060204Google Scholar

    [52]

    Mohamedsedik M, Li L J, Xie B S 2021 Phys. Rev. D 104 016009Google Scholar

    [53]

    Li L J, Mohamedsedik M, Xie B S 2021 Phys. Rev. D 104 036015Google Scholar

    [54]

    Li Z L, Lu D, Xie B S 2015 Phys. Rev. D 92 085001Google Scholar

    [55]

    Li Z L, Li Y J, Xie B S 2017 Phys. Rev. D 96 076010Google Scholar

    [56]

    Li Z L, Xie B S, Li Y J 2019 J. Phys. B:At. Mol. Opt. Phys. 52 025601Google Scholar

    [57]

    李子良, 努尔曼古丽·阿卜杜克热木, 谢柏松 2016 物理学进展 36 129

    Li Z L, Abdukerim Nuriman, Xie B S 2016 Progress in Phys. 36 129

    [58]

    谢柏松, 李子良, 唐琐, 刘杰 2017 物理 46 713Google Scholar

    Xie B S, Li Z L, Tang S, Liu J 2017 Physics 46 713Google Scholar

    [59]

    Keldysh L V 1965 Sov. Phys. JETP 20 1307

    [60]

    Bialynicki-Birula I, Gornicki P, Rafelski J 1991 Phys. Rev. D 44 1825

    [61]

    Hebenstreit F 2011 Ph. D. Dissertation arXiv: 1106.5965

    [62]

    Greiner W 2000 (3 rd Ed. ) (Berlin: Springer)

    [63]

    Schmidt S M, Blaschke D, Röpke, G, Prozorkevich A V, Smolyansky S A, Toneev V D 1999 Phys. Rev. D. 59 094005Google Scholar

    [64]

    Wang L, Li L J, Mohamedsedik M, An R, Li J J, Xie B S, Zhang F S 2021 arXiv: 2109.05399

    [65]

    Kamiński J Z, Twardy M, Krajewska K 2018 Phys. Rev. D 98 056009Google Scholar

  • 图 1  一色脉冲激光场下正负电子对的数密度与原初频率的依赖关系(取自参考文献[34])

    Fig. 1.  Electron-positron number density vs the original frequency in one-color pulse laser field (from Ref. [34]) .

    图 2  在不同啁啾参数下产生的粒子数密度与场极化度的依赖关系(取自参考文献[46])

    Fig. 2.  The number density of created particles as a function of the field polarization $ \delta $ for different chirp parameters b (from Ref. [46]).

    图 3  圆极化时在不同啁啾参数下产生的粒子的动量谱(取自参考文献[46])

    Fig. 3.  Momentum spectra of produced pairs for circular polarization (from Ref. [46]).

    图 4  在调制幅度$ b=1.0 $下不同啁啾调制频率$ {\omega }_{\mathrm{m}}=0, \mathrm{ }0.07, \mathrm{ }0.1 $时产生的粒子对的动量谱(取自参考文献[50])

    Fig. 4.  Momentum spectra of produced pairs in the field Eq.(39) with $ {\omega }_{\mathrm{m}}=0, \mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }0.07, \mathrm{ }0.1 $ for (a)–(c), respectively when $ b=1.0 $ is fixed (from Ref. [50]).

    图 5  高频$ \omega =0.7 $下取不同啁啾参数$ b $时产生的粒子对的约化动量谱(取自参考文献[42])

    Fig. 5.  Reduced momentum spectra of produced pairs in the field Eq.(40) with $ b=0.00078 $ for (a) and $ b=0.0016 $ for (b), respectively, when high frequency $ \omega =0.7 $ is fixed (from Ref. [42]).

    图 6  $ \omega =0.7 $下粒子对的约化数密度与场的空间尺度$ \lambda $的关系(取自参考文献[42])

    Fig. 6.  Reduced number of produced pairs in the field Eq.(40) with respect to spatial extent $ \lambda $ when $ \omega =0.7 $ (from Ref. [42]).

    图 7  高频$ \omega =0.7 $下不同啁啾不同空间尺度时产生的粒子对约化动量谱(取自参考文献[52])

    Fig. 7.  Reduced momentum spectra of produced pairs in the field Eq.(41) for high frequency field with $ \omega =0.7 $ (from Ref. [52]) .

    图 8  $ \omega =0.7 $下粒子对的约化数密度与场的空间尺度$ \lambda $的关系(取自参考文献[52])

    Fig. 8.  Reduced number of produced pairs in the field Eq.(41) with respect to spatial extent $ \lambda $ when $ \omega =0.7 $ (from Ref. [52]).

