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Energetic electron beam can be generated through the directlaser acceleration (DLA) mechanism when high power picosecond laser propagates in underdense plasma, and the electron yield can reach several hundred nC, which has a great application in driving secondary radiations, such as bremsstrahlung radiation and betatron radiation. When a linearly polarized laser is used, the beam divergence is always larger in the laser polarization direction. What is more, the forked spectral-spatial distribution is observed in the experiments driven by femtosecond laser where DLA is combined with the laser wakefield acceleration (LWFA). The forked distribution is regarded as an important feature of DLA. However, an analytical explanation for both the bigger divergence and the forked spectral-spatial distribution is still lacking. Two-dimensional (2D) particle-in-cell simulations of picosecond laser propagating in underdense plasma are conducted in this paper to show how the fork is formed in DLA. The fork structure is a reflection of the distribution of electron transverse velocity. We find that when electrons are accelerated longitudinally, the transverse oscillation energy in the laser polarization direction increases correspondingly. If the electron energy is high enough, the transverse oscillation energy will increase linearly with the electron energy. As a result, the most energetic electrons will have an equal amplitude of vy, where vy denotes the velocity in the laser polarization direction. For a single electron, the distribution of its transverse velocity over a long period
$\dfrac{{{\rm d}P}}{{{\rm d}{v_y}}}$ , will peak at ±vm (vm denotes the amplitude of vy). If all the electrons have the same vm, the distribution of vy at a given time will be the same as$\dfrac{{{\rm d}P}}{{{\rm d}{v_y}}}$ . That means they will split transversely, leading to a forked spectral-spatial distribution. By using a simplified model, the analytical expression of vm is derived, showing good agreement with vm in the PIC simulation. However, the oscillation energy in the direction perpendicular to polarization will decrease when electrons are accelerated longitudinally (acceleration damping). As a consequence, the divergence perpendicular to the polarization direction will be smaller. Our research gives a quantitative explanation for the transverse distribution of electrons generated by DLA. With some modification, it can also be used in DLA combined LWFA to better control the dephasing length.-
Keywords:
- direct laser acceleration /
- transverse distribution
[1] Tajima T, Dawson J 1979 Phys. Rev. Lett. 43 267
Google Scholar
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Google Scholar
[3] Faure J, Glinec Y, Pukhov A, Kiselev S, Gordienko S, Lefebvre E, Rousseau J P, Burgy F, Malka V 2004 Nature 431 541
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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
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Google Scholar
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Google Scholar
[15] Nilson P M, Mangles S P D, Willingale L, Kaluza M C, Thomas A G R, Tatarakis M, Clarke R J, Lancaster K L, Karsch S, Schreiber J, Najmudin Z, Dangor A E, Krushelnick K 2010 New J. Phys. 12 045014
Google Scholar
[16] Tsakiris G D, Gahn C, Tripathi V K 2000 Phys. Plasmas 7 3017
Google Scholar
[17] Pukhov A, Sheng Z M, Meyer-ter-Vehn J 1999 Phys. Plasmas 6 2847
Google Scholar
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Google Scholar
[19] Gallardo González I, Ekerfelt H, Hansson M, Audet T L, Aurand B, Desforges F G, Dufrénoy S D, Persson A, Davoine X, Wahlström C G, Cros B, Lundh O 2018 New J. Phys. 20 053011
Google Scholar
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Google Scholar
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Google Scholar
[22] 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 2002 International Conference on Computational Science Amsterdam, The Netherlands, April 21−24, 2002 p342
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图 1 PIC模拟中
$t = 5965\omega _0^{ - 1}$ 时刻的(a)激光强度包络, (b)电子的电荷密度分布与(c)通道内的聚焦场${E_{\rm{s}}} = {E_{y{\rm{s}}}} - $ $c{B_{z{\rm{s}}}} $ , 模拟中, 等离子体密度为2 × 1019 cm–3, 激光脉宽为0.8 ps, a0 = 3Figure 1. (a) The laser envelope; (b) electron density; (c) channel focusing force
${E_{\rm{s}}} = {E_{y{\rm{s}}}} - c{B_{z{\rm{s}}}}$ at$t = 5965\omega _0^{ - 1}$ into the simulation, in which the plasma density is 2 × 1019 cm–3 and the laser have a duration 0.8 ps with a0 = 3.
图 2
$t = 5965\omega _0^{ - 1}$ 时刻电子在相空间的分布 (a)电子在能量-vy相空间的分布, 白色虚线是电子横向速度振幅的理论值, 右侧的黑色实线代表着能量大于60 MeV的电子的vy的分布, 为了更好地展示, 其计数值做了归一化处理; (b)能量在60—70 MeV之间的电子在y-py相空间的分布Figure 2. Electron phase space at
$t = 5965\omega _0^{ - 1}$ : (a) Energy -vy phase space, the white dashed lines denote the amplitude of vy from analytical solution,the black solid line denotes the vy distribution of electrons above 60 MeV, the counts are normalized to achieve a better illustration; (b) the y-py phase space of electrons within energy range from 60 MeV to 70 MeV.
