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# Laboratory evidence for proton energization by collisionless shock surfing

## Abstract

Charged particles can be accelerated to high energies by collisionless shock waves in astrophysical environments, such as supernova remnants. By interacting with the magnetized ambient medium, these shocks can transfer energy to particles. Despite increasing efforts in the characterization of these shocks from satellite measurements at Earth’s bow shock as well as powerful numerical simulations, the underlying acceleration mechanism or a combination thereof is still widely debated. Here we show that astrophysically relevant super-critical quasi-perpendicular magnetized collisionless shocks can be produced and characterized in the laboratory. We observe the characteristics of super-criticality in the shock profile as well as the energization of protons picked up from the ambient gas to hundreds of kiloelectronvolts. Kinetic simulations modelling the laboratory experiment identified shock surfing as the proton acceleration mechanism. Our observations not only provide direct evidence of early-stage ion energization by collisionless shocks but also highlight the role played by this particular mechanism in energizing ambient ions to feed further stages of acceleration. Furthermore, our results open the door to future laboratory experiments investigating the possible transition to other mechanisms, when increasing the magnetic field strength, or the effect that induced shock front ripples could have on acceleration processes.

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## Data availability

All data needed to evaluate the conclusions in the paper are present in the paper. Experimental data and simulations are archived on the servers at LULI and LERMA laboratories, respectively, and are available from the corresponding author upon reasonable request.

## Code availability

The code used to generate the data shown in Fig. 1b is created using FLASH. The code used to generate a part of Figs. 3 and 4 is created using SMILEI. Both codes are detailed in Methods.

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## Acknowledgements

We thank the teams of LULI (France) and JLF (USA) laser facilities for their expert support, as well the Dresden High Magnetic Field Laboratory at Helmholtz-Zentrum Dresden-Rossendorf for the development of the pulsed power generator used at LULI. We thank the SMILEI dev team for technical support. We also thank Ph. Savoini (Sorbonne University, France) and L. Gremillet and C. Ruyer (CEA, France) for discussions. W.Y. thanks R. Li (SZTU, China) for discussions. This work was supported by funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement no. 787539; J.F.). The computational resources of this work were supported by the National Sciences and Engineering Research Council of Canada (NSERC), Fonds québécois de la recherche sur la nature et les technologies (FRQNT) - Projet Samuel-de Champlain 293688) and Compute Canada (Job: pve-323-ac; P.A.). Part of the experimental system is covered by a patent (1000183285, 2013, INPI-France). The FLASH software used was developed, in part, by the Flash Center for Computational Science at the University of Chicago supported by the DOE NNSA, ASC, and the DOE Office of Science, ASCR. The research leading to these results is supported by Extreme Light Infrastructure Nuclear Physics (ELI-NP) Phase II, a project co-financed by the Romanian Government and European Union through the European Regional Development Fund (S.N.C., S.K., V.N. and D.C.P.), and by the project ELI-RO-2020-23 funded by IFA, Romania (J.F.). JIHT RAS team members are supported by the Ministry of Science and Higher Education of the Russian Federation (State Assignment No. 075-00460-21-00; E.D.F. and S.P.). The reported study was funded by the Russian Foundation for Basic Research, project no. 19-32-60008 (E.D.F.).

## Author information

Authors

### Contributions

J.F. and S.N.C. conceived the project. A.F., S.N.C., K.B., J.B., S.B., S.K., V.L., V.N., S.P., D.C.P., G.R. and J.F. performed the experiments. A.F., E.D.F., S.N.C., K.B., R.D., S.P. and J.F. analysed the data. X.R. performed and analysed the FLASH simulations, while W.Y. and A.F. performed and analysed the SMILEI simulations, both with discussions with P.A., A.C., Q.M., X.R., E.d.H. and J.F. W.Y., S.N.C. and J.F. wrote the bulk of the paper, with major contributions from K.B., M.M. and S.O. All the authors commented and revised the paper.

### Corresponding author

Correspondence to J. Fuchs.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review informationNature Physics thanks Kai Germaschewski and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 X-ray emissivity of Lyα line measured by the FSSR.

The red curve represents the piston plasma emission in the range 0–10 mm in the case when the unmagnetized piston expands in the ambient gas. The black curve represents the same but when additionally, the transverse external magnetic field was applied.

### Extended Data Fig. 2 Time sequence of experimental density measurement.

(integrated along the line of sight) recorded in the two different and complementary xy and xz planes in order to characterize in three-dimensions the overall plasma. Each image corresponds to a different laser shot. Specifically, the images shown in panels (a1-a4) correspond to the case without the external magnetic field; the images shown in panels (b1-b4) and (c1-c4) correspond to the case with the external magnetic field, which is aligned along the z-axis, the difference between panels (b1-b4) and (c1-c4) is the direction of the optical probing, which is along the z-axis for panels (b1-b4) and along the y-axis for panels (c1-c4). The color scale shown at the bottom applies to all images. The images shown in panels (d1-d4) correspond to the lineouts along the thin dark lines shown in each images of panels (a1-a4), (b1-b4) and (c1-c4). From top to bottom, each row represents a different time, that is, 2/4/6/8 ns. Magnetic field directions are indicated at the top of each column. Orange and green arrows indicate the piston and the shock front, respectively.