    图 9  低频$ \omega =0.1 $下不同啁啾不同空间尺度时产生的粒子对约化动量谱(取自参考文献[52])

    Fig. 9.  Reduced momentum spectra of produced pairs in the field Eq.(41) for low frequency field with $ \omega =0.1 $ (from Ref. [52]).

    图 10  不同啁啾不同空间尺度时产生的粒子对约化动量谱(取自参考文献[53])

    Fig. 10.  Reduced momentum spectra of produced pairs in the field Eq.(42) for different chirping (from Ref. [53]).

    图 11  粒子对约化数密度的增强因子与场的空间尺度$ \lambda $的关系(取自参考文献[53])

    Fig. 11.  Enhancement factor of reduced number of produced pairs in the field Eq.(42) with respect to spatial extent $ \lambda $ (from Ref. [53]) .

    图 12  产生的粒子对的数目与啁啾参数的依赖关系(取自参考文献[64])

    Fig. 12.  Number of produced pairs in the field Eq. (43) with respect to chirping parameter (from Ref. [64]).

    图 13  电子数目随着基频和啁啾参数变化的等高线图(取自参考文献[64])

    Fig. 13.  The contour plot of the electron number varying with the fundamental frequency and the chirp parameter (from Ref. [64]).

    图 14  不同的调制频率参数下频率调制的势阱的频谱(取自参考文献[64])

    Fig. 14.  The frequency spectrum of frequency modulated potential well with different modulation parameters (from Ref. [64]).

    图 15  固定频率(黑色虚线)和啁啾频率(红色实线)下产生电子的能谱(取自参考文献[64])

    Fig. 15.  Energy spectrum of created electrons under the fixed frequency (the black dotted curve) and the chirp frequency (the red solid curve) (from Ref. [64]).

    图 16  动量为0时的时间复平面上的转变点(取自参考文献[53])

    Fig. 16.  The turning points of complex time-plane when the momentum is zero (from Ref. [53]).

    表 1  空间尺度$ \lambda =10 $时不同啁啾下(31)式对称啁啾场与(30)式的非对称啁啾场数密度及其比值(参看文献[52])

    Table 1.  Reduced pair number and ratio of symmetric and asymmetric fields for different chirping when$ \lambda =10 $ (from Ref. [52]) .

    b($ \omega /\tau ) $$ {N}_{\mathrm{s}\mathrm{y}\mathrm{m}} $$ {N}_{\mathrm{a}\mathrm{s}\mathrm{y}\mathrm{m}} $$ {N}_{\mathrm{s}\mathrm{y}\mathrm{m}}/{N}_{\mathrm{a}\mathrm{s}\mathrm{y}\mathrm{m}} $
    0.050.26800.16631.612
    0.100.32740.15612.097
    0.200.31780.17911.774
    0.501.43400.74741.919
    下载: 导出CSV

    表 2  优化空间尺度和啁啾参数下单个啁啾场或两个啁啾场的增强因子(参看文献[53])

    Table 2.  Optimal spatial scales related to the optimal enhancement factor at the chosen optimal chirp parameters (from Ref. [53]).

    Different
    chirping
    Chirp parameter
    ($ {\omega }_{i}/\tau $), ($ i=\mathrm{1, 2} $)
    Spatial
    scale/m–1
    $\displaystyle\frac{N_{\rm 1s+2w} } {N_{\rm 1s}+ N_{\rm 2w}}$
    Only $ {b}_{1} $$ {b}_{1}=0.9 $$ \lambda =2.4 $94.756
    Only $ {b}_{2} $ $ {b}_{2}=0.3 $$ \lambda =2.4 $133.584
    $ {b}_{1} $ and $ {b}_{2} $ $ {b}_{1}={b}_{2}=0.3 $$ \lambda =2.4 $132.517
    下载: 导出CSV

    表 3  不同的基频下产生的电子数目的最大值和最小值以及二者之间的比值(参看文献[64])

    Table 3.  The maximum, the minimum number of created electrons and the ratio between them for different fundamental frequencies (from Ref. [64]).

