在本論文 , 粒子模擬（PIC）用來研究當運用氮氣的過程中次兆瓦~數兆瓦的雷射造出來的LWFA的功效。運用此方法，高密度等離子體（會引起自聚焦效應和自調製不穩定性，從而極大地提高雷射強度，使其能夠驅動非線性等離子體波來加速電子。若240 um 毫升對含有 H_{2}-N_{2} 混合物的氣室施加0.5-TW，1030 nm激光脈衝，等離子體密度 n_{e} > 7.3x 10^{19} cm^{-3} 給予激光功率P_{L}~2 P_{cr}有利於實現LWFA。結果表明，氮摻雜比率在1％至3％之間可以提供最佳性能，由此產生的電子擴展到40 MeV的能量，電荷為6.2 pC （> 20 MeV）。相反，使用大於5% 的高摻雜率會引起強烈的電離誘導的漂移脈衝，從而使LWFA輸出變差，當施加10％的摻雜率時，會產生能量小於20 MeV的電子。另一方面，當〜3-TW脈衝聚焦到由152- um 在背壓約為600 psi的小孔中，創建了高斯分佈的硝酸等離子體，其半峰全寬（FWHM）的寬度為860 um，而 〜 n_{e} = 2.8x 10^{19} cm^{-3} 則實現了極少的數兆瓦LWFA。相應的PIC模擬表明，自聚焦驅動脈衝的峰值可以電離 和 離子化，從而實現電離誘導的注入。另外，當驅動脈沖和激發的等離子體氣泡移動到氣體靶的後側時，發生下斜坡注入以進一步增加加速電子的數量。結果是受刺激的光譜顯示出在17兆電子伏的峰和一堆電荷33的C （> 5兆電子伏）與20 毫弧度得到發散。基於所測量的結果用於表徵從152- um 孔口產生的氣體射流，把光譜的高度從300 um 減少至100 um 能得到更高的等離子體密度，為 〜 n_{e} = 8x 10^{19} cm^{-3}。因此，相應的模擬結果表明，可以以1.5 TW的低激光峰值功率驅動LWFA，從中可以得到能量峰值為 7 MeV和束電荷 12.1 pC（> 5 MeV）的輸出電子

In this thesis, particle-in-cell (PIC) simulations are used to investigate the performance of laser wakefield acceleration (LWFA) driven by sub-terawatt (TW) and few-TW laser pulses when gas targets containing nitrogen are applied. In this scheme, a high plasma density n_{e} > 7.3x 10^{19} cm^{-3} can induce the self-focusing effect and self-modulation instability to greatly enhance the laser intensity to a level of capable of driving non-linear plasma waves for electron acceleration. In the case a 240-um long gas cell containing H_{2}-N_{2} mixture is applied with 0.5-TW,1030 nm laser pulses, the plasma density (n_{e} = 7.3x 10^{19} cm^{-3}) that gives the laser power P_{L}~2 P_{cr} is favorable for realizing LWFA. Results show that Nitrogen doping ratio between 1\% to 3\% can provide the best performance, from which electron with energies extending to 40 MeV are generated with a charge of 6.2 pC ( > 20 MeV). In contrast, using a high doping ratio > 5% can induce a strong ionization-induced defocusing the driving pulse to deteriorate the LWFA output, from which electrons are generated with energies < 20 MeV when 10% doping ratio is applied. On the other hand, when ~3-TW pulses are focused onto a pure nitrogen gas jet produced from a 152-um orifice with a backing pressure ~ 600 psi, Gaussian-distributed nitrogen plasmas with a width of 860 um in full-width at half maximum (FWHM) and n_{e} = 2.8x 10^{19} cm^{-3} are created to realize few–TW LWFA. The corresponding PIC simulations show that the peak of self-focused driving pulse can ionize $ N^{5+} $ and $ N^{6+} $ ions to realize ionization-induced injection. In addition, down-ramp injection occurs to further increase the number of accelerated electrons when the driving pulse and the excited plasma bubble move to the rear side of the gas target. As a result, the stimulated spectrum exhibits a peak at 17 MeV and a bunch charge of 33 pC ( > 5 MeV) with 20 mrad divergence is obtained. Based on the measured result for characterizing the gas jet produced from 152-$ \mu $m orifice, reducing the beam height from 300 um to 100 um can obtain a higher plasma density to n_{e} = 8x 10^{19} cm^{-3}. Therefore, the corresponding simulation results show that LWFA can be driven with a low laser peak power of 1.5 TW, from which output electron with energy peak at 7 MeV and bunch charge of 12.1 pC (> 5 MeV) can be acquired.

