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In laser wake field acceleration, it is relatively easy to achieve and control electron injection by adopting a plasma density gradient. This scheme of plasma density gradient injection has been studied in recent years both theoretically and experimentally, but thus far theoretical studies have been done mostly by particle-in-cell simulations. In this paper the density gradient injection and acceleration of electrons are studied with a newly developed analytic approach. The energy threshold for electron injection versus plasma density gradient scale length is given. It is shown that in the plasma density gradient region, the energy threshold of electron injection becomes lower at later times after the driving laser pusle or when the gradient becomes sharper. Evolution of plasma wave's phase velocity and motion of the background electrons in the plasma density gradient are worked out in the linear plasma wave regime, i.e. the normalized laser intensity is a0～1. The energy, the location, and the timing of the injected electrons are obtained. Separatrices of test electrons in the gradient region are obtained by Hamiltonian theory. The influence of injection timing in the density gradient region on the succeeding acceleration in the homogeneous plasma density region is also discussed. It is indicated that whether the injected electrons may be accelerated efficiently or not in the homogeneous region depends on both the energy of the electrons and the phase of the plasma wave at the gradient-to-homogeneous turning point. The analytic results are confirmed by particle-in-cell simulations.
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Keywords:
- electron injection /
- plasma wave /
- density gradient
[1] Tajima T, Dawson J M 1979 Phys. Rev. Lett. 43 267
[2] Dong K G, Gu Y Q, Zhu B, Wu Y C, Cao L F, He Y L, Liu H J, Hong W, Zhou W M, Zhao Z Q, Jiao C Y, Wen X L, Zhang B H, Wang X F 2010 Acta Phys. Sin. 59 8733 (in Chinese) [董克攻, 谷渝秋, 朱斌, 吴玉迟, 曹磊峰, 何颖玲, 刘红杰, 洪伟, 周维民, 赵宗清, 焦春晔, 温贤伦, 张保汉, 王晓方 2010 59 8733]
[3] Lundh O, Lim J, Rechatin C, Ammoura L, Ben-Ismal A, Davoine X, Gallot G, Goddet J P, Lefebvre E, Malka V, Faure J 2011 Nat. Phys. 7 219
[4] Gonsalves A J, Nakamura K, Lin C, Panasenko D, Shiraishi C, Sokollik T, Benedetti C, Schroeder C B, Geddes C G R, van Tilborg J, Osterhoff J, Esarey E, Toth C, Leemans W P 2011 Nat. Phys. 7 862
[5] Bulanov S, Naumova N, Pegoraro F, Sakai J 1998 Phys. Rev. E 58 R5257
[6] Tomassini P, Galimbert M, Giulietti A, Giulietti D, Gizzi L A, Labate L, Pegoraro F 2003 Phys. Rev. ST Accel. Beams 6 121301
[7] Brantov A V, Esirkepov T Z, Kando M, Kotaki H, Bychenkov V Yu, Bulanov S V 2008 Phys. Plasmas 15 073111
[8] Schmid K, Buck A, Sears C M S, Mikhailova J M, Tautz R, Herrmann D, Geissler M, Krausz F, Veisz L 2010 Phys. Rev. ST Accel. Beams 13 091301
[9] Nieter C, Cary J R 2004 J. Comput. Phys. 196 448
[10] Esarey E, Schroeder C B, Leemans W P 2009 Rev. Mod. Phys. 81 1229
[11] Gorbunov L M, Kirsanov V I 1987 Sov. Phys. JETP 66 290
[12] Esarey E, Pilloff M 1995 Phys. Plasmas 2 1432
[13] Suk H, Barov N, Rosenzweig J B, Esarey E 2001 Phys. Rev. Lett. 86 1011
[14] Ma Z N, Wang X F 2011 High Power Laser Part. Beams 23 2687 (in Chinese) [马占南, 王晓方 2011 强激光与粒子束 23 2687]
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[1] Tajima T, Dawson J M 1979 Phys. Rev. Lett. 43 267
[2] Dong K G, Gu Y Q, Zhu B, Wu Y C, Cao L F, He Y L, Liu H J, Hong W, Zhou W M, Zhao Z Q, Jiao C Y, Wen X L, Zhang B H, Wang X F 2010 Acta Phys. Sin. 59 8733 (in Chinese) [董克攻, 谷渝秋, 朱斌, 吴玉迟, 曹磊峰, 何颖玲, 刘红杰, 洪伟, 周维民, 赵宗清, 焦春晔, 温贤伦, 张保汉, 王晓方 2010 59 8733]
[3] Lundh O, Lim J, Rechatin C, Ammoura L, Ben-Ismal A, Davoine X, Gallot G, Goddet J P, Lefebvre E, Malka V, Faure J 2011 Nat. Phys. 7 219
[4] Gonsalves A J, Nakamura K, Lin C, Panasenko D, Shiraishi C, Sokollik T, Benedetti C, Schroeder C B, Geddes C G R, van Tilborg J, Osterhoff J, Esarey E, Toth C, Leemans W P 2011 Nat. Phys. 7 862
[5] Bulanov S, Naumova N, Pegoraro F, Sakai J 1998 Phys. Rev. E 58 R5257
[6] Tomassini P, Galimbert M, Giulietti A, Giulietti D, Gizzi L A, Labate L, Pegoraro F 2003 Phys. Rev. ST Accel. Beams 6 121301
[7] Brantov A V, Esirkepov T Z, Kando M, Kotaki H, Bychenkov V Yu, Bulanov S V 2008 Phys. Plasmas 15 073111
[8] Schmid K, Buck A, Sears C M S, Mikhailova J M, Tautz R, Herrmann D, Geissler M, Krausz F, Veisz L 2010 Phys. Rev. ST Accel. Beams 13 091301
[9] Nieter C, Cary J R 2004 J. Comput. Phys. 196 448
[10] Esarey E, Schroeder C B, Leemans W P 2009 Rev. Mod. Phys. 81 1229
[11] Gorbunov L M, Kirsanov V I 1987 Sov. Phys. JETP 66 290
[12] Esarey E, Pilloff M 1995 Phys. Plasmas 2 1432
[13] Suk H, Barov N, Rosenzweig J B, Esarey E 2001 Phys. Rev. Lett. 86 1011
[14] Ma Z N, Wang X F 2011 High Power Laser Part. Beams 23 2687 (in Chinese) [马占南, 王晓方 2011 强激光与粒子束 23 2687]
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