    $ {\omega }_{0}/{c}^{2} $$ {N}_{\mathrm{m}\mathrm{i}\mathrm{n}}(b=0) $$ {N}_{\mathrm{m}\mathrm{a}\mathrm{x}} $$ R({N}_{\mathrm{m}\mathrm{a}\mathrm{x}}/{N}_{\mathrm{m}\mathrm{i}\mathrm{n}}) $
    0.11.874.58 ($ b=1.8{c}^{2}/{t}_{1} $)2.45
    0.21.854.69 ($ b=1.7{c}^{2}/{t}_{1} $)2.54
    0.51.774.76 ($ b=1.6{c}^{2}/{t}_{1} $)2.69
    1.02.305.13 ($ b=1.2{c}^{2}/{t}_{1} $)2.23
    1.54.185.39 ($ b=0.8{c}^{2}/{t}_{1} $)1.29
    1.95.425.65 ($ b=0.1{c}^{2}/{t}_{1} $)1.04
    下载: 导出CSV
  • [1]

    Dirac P A M 1928 Proc. R. Soc. A 118 351

    [2]

    Anderson C D 1933 Phys. Rev. 43 491Google Scholar

    [3]

    Sauter F 1931 Z. Phys. 69 742Google Scholar

    [4]

    Heisenberg W, Euler H 1936 Z. Phys. 98 714Google Scholar

    [5]

    Schwinger J 1951 Phys. Rev. 82 664Google Scholar

    [6]

    Ritus V I 1985 J. Sov. Laser Res. 6 497Google Scholar

    [7]

    Piazza A D 2011 Rev. Mod. Phys. 84 1177

    [8]

    Gelis F, Tanji N 2016 Prog. Part. Nucl. Phys. 87 1Google Scholar

    [9]

    Strickland D, Mourou G 1985 Opt. Commun. 55 447Google Scholar

    [10]

    Ringwald A 2001 Phys. Lett. B 510 107Google Scholar

    [11]

    Yanovsky V P, Chvykov V, Kalinchenko G, Rousseau P, Krushelnick K 2008 Opt. Express 16 2109Google Scholar

    [12]

    Heinzl T, Ilderton A 2009 Eur. Phys. J. D 55 359Google Scholar

    [13]

    Marklund M, Lundin J 2009 Eur. Phys. J. D 55 319Google Scholar

    [14]

    Dunne G V 2009 Eur. Phys. J. D 55 327Google Scholar

    [15]

    Pike O J, Mackenroth F, Hill E G, Rose S J 2014 Nat. Photonics 8 434Google Scholar

    [16]

    https://www.eli -beams .eu/. [2022-1-21]

    [17]

    Schuetzhold R, Gies H, Dunne G 2008 Phys. Rev. Lett. 101 130404Google Scholar

    [18]

    Bell A R, Kirk J G 2008 Phys. Rev. Lett. 101 2952

    [19]

    Dunne G V, Gies H, Schützhold R 2009 Phys. Rev. D 80 111301Google Scholar

    [20]

    Piazza A D, E Lötstedt, Milstein A I, Keitel C H 2009 Phys. Rev. Lett. 103 170403Google Scholar

    [21]

    Bulanov S S, Mur V D, Narozhny N B, Nees J, Popov V S 2010 Phys. Rev. Lett. 104 220404Google Scholar

    [22]

    https://xcels.iapras .ru /news .html[2022-1-21]

    [23]

    http://www.hibef.eu[2022-1-21]

    [24]

    Nikishov A I 1969 Sov. Phys. JETP 30 660

    [25]

    Brezin E, Itzykson C 1970 Phys. Rev. D 2 1191Google Scholar

    [26]

    Marinov M S, Popov V S 1977 Fortschr. Phys. 25 373Google Scholar

    [27]

    Nikishov A I 1985 J. Sov. Laser Res. 6 619Google Scholar

    [28]

    Gies H, Klingmüller K 2005 Phys. Rev. D 72 065001

    [29]

    Dunne G, Wang Q H, Gies H, Schubert C 2006 Phys. Rev. D 73 065028

    [30]

    Xie B S, Melike M, Sayipjamal D 2012 Chin. Phys. Lett. 29 021102Google Scholar

    [31]

    Schneider C, Schützhold R 2016 J. High Energy Phys. 02 164Google Scholar

    [32]

    Kluger Y, Eisenberg J M, Svetitsky B, Cooper F, Mottola E 1991 Phys. Rev. Lett. 67 2427Google Scholar

    [33]

    Alkofer R, Hecht M B, Roberts C D, Schmidt S M, Vinnik D V 2001 Phys. Rev. Lett. 87 193902Google Scholar

    [34]

    Abdukerim N, Li Z L, Xie B S 2017 Chin. Phys. B 26 020301Google Scholar

    [35]

    Krekora P, Cooley K, Su Q, Grobe R 2005 Phys. Rev. Lett. 95 070403Google Scholar

    [36]

    Lv Q Z, Liu Y, Li Y J, Grobe R, Su Q 2013 Phys. Rev. Lett. 111 183204Google Scholar