Abbreviation. . . . . . . .. . . . . . . .. . . . . . . .. . . .. .i
摘要. . . . . . . .. . . . . . . .. . . . . . . .. . . .. ... . . .ii
Abstract. . . . . . . .. . . . . . . .. . . . . . . .. . . .. ... .iii
Acknowledgment. . . . . . . .. . . . . . . .. . . . . . . .. . . ..v
Contents. . . . . . . .. . . . . . . .. . . . . . . .. . . . .. ..vi
List of Tables. . . . . . . .. . . . . . . .. . . . . . . . . . ..viii
List of Figures. . . . . . . .. . . . . . . .. . . . . . . .. . . .ix
1 Introduction . . . . . . . .. . . . . . . .. . . . . . . .. . . . 1
1.1 Principle of particle accelerator . . . . . . . . . . . . . . 2
1.2 Laser wakefield acceleration (LWFA) . . . . . . . . . . . . . . 4
1.3 Application of electrons generated from LWFA . . . . . . . . . .6
1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . .8
2 Principle of laser wakefield acceleration . . . . . .. . . . . . .10
2.1 Non-linear effect . . . . . . . . . . . . . . . . .. . . . . . .10
2.1.1 Relativistic self-focusing . . . . . . . . . . . . . . . . . .10
2.1.2 Self-modulated laser wakefield acceleration . . . . . . . . . 11
2.2 Self-injection regime . . . . . . . . . . . . . . . . . . . . .12
2.3 The physical limitation on LWFA . . . . . . . . . . . . . . . . 14
2.3.1 Electron dephasing . . . . . . . . . . . . . . . . . . . . . .14
2.3.2 Diffraction and depletion of the driving pulse . . . . . . . .15
2.4 Motivation of developing sub-TW or few-TW LWFA . . . . . . . . .16
2.5 Improvement of LWFA with ionization-induced injection . .. . . .18
3 Introduction to particle-in-cell simulation . . . . . . . .. . . .21
3.1 Overview of particle-in-cell simulation . . . . . . . . . . . .21
3.2 Our computational resources . . . . . . . . . . . . . . . . . .25
4 Simulation result . . . . . . . . . . . . . .. . . . . . . . . . .26
4.1 Sub-TW LWFA performed with mixture of H2 -N2 . . . . . . . . . .26
4.1.1 Simulation model . . . . . . . . . . . . . . . . . . . . . . .26
4.1.2 Influence of ionization injection with low doping ratio . . . 28
4.1.3 Influence of the use of comparatively high nitrogen doping ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .36
4.1.4 Summary and prospective work . . . . . . . . . . . . . . . ..43
4.2 Few-TW LWFA conducted with pure Nitrogen gas jet . . . . .. . . 46
5 Conclusion . . . . . . . . . . . . . .. . . . . . . . . . . . . . 54

1. F. Albert and A. G. R. Thomas, ”Applications of laser wakefield accelerator-based light sources”,Plasma Phys. Controlled Fusion 58, 103001 (2016).
2. T. Tajima and M. Dawson,”Laser Electron Accelerator”, Phys. Rev. Lett. 43 267 (1979)
3. E. Esarey, C. B. Schroeder, and W. P. Leemans, ”Physics of laser-driven plasma-based electron accelerators”,Rev. Mod. Phys, 81, 1229, (2009)
4. W. P. Leemans, B. Nagler, A. J. Gonsalves, C. Toth, K. Nakamura, C. G. R. Geddes,E. Esarey, C. B. Schroeder, and S. M. Hooker, ”GeV electron beams from a centimetrescale accelerator”,Nature Phys. 2, 696 (2006).