### Extended Data Fig. 3 Temporal evolution of the electron temperature.

obtained from the solution of $$1.5{n}_{e}{d}_{t}{T}_{e}={\nu }_{B}{I}_{0}{e}^{-{t}^{2}/{\tau }^{2}}$$. Here, ne = 1018 cm−3, νB is the inverse Bremsstrahlung absorption coefficient from the NRL formulary (p.58/Eq.32). The laser energy is 15 J, with duration τ = 3 ns, defocused focal spot d = 200μm and wavelength λl = 528 nm, leading to an maximum intensity of I0 = 1.5 × 1013 W  cm−2, and the initial electron temperature Te0 = 10 eV (left axis, blue). The intensity evolution of the laser (ITS) is superimposed as a red line (right axis).

### Extended Data Fig. 4 Examples of plasma density and temperature measurement of the shock downstream (DS).

(a) Schematic diagram of the collective Thomson scattering (TS) diagnostic deployed at LULI2000. The measurement is performed, in a fixed volume (see Methods) through which the shock is sweeping, 4.3 mm away from the solid target surface, separating the downstream (DS) and upstream (US) regions. Panels (b) and (c) show TS measurement on the ion waves in the plasma, allowing to retrieve the local electron and ion temperatures, as stated. The vertical axis represents the amplitude of the scattered light; the horizontal axis represents the wavelength (λ) of the scattered light. Both measurements are performed 3 ns after the shock has passed, but (b) corresponds to the case without external B-field, while (c) corresponds to the case with B = 20 T applied. Solid lines – experimental data profiles; dashed lines – theoretical spectra, from which we extract the electron plasma density as well as the electron and ion temperatures in the plasma. The stated uncertainties in the retrieved plasma parameters represent the possible variation of the parameters of the theoretical fit, while still fitting well the data, as well as the shot-to-shot variations observed in the same conditions.

### Extended Data Fig. 5 Examples of plasma density and temperature measurement upstream (US) and downstream (DS) of the shock.

(a) and (c) Schematic diagram of the collective Thomson scattering (TS) diagnostic deployed at LULI2000. The measurement is performed, in a fixed volume (see Methods) through which the shock is sweeping, 4.3 mm away from the solid target surface. Panel (b) illustrates a TS measurement on the electron waves in the plasma, allowing the retrieve the local electron density and temperature, as stated. The measurement is performed 3 ns before the shock sweeps through (as illustrated in (a)). Panel (d) corresponds to the measurement performed at the same location, 1 ns after the shock has passed (as illustrated in (c)). For both panels (b) and (d), the vertical axis represents the amplitude of the scattered light; the horizontal axis represents the wavelength (λ) of the scattered light. Solid lines – experimental data profiles; dashed lines – theoretical spectra, from which we extract the electron plasma density as well as the electron temperature in the plasma. The stated uncertainties in the retrieved plasma parameters represent the possible variation of the parameters of the theoretical fit, while still fitting well the data, as well as the shot-to-shot variations observed in the same conditions.

### Extended Data Fig. 6 Maps of the magnetic field in the MHD simulations.

2 ns after the start of the plasma piston expansion inside the magnetized ambient medium. Shown are two-dimensional cross-section in the (a) xy and (b) xz planes, the latter with the corresponding magnetic field lines. The target is located on the left side of the box and the laser comes from the right side, as in the experiment. The colormap represents the strength of Bz in the unit of Tesla.

### Extended Data Fig. 7 Proton phase space evolution in the PIC simulations.

The horizontal axis (x) is the proton position and the vertical axis (vx) is the proton velocity along the x-direction. The first row corresponds to the high-velocity case with initial velocity of 1500 km/s, while the second row is for the low-velocity one with initial velocity of 500 km/s (see text for more details), at (a) & (d) 0.5 ns, (b) & (e) 1.5 ns, and (c) & (f) 2.5 ns. The colorbar represents the normalized particle number N in logarithm scale.

### Extended Data Fig. 8 Extended proton energy spectra.

(a) Energy spectrum from the experiment represented by red dots (averaged over 5 shots) with blue error bars (correspond to one sigma deviation from the average), fitted by a power-law function (purple dashed line); together with PIC simulated spectra at t = 2.6 ns (black solid line) and t = 5.1 ns (green solid line). The horizontal axis (Ep) represents the kinetic energy of the protons, while the vertical axis represents the number of protons per bin of energy (dN/dE), divided by the solid angle (dΩ) subtended by the entrance pinhole of the spectrometer (in the case of the experimental spectrum). Note that the absolute scale in proton numbers applies only to the experimental spectrum; the simulated spectra are adjusted to the experimental one. The latter is also fitted by a power-law function (green dashed line). (b) The same experimental data, as well as the simulations with and w/o collisions (green dashed line and black solid line, respectively). (c) Energy spectra of protons in cases of different B-field strength, overlaid on the same experimental data. The B-field strength is varied by varying the angle between the B-field direction (along z) and the on-axis shock propagation direction (along x) in the xz-plane.

### Extended Data Fig. 9 Extended PIC simulation results.

(a)-(e) Lineouts of density (ni) and EM fields (Bz, Ey, and Ex), as well as the corresponding phase-space distribution (Vx) at the same position and time as in Fig. 4c in the main paper, that is, from 0.4 mm to 1.2 mm at 1.5 ns, in SI units. (f) Trajectories of six randomly selected protons energized from the ambient gas in the x − t diagram, overlaid on the proton density map in the contact discontinuity reference frame; all this for a simulation run over 5.31 ns, that is, over longer time than the simulation shown in the paper.

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Yao, W., Fazzini, A., Chen, S.N. et al. Laboratory evidence for proton energization by collisionless shock surfing. Nat. Phys. 17, 1177–1182 (2021). https://doi.org/10.1038/s41567-021-01325-w

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