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High-energy proton beams have broad application prospects in medical imaging, tumor therapy and nuclear fusion physics. Laser plasma acceleration is a new particle acceleration method with great potential because its acceleration gradient can reach 103–106 times that of traditional acceleration method, so it can theoretically accelerate electrons and ions to high energies in the scale of a few centimeters to a few meters. Radiation pressure acceleration (RPA) is considered to be the most promising mechanism of high energy proton acceleration in laser plasma acceleration, but the Rayleigh-Taylor instability (RTI) inherent in the process of radiation pressure acceleration will cause transverse density modulation on the target surface, resulting in the premature termination of the proton acceleration process and the failure to obtain high energy proton beams. In order to obtain high-energy proton beams, an acceleration scheme combining radiation pressure acceleration with laser wakefield is proposed. In this scheme, a high-energy proton beam with peak energy of 22.2 GeV, cut-off energy of 36.4 GeV and charge of 0.67 nC is obtained by adding a uniform density plasma channel at the back end of the thin target with critical density, the cut-off energy of the high energy proton can be increased by two orders of magnitude compared with the proton only in the radiation pressure acceleration process. The results confirm that in a uniform-density plasma channel connected behind a thin target, the laser wakefield can capture protons pre-accelerated by the radiation pressure process and maintain the acceleration for a long period of time, finally obtain high-energy protons. The acceleration of protons in plasma channels with different uniform densities is also investigated in this work, and it is found that the higher the density, the higher the peak energy, cut-off energy and charge of the accelerated protons are. The combined acceleration scheme is instructive for the generation and application of high-energy proton beams.
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Keywords:
- radiation pressure acceleration /
- laser wakefield acceleration /
- high-energy proton beam /
- plasma channel
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图 1 (a) 圆偏振激光驱动RPA与激光尾波场组合加速模型. 紫色部分代表厚度为5 μm的临界密度薄靶, 橙色部分代表均匀密度等离子体通道. (b) 薄靶和等离子体通道的密度以及位置分布
Figure 1. (a) Combined acceleration model of RPA and LWFA driven by circular polarization laser. The purple part represents a critical density thin target with a thickness of 5 μm, and the orange part represents a uniform density plasma channel. (b) Density and positional distribution of thin target and plasma channel.
图 2 等离子体密度分别为(a)$ 1\times 10^{20}\; {\rm{cm}}^{-3} $和(b)$ 7\times 10^{20}\; {\rm{cm}}^{-3} $的情况下$ \xi'\text{ - }p_{\rm{i}}' $相空间中的质子捕获区域. $ h(\xi', p_{\rm{i}}')= $$ 1 $(黑色实线)划分了质子捕获区域和非捕获区域. 当质子的哈密顿量 $ h(\xi', p_{\rm{i}}')<1 $(红色虚线)时, 质子可以被尾波场捕获
Figure 2. The proton capture region in $ \xi'\text{ - }p_{\rm{i}}' $ phase space for plasma densities of (a) $ 1\times 10^{20}\; {\rm{cm}}^{-3} $ and (b) $ 7\times 10^{20} \; {\rm{cm}}^{-3}$. $ h(\xi', p_{\rm{i}}')=1 $ (black solid line) delineates the proton capture region and the non-capture region. When the Hamiltonian of the proton is $ h(\xi', p_{\rm{i}}')<1 $(red dotted line), the proton can be captured by the wakefield.
图 3 (a) 在t = 14 fs, 红线位置处横向切片的电子密度波纹; (b) t = 14 fs, z =0 μm平面纵向切片的电子密度
Figure 3. (a) Electron density ripples in transverse slices at t = 14 fs at the position of the red line; (b) electron density in longitudinal slices in the z = 0 μm plane at t = 14 fs.
图 4 等离子体通道密度为$ 7\times 10^{20} $ $ {\rm{cm}}^{-3} $时, RTI线性发展过程中密度波纹的演化 (a)—(c)为不同时刻在y-z平面横向切片的电子密度空间分布; (d) t = 30 fs时在y-z平面横向切片的质子密度空间分布
Figure 4. Evolution of density ripples during linear development of RTI at plasma channel density is $ 7\times 10^{20} \; {\rm{cm}}^{-3} $: (a)–(c) The spatial distributions of electron density in transverse slices of the y-z plane at different moments; (d) spatial distribution of proton density in transverse slices of the y-z plane at t = 30 fs.