5. C. E. Clayton, J. E. Ralph, F. Albert, R. A. Fonseca, S. H. Glenzer, C. Joshi, W. Lu, K. A. Marsh, S. F. Martins, W. B. Mori, A. Pak, F. S. Tsung, B. B. Pollock, J. S.Ross, L. O. Silva, and D. H. Froula, ”Self-Guided Laser Wakefield Acceleration beyond
1 GeV Using Ionization-Induced Injection”,Phys. Rev. Lett. 105, 105003 (2010).
6. C. G. R. Geddes, C. Toth, J. van Tilborg, E. Esarey, C. B. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. P. Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding,” Nature, 431, (2004)
7. J. Faure, Y. Glinec, A. Pukhov, S. Kiselev, S. Gordienko, E. Lefebvre, J.-P. Rousseau, F. Burgy, and V. Malka,“A laser-plasma accelerator producing monoenergetic electron beams,” Nature, 431, (2004).
8. C. Chiu, M. Fomytskyi, F. Grigsby, F. Raischel, M. Downer, and T. Tajima. ”Laser electron accelerators for radiation medicine: a feasibility study.”, Medical Physics,
25,(2003).
9. S. V. Bulanov and V. S. Khoroshkov. ”Feasibility of using laser ion accelerators in proton therapy.” Plasma Physics Reports, 28 (2002).
10. B.Dotson,”How Particle Accelerators Work” (2014). Retrieved from
https://www.energy.gov/articles/how-particle-accelerators-work.
11. A. W. Chao and M. Tigner. Handbook of Accelerator Physics and Engineering. World Scientific Pub. Co. (1998)
12. F. F. Chen, ”Introduction to plasma physics”. New York: Plenum Press, 1974.
13. D. Gordon, K.C.Tzeng, C.E. Clayton, A.E. Dango, V. Malka, K.A. Mars, A. Modena, W.B. Mori, P. Muggli, Z. Najmudin, ”Observation of Electron Energies Beyond the
Linear Dephasing Limit from a Laser-Excited Relativistic Plasma Wave”, Phys. Rev. Lett. 80, 2133 (1998).
14. V. Malka, S. Fritzler, E. Lefebvre, M.M. Aleonard, F. Burgy, J. P. Chambaret, J.F. Chemin, K. Krushelnick ,G. Malka, S.P. Mangles, Z. Najmudin, M. Pittman, J.P. Rousseau, J.N. Scheurer, B. Walton, A.E. Dangor, ”Electron Acceleration by a Wake Field Forced by an Intense Ultrashort Laser Pulse”, Science 298, 1596 (2002).
15. C.-T. Hsieh, C.-M. Huang, C.-L. Chang, Y.-C. Ho, Y.-S. Chen, J.-Y. Lin, J. Wang, and S.-Y. Chen,”Tomography of Injection and Acceleration of Monoenergetic Electrons in a Laser-Wakefield Accelerator ”, Phys. Rev. Lett. 96, 095001 (2006).
16. O. Lundh, J. Lim, C. Rechatin, L. Ammoura, A. Ben-Ismail, X. Davoine, G. Gallot, J. Goddet, E. Lefebvre, V. Malka, and J. Faure, ”Few femtosecond, few kiloampere electron bunch produced by a laser–plasma accelerator”, Nat. Phys. 7, 219 (2011).
17. A. Buck, M. Nicolai, K. Schmid, C. M. S. Sears, A. Svert, J. M. Mikhailova, F. Krausz, M. C. Kaluza, and L. Veisz, ”Real-time observation of laser-driven electron acceleration”,Nat. Phys. 7, 543 (2011).
18. D. L. Fisher and T. Tajima, ”Enhanced Raman forward scattering”, Phys. Rev. E 53, 1844–1851 (1996)
19. A. Giulietti, N. Bourgeois, T. Ceccotti, X. Davoine, S. Dobosz, P. D’ Oliveira, M Galimberti, J. Galy, A. Gamucci, D. Giulietti, L. A. Gizzi, D. J. Hamilton, E. Lefebvre, L. Labate, J. R. Marques, P. Monot, H. Popescu, F. Reau, G. Sarri, P. Tomassini, and
P. Martin,”Intense-Ray Source in the Giant-Dipole-Resonance Range Driven by 10-TW Laser Pulses” Phys. Rev. Lett. 101 105002 ( 2008)