图 3 在
$t = 4965\omega _0^{ - 1}$ 到$t = 6965\omega _0^{ - 1}$ 这段时间内100个被追踪的电子的能量γ以及横向能量${\epsilon_y}$ 的变化, 图中红色实线是根据等式(17)拟合得到的结果Figure 3. The transverse energy
${\epsilon_y}$ of 100 electrons as a function of γ from$t = 4965\omega _0^{ - 1}$ to$t = 6965\omega _0^{ - 1}$ . The red dashed line is the fitted result according to Eq. (17).
图 4 (a)电子速度振幅
${v_{\rm{m}}}$ 的三种不同展宽; (b)三种展宽下对应的vy的分布Figure 4. (a) Three distributions of
${v_{\rm{m}}}$ ; (b) the corresponding distributions of vy. -
[1] Tajima T, Dawson J 1979 Phys. Rev. Lett. 43 267
Google Scholar
[2] Esarey E, Schroeder C B, Leemans W P 2009 Rev. Mod. Phys. 81 1229
Google Scholar
[3] Faure J, Glinec Y, Pukhov A, Kiselev S, Gordienko S, Lefebvre E, Rousseau J P, Burgy F, Malka V 2004 Nature 431 541
Google Scholar
[4] Geddes C, Toth C, van Tilborg J, Esarey E, Schroeder C, Bruhwiler D, Nieter C, Cary J, Leemans W 2004 Nature 431 538
Google Scholar
[5] Mangles S, Murphy C, Najmudin Z, Thomas A, Collier J, Dangor A, Divall E, Foster P, Gallacher J, Hooker C 2004 Nature 431 535
Google Scholar
[6] Lu W, Tzoufras M, Joshi C, Tsung F S, Mori W B, Vieira J, Fonseca R A, Silva L O 2007 Phys. Rev. ST Accel. Beams 10 061301
Google Scholar
[7] Gahn C, Tsakiris G, Pukhov A, Meyer-ter-Vehn J, Pretvyler G, Thirolf P, Habs D, Witte K 1999 Phys. Rev. Lett. 83 4772
Google Scholar
[8] Mangles S P D, Walton B R, Tzoufras M, Najmudin Z, Clarke R J, Dangor A E, Evans R G, Fritzler S, Gopal A, Hernandez-Gomez C, Mori W B, Rozmus W, Tatarakis M, Thomas A G R, Tsung F S, Wei M S, Krushelnick K 2005 Phys. Rev. Lett. 94 245001
Google Scholar
[9] Willingale L, Thomas A G R, Nilson P M, Chen H, Cobble J, Craxton R S, Maksimchuk A, Norreys P A, Sangster T C, Scott R H H, Stoeckl C, Zulick C, Krushelnick K 2013 New J. Phys. 15 025023
Google Scholar
[10] Albert F, Lemos N, Shaw J L, Pollock B B, Goyon C, Schumaker W, Saunders A M, Marsh K A, Pak A, Ralph J E, Martins J L, Amorim L D, Falcone R W, Glenzer S H, Moody J D, Joshi C 2017 Phys. Rev. Lett. 118 134801
Google Scholar
[11] Lemos N, Albert F, Shaw J L, Papp D, Polanek R, King P, Milder A, Marsh K A, Pak A, Pollock B 2018 Plasma Phys. Contr. F. 60
[12] Sarri G, Poder K, Cole J M, Schumaker W, Piazza A D, Reville B, Dzelzainis T, Doria D, Gizzi L A, Grittani G 2015 Nat. Commun. 6 6747
Google Scholar
[13] Ledingham K W D, Mckenna P, Singhal R P 2003 Science 300 1107
Google Scholar
[14] Qi W, Zhang X, Zhang B, He S, Zhang F, Cui B, Yu M, Dai Z, Peng X, Gu Y 2019 Phys. Plasmas 26 043103
Google Scholar
[15] Nilson P M, Mangles S P D, Willingale L, Kaluza M C, Thomas A G R, Tatarakis M, Clarke R J, Lancaster K L, Karsch S, Schreiber J, Najmudin Z, Dangor A E, Krushelnick K 2010 New J. Phys. 12 045014
Google Scholar
[16] Tsakiris G D, Gahn C, Tripathi V K 2000 Phys. Plasmas 7 3017
Google Scholar
[17] Pukhov A, Sheng Z M, Meyer-ter-Vehn J 1999 Phys. Plasmas 6 2847
Google Scholar
[18] Shaw J L, Lemos N, Amorim L D, Vafaei-Najafabadi N, Marsh K A, Tsung F S, Mori W B, Joshi C 2017 Phys. Rev. Lett. 118 064801
Google Scholar
[19] Gallardo González I, Ekerfelt H, Hansson M, Audet T L, Aurand B, Desforges F G, Dufrénoy S D, Persson A, Davoine X, Wahlström C G, Cros B, Lundh O 2018 New J. Phys. 20 053011
Google Scholar
[20] Zhang X, Khudik V N, Shvets G 2015 Phys. Rev. Lett. 114 184801
Google Scholar
[21] Shaw J L, Lemos N, Marsh K A, Froula D H, Joshi C 2018 Plasma Phys. Contr. F. 60 044012
Google Scholar
[22] 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 2002 International Conference on Computational Science Amsterdam, The Netherlands, April 21−24, 2002 p342
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