图 5 等离子体通道密度为$ 7\times 10^{20} \; {\rm{cm}}^{-3} $时, RTI在非线性发展过程中电子密度气泡的演化 (a)—(d)为不同时刻在y-z平面横向切片的电子密度空间分布
Figure 5. Evolution of electron density bubbles during nonlinear development of RTI at plasma channel densities of $ 7\times 10^{20} \; {\rm{cm}}^{-3} $: (a)–(d) The spatial distributions of electron density in transverse slices of the y-z plane at different moments.
图 6 等离子体通道密度为$ 3\times 10^{20}\;{\rm{cm}}^{-3} $时, RTI在非线性发展过程中电子密度气泡的演化 (a)—(d)不同时刻在y-z平面横向切片的电子密度空间分布
Figure 6. Evolution of electron density bubbles during nonlinear development of RTI at plasma channel densities of $ 3\times 10^{20}\;{\rm{cm}}^{-3} $: (a)–(d) The spatial distributions of electron density in transverse slices of the y-z plane at different moments.
图 7 (a)—(d), (e)—(h), (i)—(l)为质子在纯RPA加速过程中, 不同时刻激光驱动等离子体纵向尾波场、电子密度空间分布、质子密度空间分布和质子束能谱; (a)—(c), (e)—(g), (i)—(k)为模拟窗口在z = 0 μm平面上的纵向切片
Figure 7. (a)–(d), (e)–(h), (i)–(1) are longitudinal wakefield of laser-driven plasma, spatial distribution of electron density, spatial distribution of proton density and the energy spectrum of proton beam at different times during pure RPA; (a)–(c), (e)–(g), (i)–(k) are longitudinal slices of the simulation window on the z = 0 μm plane.
图 8 密度为$ 1\times 10^{20}\; {\rm{cm}}^{-3} $的等离子体通道 (a)—(d), (e)—(h), (i)—(l)分别是在不同时刻激光驱动等离子体纵向尾波场, 电子密度空间分布, 质子密度空间分布和质子能谱图; (a)—(c), (e)—(g), (i)—(k)为模拟窗口在z = 0 μm平面上的纵向切片
Figure 8. In a uniform-density plasma channel with a density of $ 1\times 10^{20} \; {\rm{cm}}^{-3} $: (a)–(d), (e)–(h), (i)–(1) are longitudinal component of laser-driven plasma wakefield, spatial distribution of electron density, spatial distribution of proton density and the energy spectrum of proton beam at different times. (a)–(c), (e)–(g), (i)–(k) are longitudinal slices of the simulation window on the z = 0 μm plane.
图 9 (a)不同均匀密度等离子体通道中被加速质子截止能量随时间的变化; (b)不同均匀密度等离子体通道中被加速质子峰值能量随时间的变化
Figure 9. (a) Variation of the cut-off energy of accelerated protons with time in plasma channels of different uniform densities; (b) variation of the peak energy of accelerated protons with time in plasma channels of different uniform densities.
图 10 不同均匀密度等离子体通道中被加速质子电荷量随时间的变化
Figure 10. Variation of accelerated proton charge with time in plasma channels of different uniform densities.
图 11 密度为$ 7\times 10^{20}\; {\rm{cm}}^{-3} $的等离子体通道 (a)—(d), (e)—(h), (i)—(l)分别是在不同时刻激光驱动等离子体纵向尾波场, 电子密度空间分布, 质子密度空间分布和质子能谱图; (a)—(c), (e)—(g), (i)—(k)为模拟窗口在z = 0 μm平面上的纵向切片
Figure 11. In a uniform-density plasma channel with a density of $ 7\times 10^{20} \; {\rm{cm}}^{-3} $: (a)–(d), (e)–(h) and (i)–(1) are longitudinal wakefield of laser-driven plasma, spatial distribution of electron density, spatial distribution of proton density and the energy spectrum of proton beam at different times; (a)–(c), (e)–(g), (i)–(k) are longitudinal slices of the simulation window on the z = 0 μm plane.
表 1 纯RPA加速质子模拟参数. 高斯$(x, x_0, \omega)$函数可以表示为$f(x)= \exp[-((x-x_0)/{\omega})^2]$, 其中变量x以$x_0$为中心, 特征宽度为ω, 激光在y和z方向上的强度分布满足高斯分布
Table 1. Simulation parameters of proton acceleration in pure RPA. The Gauss $(x, x_0, \omega)$ function can be expressed as $f(x)= \exp[-((x-x_0)/\omega)^2]$, where the variable x centered on $x_\mathrm{{0} }$ with a characteristic width ω. The intensity distribution of the laser satisfies Gaussian distribution in the y and z directions.