20. S. Kneip, C. McGuffey, F. Dollar, M. S. Bloom, V. Chvykov, G. Kalintchenko,K.
Krushelnick, A. Maksimchuk, S. P. D. Mangles, T. Matsuoka, Z. Najmudin,C. A. J. Palmer, J. Schreiber, W. Schumaker,2 A. G. R. Thomas, and V. Yanovsky,”X-ray phase contrast imaging of biological specimens with femtosecondpulses of betatron radiation
from a compact laser plasma wakefield accelerator”, Appl. Phys. Lett. 99, 093701 (2011)
21. M. D. Perry ,J. A. Sefcik ,T. Cowan , S. Hatchett , A. Hunt ,M. Moran ,D. Pennington,R. Snavely and S. C. Wilks , ”Hard x-ray production from high intensity laser solid interactions”,Rev. Sci. Instrum. 70 265–9 (1999)
22. C. Courtois, R. Edwards, A. Compant La Fontaine, C. Aedy, S. Bazzoli, J. L. Bourgade,
J. Gazave1, J. M. Lagrange, O. Landoas, L. Le Dain, D. Mastrosimone, N. Pichoff, G. Pien, and C. Stoeck, ”Characterisation of a MeV Bremsstrahlung x-ray source produced from a high intensity laser for high areal density object radiography”,Phys. Plasmas 20 083114 (2013)
23. E. Esarey, P. Sprangle, J.Krall and A. Ting,”Overview of Plasma-Based Accelerator Concepts ”, IEEE Trans. Plamsa Sci. 24, 252 (1996)
24. G.-Z. Sun, E. Ott, Y. C. Lee, and P. Guzdar,”Self-focusing of short intense pulses in plasmas”, Phys. Fluids 30, 526 (1987).
25. T. M. Antonsen, Jr. and P. Mora, ”Self-focusing and Raman scattering of laser pulses in tenuous plasmas ”, Phys. Plasmas 5, 1440 (1993)
26. K. Nakamura, B. Nagler, C. Toth, C. G. R. Geddes, C. B. Schroeder, E. Esarey, W. P. Leemans, A. J. Gonsalves, and S. M. Hooker,”GeV electron beams from a centimeter-scale channel guided laser wakefield accelerator”, Phys. Plasmas 14, 056708 (2007).
27. W. Lu, M. Tzoufras, C. Joshi,F. S. Tsung, W. B. Mori,J. Vieira, R. A. Fonseca, and L. O. Silva,”Generating multi-GeV electron bunches using single stage laser wakefield acceleration in a 3D nonlinear regime”,PHYS REV SPEC TOP-AC,10, 061301 (2007)
28. S. Gordienko and A. Pukhov,”Scalings for ultrarelativistic laser plasmas and quasimonoenergetic electrons”, Phys. Plasmas,12, 043109 (2005)
29. S. Y. Kalmykov, A. Beck, A. Yi, V. N. Khudik, M. C. Downer, E. Lefebvre, B. A. Shadwick, and D. P. Umstadter, ”Electron self-injection into an evolving plasma bubble: Quasi-monoenergetic laserplasma acceleration in the blowout regime”,Phys. Plasmas
18, 056704 (2011).
30. F. Albert, R. Shah, K. Ta. Phuoc, R. Fitour, F. Burgy, J. P. Rousseau, A. Tafzi, D. Douillet, T. Lefrou, and A. Rousse, ”Betatron oscillations of electrons accelerated in laser wakefields characterized by spectral x-ray analysis”,Phys. Rev. E 77, 056402
(2008).
31. J. Ju, K. Svensson, H. Ferrari, A. D€opp, G. Genoud, F. Wojda, M. Burza, A. Persson,
O. Lundh, C.-G. Wahlstr€om, and B. Cros, ”Study of electron acceleration and x-ray radiation as a function of plasma density in capillary-guided laser wakefield accelerators”,Phys. Plasmas. 20, 083106 (2013).
32. D. H. Froula, C. E. Clayton, T. Doppner, K. A. Marsh, C. P. J. Barty, L. Divol, R. A. Fonseca, S. H. Glenzer, C. Joshi, W. Lu, S. F. Martins, P. Michel, W. B. Mori, J. P. Palastro, B. B. Pollock, A. Pak, J. E. Ralph, J. S. Ross, C. W. Siders, L. O. Silva,
and T. Wang, ”Measurements of the Critical Power for Self-Injection of Electrons in a Laser Wakefield Accelerator ”,Phys. Rev. Lett 103, 215006 (2009).
