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Exploring laser-wakefield-accelerator regimes for near-term lasers using particle-in-cell simulation in Lorentz-boosted frames


Plasma-based acceleration offers compact accelerators with potential applications for high-energy physics and photon sources. The past five years have seen an explosion of experimental results with monoenergetic electron beams up to 1 GeV on a centimetre-scale, using plasma waves driven by intense lasers. The next decade will see tremendous increases in laser power and energy, permitting beam energies beyond 10 GeV. Leveraging on the Lorentz transformations to bring the laser and plasma spatial scales together, we have reduced the computational time for modelling laser–plasma accelerators by several orders of magnitude, including all the relevant physics. This scheme enables the first one-to-one particle-in-cell simulations of the next generation of accelerators at the energy frontier. Our results demonstrate that, for a given laser energy, choices in laser and plasma parameters strongly affect the output electron beam energy, charge and quality, and that all of these parameters can be optimized.

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Figure 1: Simulation results for a LWFA in the bubble regime with a 250 J laser in the laboratory frame.
Figure 2: Simulation results for a LWFA in the self-guiding/self-injection blowout regime of a 250 J laser.
Figure 3: Simulation results for a LWFA in the external-guiding/external-injection blowout regime of a 250 J laser.
Figure 4: Comparison of laser/plasma matching conditions for the three regimes studied.


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This work was partially supported by Fundação Calouste Gulbenkian, by Fundação para a Ciência e a Tecnologia, under grants PTDC/FIS/66823/2006 and SFRH/BD/35749/2007 (Portugal), Laserlab-Europe/LAPTECH, EC FP7 Contract No. 228334, by the US Department of Energy (DOE) under grant numbers DE-FC02-07ER41500, DE-FG02-92ER40727 and DE-FG52-09NA29552, by the NSF under grant numbers PHY-0904039 and PHY 0936266 and by the University of California Lab Research Program. S.F.M. and L.O.S. would like to thank KITP, where a part of this research was concluded, partially supported by the National Science Foundation under Grant number PHY05-51164. We thank the DEISA Consortium (, co-funded through the EU FP6 project RI-031513 and the FP7 project RI-222919, for support within the DEISA Extreme Computing Initiative. The simulations presented here were produced using IST Cluster (IST/Portugal), Dawson cluster (UCLA), Jügene (Jülich, Germany) and NERSC supercomputers.

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S.F.M., code development, simulations, data analysis and manuscript preparation; R.A.F., code development; W.L., data analysis; W.B.M. and L.O.S., result analysis and manuscript writing.

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Correspondence to L. O. Silva.

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Martins, S., Fonseca, R., Lu, W. et al. Exploring laser-wakefield-accelerator regimes for near-term lasers using particle-in-cell simulation in Lorentz-boosted frames. Nature Phys 6, 311–316 (2010).

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