    [37]

    Wang L, Wu B B, Xie B S 2019 Phys. Rev. A 100 022127Google Scholar

    [38]

    Hebenstreit F, Alkofer R, Gies H 2011 Phys. Rev. Lett. 107 180403Google Scholar

    [39]

    Kohlfürst C 2015 Ph. D. Dissertation arXiv: 1512.06082

    [40]

    Xie B S, Li Z L, Tang S 2017 Matter Radiat. Extremes 2 225Google Scholar

    [41]

    Kohlfürst C, Alkofer R 2018 Phys. Rev. D 97 036026Google Scholar

    [42]

    Ababekri M, Dulat S, Xie B S, Zhang J 2020 Phys. Lett. B 810 135815Google Scholar

    [43]

    Kohlfürst C 2020 Phys. Rev. D 101 096003Google Scholar

    [44]

    Hebenstreit F, Alkofer R, Dunne G V, Gies H 2009 Phys. Rev. Lett. 102 150404Google Scholar

    [45]

    Dumlu C K 2010 Phys. Rev. D 82 045007Google Scholar

    [46]

    Olugh O, Li Z L, Xie B S, Alkofer R 2019 Phys. Rev. D 99 036003Google Scholar

    [47]

    Orthaber M, Hebenstreit F, Alkofer R 2011 Phys. Lett. B 698 80Google Scholar

    [48]

    Ababekri M, Xie B S, Zhang J 2019 Phys. Rev. D 100 016003Google Scholar

    [49]

    Olugh O, Li Z L, Xie B S 2020 Phys. Lett. B 802 135259Google Scholar

    [50]

    Gong C, Li Z L, Xie B S, Li Y J 2020 Phys. Rev. D 101 016008Google Scholar

    [51]

    Wang K, Hu X H, Dulat S, Xie B S 2021 Chin. Phys. B 30 060204Google Scholar

    [52]

    Mohamedsedik M, Li L J, Xie B S 2021 Phys. Rev. D 104 016009Google Scholar

    [53]

    Li L J, Mohamedsedik M, Xie B S 2021 Phys. Rev. D 104 036015Google Scholar

    [54]

    Li Z L, Lu D, Xie B S 2015 Phys. Rev. D 92 085001Google Scholar

    [55]

    Li Z L, Li Y J, Xie B S 2017 Phys. Rev. D 96 076010Google Scholar

    [56]

    Li Z L, Xie B S, Li Y J 2019 J. Phys. B:At. Mol. Opt. Phys. 52 025601Google Scholar

    [57]

    李子良, 努尔曼古丽·阿卜杜克热木, 谢柏松 2016 物理学进展 36 129

    Li Z L, Abdukerim Nuriman, Xie B S 2016 Progress in Phys. 36 129

    [58]

    谢柏松, 李子良, 唐琐, 刘杰 2017 物理 46 713Google Scholar

    Xie B S, Li Z L, Tang S, Liu J 2017 Physics 46 713Google Scholar

    [59]

    Keldysh L V 1965 Sov. Phys. JETP 20 1307

    [60]

    Bialynicki-Birula I, Gornicki P, Rafelski J 1991 Phys. Rev. D 44 1825

    [61]

    Hebenstreit F 2011 Ph. D. Dissertation arXiv: 1106.5965

    [62]

    Greiner W 2000 (3 rd Ed. ) (Berlin: Springer)

    [63]

    Schmidt S M, Blaschke D, Röpke, G, Prozorkevich A V, Smolyansky S A, Toneev V D 1999 Phys. Rev. D. 59 094005Google Scholar

    [64]

    Wang L, Li L J, Mohamedsedik M, An R, Li J J, Xie B S, Zhang F S 2021 arXiv: 2109.05399

    [65]