33. C. D. Decker and W. B. Mori,”Group Velocity of Large Amplitude Electromagnetic Waves in a Plasma”,Phys. Rev. Lett.,51, 1364 (1995)
34. M. D. Perry and G. Mourou,”Terawatt to Petawatt Subpicosecond Lasers”,Science,264, (1994)
35. V. Malka, J. Faure, Y. A. Gauduel, E. Lefebvre, A. Rousse, and K. Ta Phuoc, ”Principles of laser–plasma accelerators”,Nature Phys. 4, (2008).
36. Z-H He1, B Hou, J A Nees, J H Easter, J Faure, K Krushelnic1 and A G R Thomas,”High repetition-rate wakefield electron source generated by few-millijoule, 30 fs laser pulses on a density downramp”,New J. Phys, 15, 053016 (2013)
37. C. McGuffey, A. G. R. Thomas, W. Schumaker, T. Matsuoka, V. Chvykov, F. J. Dollar, G. Kalintchenko, V. Yanovsky, A. Maksimchuk, and K. Krushelnick, ”Ionization Induced Trapping in a Laser Wakefield Accelerator”,Phys. Rev. Lett. 104, 025004 (2010).
38. E. Oz, S. Deng, T. Katsouleas, P. Muggli, C. D. Barnes, I. Blumenfeld, F. J. Decker, P.
Emma, M. J. Hogan, R. Ischebeck, R. H. Iverson, N. Kirby, P. Krejcik, C. O’ Connell, R. H. Siemann, D. Walz, D. Auerbach, C. E. Clayton, C. Huang, D. K. Johnson, C. Joshi, W. Lu, K. A. Marsh, W. B. Mori, and M. Zhou, ”Ionization-Induced Electron Trapping in Ultrarelativistic Plasma Wakes”, Phys. Rev. Lett. 98, 084801 (2007).
39. T. P. Rowlands-Rees, C. Kamperidis, S. Kneip, A. J. Gonsalves, S. P. D. Mangles, J. G. Gallacher, E. Brunetti, T. Ibbotson, C. D. Murphy, P. S. Foster, M. J. V. Streeter, F. Budde, P. A. Norreys, D. A. Jaroszynski, K. Krushelnick, Z. Najmudin, and S. M. Hooker, ”Enhancement of injection and acceleration of electrons in a laser wakefield accelerator by using an argon-doped hydrogen gas jet and optically preformed plasma waveguide”,Phys. Rev. Lett. 100, 105005 (2008).
40. A. Pak, K. A. Marsh, S. F. Martins, W. Lu, W. B. Mori, and C. Joshi, ”Injection and Trapping of Tunnel-Ionized Electrons into Laser-Produced Wakes”,Phys. Rev. Lett.104, 025003 (2010).
41. C.-Y. Hsieh, M.-W. Lin, and S.-H. Chen, ”Effect of driving pulse properties on the performance of sub-terawatt laser wakefield acceleration”, AIP Adv. 8, 105009 (2018).
42. C.-Y. Hsieh, M.-W. Lin, and S.-H. Chen, ”Simulation study of the sub-terawatt laser wakefield acceleration operated in selfmodulated regime”, Phys. Plasmas 25, 023101 (2018).
43. M. Chen, E. H. Esarey, C. B. Schroeder, C. G. R. Geddes, and W. P. Leemans, ”Theory of ionization-induced trapping in laser-plasma accelerators”,Phys. Plasmas 19, 033101 (2012).
44. C. Kamperidis, V. Dimitriou, S. P. D. Mangles, A. E. Dangor, and Z. Najmudin, ”Low energy spread electron beams from ionization injection in a weakly relativistic laser
wakefield accelerator”,Plasma Phys. Controlled Fusion 56, 084007 (2014).
45. F. Li, J. F. Hua, X. L. Xu, C. J. Zhang, L. X. Yan, Y. C. Du, W. H. Huang,H. B. Chen, C. X. Tang, W. Lu, C. Joshi, W. B. Mori, and Y. Q. Gu,”Generating High Brightness Electron Beams via Ionization Injection by Transverse Colliding Lasers in a Plasma-Wakefield Accelerator”, Phys. Rev. Lett. 111, 015003 (2013).
