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Growth of concomitant laser-driven collisionless and resistive electron filamentation instabilities over large spatiotemporal scales


Collective processes in plasmas often induce microinstabilities that play an important role in many space or laboratory plasma environments. Particularly notable is the Weibel-type current filamentation instability, which is believed to drive the creation of collisionless shocks in weakly magnetized astrophysical plasmas. Here, this instability class is studied through interactions of ultraintense and short laser pulses with solid foils, leading to localized generation of megaelectronvolt electrons. Proton radiographic measurements of both low- and high-resistivity targets show two distinct, superimposed electromagnetic field patterns arising from the interpenetration of the megaelectronvolt electrons and the background plasma. Particle-in-cell simulations and theoretical estimates suggest that the collisionless Weibel instability building up in the dilute expanding plasmas formed at the target surfaces causes the observed azimuthally symmetric electromagnetic filaments. For a sufficiently high resistivity of the target foil, an additional resistive instability is triggered in the bulk target, giving rise to radially elongated filaments. The data reveal the growth of both filamentation instabilities over large temporal (tens of picoseconds) and spatial (hundreds of micrometres) scales.

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Fig. 1: Sketch of the experimental set-up.
Fig. 2: Proton radiographs showing filamentation instabilities.
Fig. 3: Numerical simulation and theory of the current filamentation instabilities.
Fig. 4: PIC-MHD simulations of the resistive filamentation and synthetic radiographs.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The code used to generate Fig. 3 and Fig. 4. is CALDER. All simulated proton radiographs, shown in Fig. 2 and Fig. 4, are generated using the ILZ code. Both codes are detailed in the Methods section.


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We thank F. Amiranoff, F. Fiuza, E. d’Humières, V. Gubchenko and V. T. Tikhonchuk for insightful discussions. We also acknowledge the support of the JLF-Titan technical teams. The simulations were performed using HPC resources at TGCC/CCRT. We acknowledge PRACE for awarding us access to TGCC/Curie (grant 2014112576). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement 654148 Laserlab-Europe and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement 787539. The research leading to these results is supported by Extreme Light Infrastructure Nuclear Physics (ELI-NP) Phase II, a project cofinanced by the Romanian Government and European Union through the European Regional Development Fund. This work was partly done within the LABEX Plas@Par project. It was supported by grants 11-IDEX-0004-02 and ANR-17-CE30-0026-Pinnacle from Agence Nationale de la Recherche. This work was also partly supported by the DFG GRK 1203 and SFB/TR18 programmes and by EPSRC grants EP/K022415/1 and EP/J002550/1. It was supported in part by the Ministry of Education and Science of the Russian Federation under contract 14.Z50.31.0007. The use of the Jupiter Laser Facility was supported by the US Department of Energy, Lawrence Livermore National Laboratory, under contract DE-AC52-07NA27344.

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Authors and Affiliations



J.F. conceived the project. B.A., S.N.C., P.A., J.B., V.D., L.L., M.N., L.R., M. Swantusch, M.B., H.P. and J.F. performed the experiment, with support from R.S., O.W. and M. Starodubtsev. B.A., S.B. and J.F. analysed the data. C. Ruyer and L.G. developed the theoretical framework and performed the simulations, with discussions with M.G. and C. Riconda. S.B. computed the synthetic proton radiographs. J.F., C. Ruyer and L.G. wrote the paper. All authors commented on the paper in its various stages.

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Correspondence to C. Ruyer, L. Gremillet or J. Fuchs.

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Peer review information Nature Physics thanks Francesco Pegoraro, Luis Silva and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–10 and discussion.

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Ruyer, C., Bolaños, S., Albertazzi, B. et al. Growth of concomitant laser-driven collisionless and resistive electron filamentation instabilities over large spatiotemporal scales. Nat. Phys. 16, 983–988 (2020).

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