窗口参数 激光参数 尺寸 $ x\times y\times z=30\;\text{μm} \times 40\; \text{μm} \times 40\; \text{μm}$ 波长 0.8 μm 格子数 $ x\times y\times z=600\times 300\times 300 $ 焦斑 14 μm 移动速度 $ v=2.95 \times 10^8 \; {\rm{m/s}} $ 时间轴上的轮廓 $ t_{\rm{profile}} =\left [\sin\left ( \pi \times \tau _{\rm{L}} /68 \right ) \right] ^{2} $ 移动开始时间 t = 100 fs 强度分布 Gauss(z, 0, 14 μm) 等离子体参数 Gauss(y, 0, 14 μm) 粒子 电子和质子 归一化矢量 304 密度 $ n_{\rm{e}}=10^{28} $ $ {\rm{m}}^{-3} $ 入射方向 x 轴 位置 $ 0< x\leqslant 0.5\;\text{μm}$ 
DownLoad: CSV
表 2 RPA与LWFA组合方案加速质子的等离子体模拟参数. 窗口参数与激光参数同表1
Table 2. The plasma simulation parameters of accelerated plasma simulation for the combined RPA and LWFA scheme. The window parameters and laser parameters are the same as in Table 1.
等离子体参数 粒子 电子和质子 密度 两层等离子体 $ a:n_{\rm{e}}=10^{28} $ $ {\rm{m}}^{-3} $ $ b_1:n_{\rm{e}} =1\times 10^{26} $ $ {\rm{m}}^{-3} $ $ b_2:n_{\rm{e}} =7\times 10^{26} $ $ {\rm{m}}^{-3} $ 位置 $ a:0< x\leqslant 5 $ μm $ b_1/b_2 $:$ 5 \;{\mathrm{μm}} < x$
DownLoad: CSV
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[1] Borghesi M, Campbell D H, Schiavi A, Haines M G, Willi O, MacKinnon A J, Patel P, Gizzi L A, Galimberti M, Clarke R J, Pegoraro F, Ruhl H, Bulanov S 2002 Phys. Plasmas 9 2214
Google Scholar
[2] Koehler A M 1968 Science 160 303
Google Scholar
[3] Mendel Jr C W, Olsen J N 1975 Phys. Rev. Lett. 34 859
Google Scholar
[4] Tabak M, Hammer J, Glinsky M E, Kruer W L, Wilks S C, Woodworth J, Campbell E M, Perry M D, Mason R J 1994 Phys. Plasmas 1 1626
Google Scholar
[5] Naumova N, Schlegel T, Tikhonchuk V T, Labaune C, Sokolov I V, Mourou G 2009 Phys. Rev. Lett. 102 025002
Google Scholar
[6] Bulanov S V, Khoroshkov V S 2002 Plasma Phys. Rep. 28 453
Google Scholar
[7] Bulanov S V, Esirkepov T Z, Khoroshkov V S, Kuznetsov A V, Pegoraro F 2002 Phys. Lett. A 299 240
Google Scholar
[8] Bulanov S V, Wilkens J J, Esirkepov T Z, Korn G, Kraft G, Kraft S D, Molls M, Khoroshkov V S 2014 Phys. Usp. 57 1149
Google Scholar
[9] Martinez B, Chen S, Bolaños S, Blanchot N, Boutoux G, Cayzac W, Courtois C, Davoine X, Duval A, Horny V, Lantuejoul I, Deroff L L, Masson-Laborde P E, Sary G, Smets B V R, Gremillet L 2022 Matter Radiat. Extremes 7 024401
Google Scholar
[10] Roth M, Jung D, Falk K, Guler N, Deppert O, Devlin M, Favalli A, Fernandez J, Gautier D, Geissel M, Haight R, Hamilton C E, Hegelich B M, Johnson R P, Merrill F, Schaumann G, Schoenberg K, Schollmeier M, T Shimada T T, Tybo J L, Wagner F, Wender S A, Wilde C H, Wurden G A 2013 Phys. Rev. Lett. 110 044802
Google Scholar
[11] Ledingham K W D, McKenna P, Singhal R P 2003 Science 300 1107
Google Scholar
[12] 马文君, 刘志鹏, 王鹏杰, 赵家瑞, 颜学庆 2021 物理学报 70 084102
Google Scholar
Wen J M, Zhi P L, Peng J W, Jia R Z, Xue Q Y 2021 Acta Phys. Sin. 70 084102
Google Scholar
[13] Macchi A, Cattani F, Liseykina T V, Cornolti F 2005 Phys. Rev. Lett. 94 165003
Google Scholar
[14] Robinson A P L, Zepf M, Kar S, Evans R G, Bellei C 2008 New J. Phys. 10 013021
Google Scholar
[15] Bulanov S S, Brantov A, Bychenkov V Y, Chvykov V, Kalinchenko G, Matsuoka T, Rousseau P, Reed S, Yanovsky V, Litzenberg D W, Krushelnick K, Maksimchuk A 2008 Phys. Rev. E 78 026412
Google Scholar