46. M. Z. Mo, A. Ali, S. Fourmaux, P. Lassonde, J. C. Kieffer, and R. Fedosejevs, ”Quasimonoenergetic electron beams from laser wakefield acceleration in pure nitrogen”,Appl. Phys. Lett. 100, 074101 (2012).
47. A. J. Goers, S. J. Yoon, J. A. Elle, G. A. Hine, and H. M. Milchberg, ”Laser wakefield acceleration of electrons with ionization injection in a pure N5+ plasma waveguide”,Appl. Phys. Lett. 104, 214105 (2014).
48. J. S. Liu, C. Q. Xia, W. T. Wang, H. Y. Lu, Ch. Wang, A. H. Deng, W. T. Li, H. Zhang, X. Y. Liang, Y. X. Leng, X. M. Lu, C. Wang, J. Z. Wang, K. Nakajima, R. X. Li, and Z. Z. Xu, ”All-Optical Cascaded Laser Wakefield Accelerator Using Ionization-Induced Injection”,Phys. Rev. Lett. 107(3), 035001 (2011).
49. B. B. Pollock, C. E. Clayton, J. E. Ralph, F. Albert, A. Davidson, L. Divol, C. Filip, S H. Glenzer, K. Herpoldt, W. Lu, K. A. Marsh, J. Meinecke, W. B. Mori, A. Pak, T. C. Rensink, J. S. Ross, J. Shaw, G. R. Tynan, C. Joshi, and D. H. Froula,”Demonstration of a Narrow Energy Spread, 0.5 GeV Electron Beam from a Two-Stage Laser Wakefield
Accelerator”,Phys. Rev. Lett. 107(4), 045001 (2011).
50. Gregor Filipic,”Principles of ” Particle in cell”simulations”,University of Ljubljana,(2008)
51. C. Nieter and J. R. Cary, ”VORPAL: a versatile plasma simulation code”, J. Comput. Phys. 196, 448 (2004).
52. J. L. Shaw, N. Vafaei-Najafabadi, K. A. Marsh, and C. Joshi, ”100 MeV injector cell for a staged laser wakefield accelerator”,AIP Conf. Proc. 1507, 315 (2012).
53. T. L. Audet, M. Hansson, P. Lee, F. G. Desforges, G. Maynard, S. Dobosz Dufrenoy, R. Lehe, J.-L. Vay, B. Aurand, A. Persson, I. Gallardo Gonzalez, A. Maitrallain, P. Monot, C.-G. Wahlstrom, O. Lundh, and B. Cros, ”Investigation of ionization-induced
electron injection in a wakefield driven by laser inside a gas cell ”, Phys. Plasmas 23, 023110 (2016).
54. F. S. Tsung, W. Lu, M. Tzoufras, W. B. Mori, C. Joshi, J. M. Vieira, L. O. Silva, and R. A. Fonseca, ”Simulation of monoenergetic electron generation via laser wakefield accelerators for 5-25 TW lasers ”, Phys. Plasmas 13, 056708 (2006).
55. J. L. Shaw, N. Lemos, K. A. Marsh, F. S. Tsung, W. B. Mori, and C. Joshi, ”Estimation of direct laser acceleration in laser wakefield accelerators using particle-in-cell simulations”,Plasma Phys. Controlled Fusion 58, 034008 (2016).
56. M. Tzoufras, W. Lu, F. S. Tsung, C. Huang, W. B. Mori, T. Katsouleas, J. Vieira, R.
A. Fonseca, and L. O. Silva, ”Beam Loading in the Nonlinear Regime of Plasma-Based Acceleration”,Phys. Rev. Lett 101, 145002 (2008)
57. D. Gustas, D. Guenot, A. Vernier, S. Dutt, F. Böhle, R. Lopez-Martens, A. Lifschitz,and J. Faure,”High-charge relativistic electron bunches from a kHz laser-plasma accelerator”,PHYS REV ACCEL BEAMS 21,013401 (2018)
58. A. J. Goers, G. A. Hine, L. Feder, B. Miao, F. Salehi, J. K. Wahlstrand, and H. M. Milchberg,”Multi-MeV Electron Acceleration by Subterawatt Laser Pulses”,Phys. Rev. Lett 115, 194802 (2015)