Skip to main content Accessibility help

Electron energy optimization by plasma density ramp in laser wakefield acceleration in bubble regime

  • M. Kaur (a1) and D. N. Gupta (a1)


Energy gain of electron beams in bubble regime of the laser wakefield accelerator can be optimized by improving the acceleration length, radial accelerating and focusing force, number of monoenergetic electrons trapped inside the bubble, and increasing dephasing length. In order to enlarge the dephasing length, the phase velocity of the plasma wave can be increased by optimizing the plasma density profile. We report the estimation of dephasing length using plasma density distribution with the flat and linear-upward profile using two-dimensional particle-in-cell simulations. The size of wakefield bubble depends on the plasma density. With a positive plasma density gradient, the size of bubble decreases. The front and trail part of wake bubble will have different phase velocity in plasma density gradient region. After density transition in constant density region, the bubble elongates and the velocity of the back part of the bubble increases so that the accelerated electron phase synchronizes with the phase of the plasma wave. In a result, the electron acceleration length enhances to improve the beam quality.


Corresponding author

Author for correspondence: D. N. Gupta, Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India. E-mail:


Hide All
Albert, F, Thomas, AGR, Mangles, SPD, Banerjee, S, Corde, S, Flacco, A, Litos, M, Neely, D, Vieiria, J, Najmudin, Z, Bingham, R, Joshi, C and Katsouleas, T (2014) Laser wakefield accelerator based light sources: potential applications and requirements. Plasma Physics and Controlled Fusion 56, 084015.
Banerjee, S, Kalmykov, SY, Powers, ND, Golovin, G, Ramanathan, V, Cunningham, NJ, Brown, KJ, Chen, S, Ghebregziabher, I, Shadwick, BA, Umstadter, DP, Cowan, BM, Bruhwiler, DL, Beck, A and Lefebvre, E (2013) Stable, tunable, quasi-monoenergetic electron beams produced in a laser wakefield near the threshold for self-injection. Physical Review ST Accelerators And Beams 16, 031302.
Benedetti, C, Schroeder, CB, Esarey, E, Rossi, F and Leemans, WP (2013) Numerical investigation of electron self-injection in the nonlinear bubble regime. Physics of Plasmas 20, 103108.
Bulanov, S, Naumova, N, Pegoraro, F and Sakai, J (1998) Particle injection into the wave acceleration phase due to nonlinear wake wave breaking. Physical Review E 58, R5257R5260.
Davoine, X, Lefebvre, E, Rechatin, C, Faure, J and Malka, V (2009) Cold optical injection producing monoenergetic, multi-GeV electron bunches. Physical Review Letters 102, 065001.
Dawson, JM (1959) Nonlinear electron oscillations in a cold plasma. The Physical Review 113, 383387.
Decker, CD and Mori, WB (1994) Group velocity of large amplitude electromagnetic waves in a plasma. Physical Review Letters 72, 490493.
Esarey, E, Schroeder, CB and Leemans, WP (2009) Physics of laser-driven plasma-based electron accelerator. Reviews of Modern Physics 81, 12291285.
Faure, J, Glinec, Y, Pukhov, A, Kiselev, S, Gordienko, S, Lefebvre, E, Rousseau, JP and Malka, V (2004) A laser-plasma accelerator producing monoenergetic electron beams. Nature 431, 541544.
Geddes, CGR, Toth, Cs, van Tilborg, J, Esarey, E, Schroeder, CB, Bruhwiler, D, Nieter, C, Cary, J and Leemans, WP (2004) High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding. Nature 431, 538541.
Gupta, DN, Hur, MS, Hwang, I, Suk, H and Sharma, A (2007) Plasma density ramp for relativistic self-focusing of an intense laser. Journal of the Optical Society of America B: Optical Physics 24, 11551159.
Hafz, NAM, Jeong, TM, Choi, IW, Lee, SK, Pae, KH, Kulagin, VV, Jung, JH, Yu, TJ, Hong, KH, Hosokai, T, Cary, JR, Ko, DK and Lee, J (2008) Stable generation of GeV-class electron beams from self-guided laser-plasma channels. Nature Photonics 2, 571577.
Hafz, NAM, Lee, SK, Jeong, TM and Lee, J (2011) Evolution of self-injected quasi-monoenergetic electron beams in a plasma bubble. Nuclear Instruments & Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment 637, S51S53.
Hansson, M, Aurand, B, Davoine, X, Ekerfelt, H, Svensson, K, Persson, A, Wahlstrom, CG and Lundh, O (2015) Down-ramp injection and independently controlled acceleration of electrons in a tailored laser wakefield accelerator. Physical Review ST Accelerators and Beams 18, 071303.
Jaroszynski, DA, Bingham, R, Brunetti, E, Ersfield, B, Gallacher, J, Van Der Geer, B, Isaac, R, Jamison, SP, Jones, D, De Loos, M, Lyachev, A, Pavlov, V, Reitsma, A, Saveliev, Y, Vieux, G and Wiggins, SM (2006) Radiation sources based on laser-plasma interactions. Philosophical Transactions of the Royal Society A 364, 689710.
Kalmykov, SY, Beck, A, Yi, SA, Khudik, VN, Downer, MC, Lefebvre, E, Shadwick, BA and Umstadter, DP (2011) Electron self-injection into an evolving plasma bubble: quasi-monoenergetic laser-plasma acceleration in the blowout regime. Physics of Plasmas 18, 056704.
