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Ion acceleration at two collisionless shocks in a multicomponent plasma

Rajesh Kumar, Youichi Sakawa, Takayoshi Sano, Leonard N. K. Döhl, Nigel Woolsey, and Alessio Morace
Phys. Rev. E 103, 043201 – Published 5 April 2021
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Article Text
  • INTRODUCTION
  • PARTICLE-IN-CELL SIMULATION
  • RESULTS
  • SUMMARY
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Intense laser-plasma interactions are an essential tool for the laboratory study of ion acceleration at a collisionless shock. With two-dimensional particle-in-cell calculations of a multicomponent plasma we observe two electrostatic collisionless shocks at two distinct longitudinal positions when driven with a linearly polarized laser at normalized laser vector potential a0 that exceeds 10. Moreover, these shocks, associated with protons and carbon ions, show a power-law dependence on a0 and accelerate ions to different velocities in an expanding upstream with higher flux than in a single-component hydrogen or carbon plasma. This results from an electrostatic ion two-stream instability caused by differences in the charge-to-mass ratio of different ions. Particle acceleration in collisionless shocks in multicomponent plasma are ubiquitous in space and astrophysics, and these calculations identify the possibility for studying these complex processes in the laboratory.

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    • Received 1 June 2020
    • Accepted 16 March 2021

    DOI:https://doi.org/10.1103/PhysRevE.103.043201

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Laser driven ion acceleration
    1. Techniques
    Particle-in-cell methods
    Plasma Physics

    Authors & Affiliations

    Rajesh Kumar1, Youichi Sakawa2,*, Takayoshi Sano2, Leonard N. K. Döhl3, Nigel Woolsey3, and Alessio Morace2

    • 1Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
    • 2Institute of Laser Engineering, Osaka University, Suita, Osaka 565-0871, Japan
    • 3York Plasma Institute, Department of Physics, University of York, Heslington, York YO10-5DD, United Kingdom

    • *sakawa-y@ile.osaka-u.ac.jp

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    Issue

    Vol. 103, Iss. 4 — April 2021

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    Images

    • Figure 1
      Figure 1

      The normalized initial electron density profile used in PIC simulations for a0=3.35. The laser is from the left-hand side of the simulation box. The density profile consists of an exponentially increasing 5μm scale-length laser-irradiated front region, followed by 5μm uniform central region, and an exponentially decreasing rear-side profile with 30μm scale length. To avoid boundary effects, the simulations use 40 and 100μm vacuum regions at the front and rear of the target, respectively.

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    • Figure 2
      Figure 2

      Phase-space of (a) protons and (b) C6+ ions for C2H3Cl plasma at a0=3.35 and at t=4.0 ps. The horizontal lines represent the lower threshold vLi for ion reflection and the shock velocity in proton density VshP. The color scale shows the number of ions in a log scale.

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    • Figure 3
      Figure 3

      (a) The electrostatic field Ex (left axis, blue line) and potential ϕ (right axis, red line) at t=3.0ps. The normalized proton nH/ncr (left axis, blue line) and carbon nC/ncr (right axis, red line) densities at (b) t=3.0ps and (c) t=4.0ps in C2H3Cl plasma for a0=10. Panel (a) is shown across a narrow longitudinal range compared with panels (b) and (c).

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    • Figure 4
      Figure 4

      The first and second columns indicate the ion phase-space and the velocity spectra respectively for a0=10 and at t=4.0ps. The velocity spectra are taken in the upstream region immediately in front of the shock across Δx=3μm. (a), (b) Results for protons from a single-component H plasma. (c), (d) Results for protons from a C2H3Cl plasma. (e), (f) Results for C6+ ions from a C2H3Cl plasma. (g), (h) Results for C6+ ions in single-component C plasma. The vertical lines in phase- space in panels (a), (c), (e), and (g) identify the position of the shock front. In panels (b), (d), (f), and (h), moving left to right, the dotted lines indicate the positions of the lower threshold velocity vLi, shock velocity Vshi, and the maximum velocity of the reflected ions, 2Vshi−vLi. The color scale shows the number of ions on a log scale.

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    • Figure 5
      Figure 5

      The phase space for (a) protons and (b) C6+ ions from a CH plasma for a0=10 and at t=4.0ps. The vertical lines identify the positions of the shock front associated with the protons (solid line) and the C6+ ions (dashed line). The horizontal lines indicate the positions of the lower threshold velocity vLP and shock velocity VshP of protons, and the maximum velocity of the reflected protons, 2VshP−vLP. The color scale shows the number of ions in a log scale.

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    • Figure 6
      Figure 6

      (a) The electron energy distribution taken at t=4.0ps in the upstream region of the shock front for different laser intensities corresponding to a0=3.35 (×), 10 (+), 20 (-), and 33 (|) for C2H3Cl. A sum of two (bulk and tail) 2D relativistic Maxwellian is used to fit to the electron energy distribution shown by the solid lines for a0=10, 20, and 33. The bulk (dotted line) and tail (dashed line) components for a0=33 are shown. (b) The electron temperatures as a function of a0.

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    • Figure 7
      Figure 7

      The a0 dependence of (a) shock velocities Vshi, (b) mean velocities of the expanding ions vmi, (c) ion-acoustic velocities csi, (d) difference between the shock velocity and mean velocity of the expanding ions vdfi=Vshi−vmi, and (e) the corresponding Mach number Mi=vdfi/csi at t=4.0 ps for protons in a single-component H plasma (∘), C6+ ions in a single-component C plasma (▵), and protons () and C6+ ions () in a multicomponent C2H3Cl plasma.

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    • Figure 8
      Figure 8

      (a) The temporal evolution of shock positions Xsh and shock velocities Vsh for protons in a single-component H plasma (shown in red) and a multicomponent C2H3Cl plasma (shown in blue) for a0=3.35. Xsh data are shown as open circles (a single-component H plasma: ) and open triangles (a multicomponent C2H3Cl plasma: ). The derivative of Xsh with respect to time gives Vsh. Xsh (dotted lines) and Vsh (solid lines) rise exponentially with time. (b) The temporal evolution of Xsh and Vsh for protons (shown in red) and C6+ ions (shown in blue) in a multicomponent C2H3Cl plasma for a0=33. Xsh data are shown as open circles (protons: ) and open triangles (C6+ ions: ). The time dependencies of Xsh and Vsh are best represented by a third-order (dotted lines) and second-order (solid lines) polynomials, respectively.

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    • Figure 9
      Figure 9

      The a0 dependence of (a) energy E per nucleon and (b) the number dN/dE at E of reflected protons and C6+ ions at the peak of the energy distribution at t=4.0 ps for protons in single-component H (◯), C6+ ions in single-component C (▵), and protons () and C6+ ions () in C2H3Cl plasmas.

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    • Figure 10
      Figure 10

      The spatial profile of electrostatic potentials in (a) a multicomponent C2H3Cl plasma and (b) a single-component hydrogen plasma at t=2.5 (blue curves) and 4.0 ps (red curves) for a0=3.35. The vertical lines indicate the position of the shock fronts.

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