[16] Steinke S, Hilz P, Schnürer M, Priebe G, Bränzel J, Abicht F, Kiefer D, Kreuzer C, Ostermayr T, Schreiber J, Andreev A A, Yu T P, Pukhov A, Sandner W 2013 Phys. Rev. Spec. Top. Accel. Beams 16 011303
Google Scholar
[17] Henig A, Steinke S, Schnürer M, Sokollik T, Hörlein R, Kiefer D, Jung D, Schreiber J, Hegelich B M, Yan X Q, ter Vehn J M, Tajima T, Nickles P V, Sandner W, Habs D 2009 Phys. Rev. Lett. 103 245003
Google Scholar
[18] Kim I J, Pae K H, Choi I W, Lee C L, Kim H T, Singhal H, Sung J H, Lee S K, Lee H W, Nickles P V, Jeong T M, Kim C M, Nam C H 2016 Phys. Plasmas 23 070701
Google Scholar
[19] Pegoraro F, Bulanov S V 2007 Phys. Rev. Lett. 99 065002
Google Scholar
[20] Yan X Q, Lin C, Sheng Z M, Guo Z Y, Liu B C, Lu Y R, Fang J X, Chen J E 2008 Phys. Rev. Lett. 100 135003
Google Scholar
[21] Chen M, Pukhov A, Sheng Z M, Yan X Q 2008 Phys. Plasmas 15 113103
Google Scholar
[22] Liu T C, Shao X, Liu C S, Su J J, Eliasson B, Tripathi V, Dudnikova G, Sagdeev R Z 2011 Phys. Plasmas 18 123105
Google Scholar
[23] Palmer C, Schreiber J, Nagel S, Dover N, Bellei C, Beg F N, Bott S, Clarke R, Dangor A E, Hassan S, Hilz P, Jung D, Kneip S, Mangles S P D, Lancaster K L, Rehman A, Robinson A P L, Spindloe C, Szerypo J, M Tatarakis M Y, Zepf M, Najmudin Z 2012 Phys. Rev. Lett. 108 225002
Google Scholar
[24] Wan Y, Pai C H, Zhang C J, Li F, Wu Y, Hua J, Lu W, Gu Y, Silva L, Joshi C, Mori W 2016 Phys. Rev. Lett. 117 234801
Google Scholar
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Google Scholar
[26] Qiao B, Kar S, Geissler M, Gibbon P, Zepf M, Borghesi M 2012 Phys. Rev. Lett. 108 115002
Google Scholar
[27] Kar S, Kakolee K F, Qiao B, Macchi A, Cerchez M, Doria D, Geissler M, McKenna P, Neely D, Osterholz J, Prasad R, Quinn K, Ramakrishna B, Sarri G, Willi O, Yuan X Y, Zepf M, Borghesi M 2012 Phys. Rev. Lett. 109 185006
Google Scholar
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Google Scholar
[29] Higginson A, Gray R J, King M, Dance R J, Williamson S D R, Butler N M H, Wilson R, Capdessus R, Armstrong C, Green J S, Hawkes S J, Martin P, Wei W Q, Mirfayzi S R, Yuan X H, Kar S, Borghesi M, Clarke R, Neely D, McKenna P 2018 Nat. Commun. 9 724
Google Scholar
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Google Scholar
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Google Scholar
[32] Zheng F L, Wang H Y, Yan X Q, Tajima T, Yu M Y, He X T 2012 Phys. Plasmas 19
Google Scholar
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Google Scholar
[34] Zhang X M, Shen B F, Ji L L, Wang F C, Wen M, Wang W P, Xu J C, Yu Y H 2010 Phys. Plasmas 17 123102
Google Scholar
[35] Tajima T, Dawson J M 1979 Phys. Rev. Lett. 43 267
Google Scholar
[36] Pukhov A, Meyer-ter Vehn J 2002 Appl. Phys. B 74 355
Google Scholar
[37] Shorokhov O, Pukhov A 2004 Laser Part. Beams 22 175
Google Scholar
[38] Wilks S C, Kruer W L, Tabak M, Langdon A B 1992 Phys. Rev. Lett. 69 1383
Google Scholar
[39] Gamaly E G 1993 Phys. Rev. E 48 2924
Google Scholar
[40] Valeo E J, Estabrook K G 1975 Phys. Rev. Lett. 34 1008
Google Scholar
[41] Estabrook K 1976 Phys. Fluids 19 1733
Google Scholar
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