    Kamiński J Z, Twardy M, Krajewska K 2018 Phys. Rev. D 98 056009Google Scholar

  • [1] 刘庆康, 张旭, 蔡洪波, 张恩浩, 高妍琦, 朱少平. 强度调制宽带激光对受激拉曼散射动理学爆发的抑制. 物理学报, 2024, 73(5): 055202. doi: 10.7498/aps.73.20231679
    [2] 李传可, 林南省, 周鲜鲜, 江淼, 李英骏. 双振荡场产生正负电子对的理论研究. 物理学报, 2024, 73(4): 044201. doi: 10.7498/aps.73.20230432
    [3] 周利娜, 胡汉卿, 刘钺强, 段萍, 陈龙, 张瀚予. 等离子体对共振磁扰动的流体和动理学响应的模拟研究. 物理学报, 2023, 72(7): 075202. doi: 10.7498/aps.72.20222196
    [4] 牟家连, 吕军光, 孙希磊, 兰小飞, 黄永盛. 环形正负电子对撞机带电粒子鉴别的飞行时间探测器. 物理学报, 2023, 72(12): 122901. doi: 10.7498/aps.72.20222271
    [5] 叶全兴, 何广朝, 王倩. 正负电子对撞中类底夸克偶素的线形. 物理学报, 2023, 72(20): 201401. doi: 10.7498/aps.72.20230908
    [6] 罗蕙一, 江淼, 徐妙华, 李英骏. 不同频率的组合振荡场下产生正负电子对. 物理学报, 2023, 72(2): 021201. doi: 10.7498/aps.72.20221660
    [7] 孙婷, 王宇, 郭任彤, 卢知为, 栗建兴. 强激光驱动高能极化正负电子束与偏振伽马射线的研究进展. 物理学报, 2021, 70(8): 087901. doi: 10.7498/aps.70.20210009
    [8] 江淼, 郑晓冉, 林南省, 李英骏. 正负电子对产生过程中不同外场宽度下的多光子跃迁效应. 物理学报, 2021, 70(23): 231202. doi: 10.7498/aps.70.20202101
    [9] 朱兴龙, 王伟民, 余同普, 何峰, 陈民, 翁苏明, 陈黎明, 李玉同, 盛政明, 张杰. 极强激光场驱动超亮伽马辐射和正负电子对产生的研究进展. 物理学报, 2021, 70(8): 085202. doi: 10.7498/aps.70.20202224
    [10] 李昂, 余金清, 陈玉清, 颜学庆. 光子对撞机产生正负电子对的数值方法. 物理学报, 2020, 69(1): 019501. doi: 10.7498/aps.69.20190729
    [11] 吴广智, 王强, 周沧涛, 傅立斌. 双势阱产生正负电子对过程中的正电子波干涉与克莱因隧穿现象. 物理学报, 2017, 66(7): 070301. doi: 10.7498/aps.66.070301
    [12] 林呈, 张华堂, 盛志浩, 余显环, 刘鹏, 徐竟文, 宋晓红, 胡师林, 陈京, 杨玮枫. 用推广的量子轨迹蒙特卡罗方法研究强场光电子全息. 物理学报, 2016, 65(22): 223207. doi: 10.7498/aps.65.223207
    [13] 辛国国, 赵清, 刘杰. 非序列双电离向饱和区过渡的电子最大关联度. 物理学报, 2012, 61(13): 133201. doi: 10.7498/aps.61.133201
    [14] 辛国国, 叶地发, 赵清, 刘杰. 原子非序列双电离的多次返回碰撞电离机理分析. 物理学报, 2011, 60(9): 093204. doi: 10.7498/aps.60.093204
    [15] 曾思良, 邹士阳, 王建国, 颜君. 数值求解三维含时Schr?dinger方程及其应用. 物理学报, 2009, 58(12): 8180-8187. doi: 10.7498/aps.58.8180
    [16] 张洪英, 陈德应, 鲁振中, 樊荣伟, 夏元钦. Ba-Sr系统激光感生碰撞能量转移的数值计算. 物理学报, 2008, 57(12): 7600-7605. doi: 10.7498/aps.57.7600
    [17] 江 阳, 于晋龙, 胡 浩, 张爱旭, 张立台, 王文睿, 杨恩泽. 信号光的调制对基于光纤光参量放大光脉冲源的改善. 物理学报, 2008, 57(5): 2994-3000. doi: 10.7498/aps.57.2994
    [18] 郑宏军, 刘山亮, 黎 昕, 徐静平. 初始啁啾对双曲正割光脉冲线性传输特性的影响. 物理学报, 2007, 56(4): 2286-2292. doi: 10.7498/aps.56.2286
    [19] 郑丽萍, 邱锡钧. 光强、频率对强激光场中的多原子分子离子增强电离行为的影响. 物理学报, 2000, 49(10): 1965-1968. doi: 10.7498/aps.49.1965
    [20] 罗辽复, 陆埮. 高能正负电子对的湮没与超窄共振ψ粒子的作用. 物理学报, 1975, 24(2): 145-150. doi: 10.7498/aps.24.145
计量
  • 文章访问数:  4957
  • PDF下载量:  103
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-01-21
  • 修回日期:  2022-03-21
  • 上网日期:  2022-06-25
  • 刊出日期:  2022-07-05

/

返回文章
返回