Kalmykov, SY, Beck, A, Yi, SA, Khudik, V, Shadwick, BA, Lefebvre, E and Downer, MC (2010) Electron self-injection into an evolving plasma bubble: the way to a dark current free GeV-scale laser accelerator. AIP Conference Proceedings 1299, 174179.
Katsouleas, T (1986) Physical mechanisms in the plasma wake-field accelerator. Physical Review A 33, 20562064.
Kaur, M and Gupta, DN (2016) Simulation of laser-driven plasma beat-wave propagation in collisional weakly relativistic plasmas. Europhysics Letters 116, 35001.
Kaur, M, Gupta, DN and Suk, H (2017) Evolution of Laser pulse shape in a parabolic plasma channel. Laser Physics 27, 015401.
Kim, C, Kim, GH, Kim, JU, Ko, IS, Lee, HJ and Suk, H (2003) Self-injection of electrons in evolution of wake wave. Conference Proceedings of the PAC 3, 18521854.
Kim, J, Kim, GJ and Yoo, SH (2011) Energy enhancement using an upward density ramp in laser wakefield acceleration. Journal of the Korean Physical Society 59, 31663170.
Kim, M, Lee, S, Kim, J, Nam, I and Suk, H (2016) Feasibility study of a laser-driven high energy electron acceleration in a long up-ramp density. Conference Proceedings of the IPAC 3, 25762578.
Kostyukov, I, Nerush, E, Pukhov, A and Seredov, DV (2009) Electron self-injection in multidimensional relativistic-plasma wake fields. Physical Review Letters 103, 175003.
Lee, S, Lee, TH, Gupta, DN, Uhm, HS and Suk, H (2015) Enhanced betatron oscillations in laser wakefield acceleration by off-axis laser alignment to a capillary plasma waveguide. Plasma Physics and Controlled Fusion 57, 075002.
Leemans, WP, Nagler, B, Gonsalves, AJ, Toth, C, Nakamura, K, Geddes, CGR, Esarey, E, Schroeder, CB and Hooker, SM (2006) GeV electron beams from a centimeter-scale accelerator. Nature Physics 2, 696699.
Li, XF, Yu, Q, Gu, YJ, Huang, S, Kong, Q and Kawata, S (2015) Bubble shape and electromagnetic field in the nonlinear regime for laser wakefield acceleration. Physics of Plasmas 22, 083112.
Lu, W, Tzoufras, M, Joshi, C, Tsung, FS, Mori, WB, Vieiria, J, Fonseca, RA and Silva, LO (2007) Generating multi-GeV electron bunches using single stage laser wakefield acceleration in a 3D nonlinear regime. Physical Review ST Accelerators and Beams 10, 061301.
Mangles, SPD, Murphy, CD, Najmudin, Z, Thomas, AGR, Collier, JL, Dangor, AE, Divall, EJ, Foster, PS, Gallacher, JG, Hooker, CJ, Jaroszynski, JA, Langley, AJ, Mori, WB, Norreys, PA, Tsung, FS, Viskup, R, Walton, BR and Krushelnick, K (2004) Monoenergtic beams of relativistic electrons from intense laser-plasma interactions. Nature 431, 535538.
Nakajima, K (2008) Compact X-ray sources: towards a table-top free-electron laser. Nature Physics 4, 9293.
Nakajima, K, Kim, H, Jeong, T and Nam, C (2015) Scaling and design of high-energy laser plasma electron acceleration. High Power Laser Science 3, 111.
Nieter, C and Cary, JR (2004) VORPAL: a versatile plasma simulation code. Journal of Computational Physics 196, 448473.
Pukhov, A and Meyer-Ter Vehn, J (2002) Laser wake field acceleration: the highly non-linear broken-wave regime. Applied Physics B: Lasers and Optics 74, 355361.
Rittershofer, W, Schroeder, CB, Esarey, E, Gruner, FJ and Leemans, WP (2010) Tapered plasma channels to phase-lock accelerating and focusing forces in laser-plasma accelerator. Physics of Plasmas 17, 063104.
Schimd, K, Buck, A, Sears, CMS, Mikhailova, JM, Tautz, R, Herrmann, D, Geissler, M, Krausz, F and Veisz, L (2010) Density-transition based electron injector for laser driven wakefield accelerators. Physical Review ST Accelerators and Beams 13, 091301.
Sprangle, P, Esarey, E and Krall, J (1996) Self-guiding and stability of intense optical beams in gases undergoing ionization. Physical Review E 54, 4211.
Tajima, T and Dawson, JM (1979) Laser electron accelerator. Physical Review Letters 43, 267270.
Toosi, ES, Mirzanejhad, S and Dorronian, D (2016) Bubble structure in laser wake-field acceleration. Laser and Particle Beams 34, 193201.
Tsung, FS, Narang, R, Mori, WB, Joshi, C, Fonseca, RA and Silva, LO (2004) Near-GeV-energy laser-wakefield acceleration of self-injected electrons in a centimeter-scale plasma channel. Physical Review Letters 93, 185002.
Wen, M, Shen, B, Zhang, X, Wang, F, Jin, Z, Ji, L, Wang, W, Xu, J and Nakajima, K (2010) Controlled electron acceleration in the bubble regime by optimizing plasma density. New Journal of Physics 12, 045010.
Yu, LL, Esarey, E, Schroeder, CB, Vay, JL, Benedetti, C, Geddes, CGR, Chen, M and Leemans, WP (2014) Two-color laser-ionization injection. Physical Review Letters 112, 125001.
Yu, Q, Gu, YJ, Li, XF, Huang, S, Kong, Q and Kawata, S (2015) Electron self-injection into the phase of a wake excited by a driver laser in a nonuniform density target. Physics of Plasmas 22, 073107.



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed