Electron Surfing and Drift Accelerations in a Weibel-Dominated High-Mach-Number Shock

Yosuke Matsumoto, Takanobu Amano, Tsunehiko N. Kato, and Masahiro Hoshino

Phys. Rev. Lett. 119, 105101 – Published 8 September 2017

Abstract

How electrons get accelerated to relativistic energies in a high-Mach-number quasiperpendicular shock is presented by means of ab initio particle-in-cell simulations in three dimensions. We found that coherent electrostatic Buneman waves and ion-Weibel magnetic turbulence coexist in a strong-shock structure whereby particles gain energy during shock surfing and subsequent stochastic drift accelerations. Energetic electrons that initially experienced the surfing acceleration undergo pitch-angle diffusion by interacting with magnetic turbulence and continuous acceleration during confinement in the shock transition region. The ion-Weibel turbulence is the key to the efficient nonthermal electron acceleration.

Received 14 November 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.105101

Physics Subject Headings (PhySH)

Buneman instability Collisionless shock in plasma Laboratory studies of space & astrophysical plasmas Particle acceleration in plasmas Plasma microinstabilities Plasma turbulence Space & astrophysical plasma Space science Weibel instability

Plasma Physics

Authors & Affiliations

Yosuke Matsumoto^1,*, Takanobu Amano², Tsunehiko N. Kato³, and Masahiro Hoshino²

¹Department of Physics, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan,†
²Department of Earth and Planetary Science, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
³Center for Computational Astrophysics, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

^*ymatumot@chiba-u.jp
^†Institute for Global Prominent Research, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan.

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Issue

Vol. 119, Iss. 10 — 8 September 2017

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Images

Figure 1
The 3D structure around the shock front ( $x = 0$ ) obtained at time $T = 7.62$ from the initiation of the experiment. The structures of (a) the electron density and (b) the $y$ -component of the magnetic field are visualized by a volume rendering technique with cross-sectional profiles in the $x − y$ ( $z = 0$ ) and $x − z$ ( $y = L_{y}$ ) planes. The quantities and the spatial scale were normalized to the upstream values and upstream ion inertia length, respectively. Videos of time evolution corresponding to (a) and (b) are provided as Supplemental Material [35].
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Figure 2
(a) The selected electron’s position at $T = 7.0$ is shown with a magenta sphere with grey lines and spheres projected onto the profiles of the $x$ -component of the electric field in the ( $z = 0$ ) and $x − z$ ( $y = L_{y}$ ) planes. The trajectory back in $7.5 Ω_{g e}^{- 1}$ , where $Ω_{g e}$ is the upstream electron gyro frequency, is expressed by magenta spheres with a gradual decrease in opacity. (b) Electron trajectory at $T = 8.1$ is in the same format as (a), but with the $y$ -component of the magnetic field profiles. (c) Particle energy (Lorentz factor $γ - 1$ ) history as a function of distance in the $x$ -direction from the shock front location. The color of the line corresponds to the time shown in the color bar. (d) Time history of the particle’s momentum with respect to the local magnetic field direction. Videos of the electron’s orbit corresponding to (a) and (b) are provided as Supplemental Material [35].
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Figure 3
(a) Probability distribution in the phase space (position in $x$ and energy) for the most energetic particles during tracking in $6.8 < T < 8.8$ . The probability is color coded on a logarithmic scale. The average values for the thermal particles are plotted with error bars representing the standard deviation in each bin. (b) The average energy of the energetic particles in $0 \leq x \leq 4$ as a function of displacement in the $y$ -direction from each particle’s initial position in the upstream region ( $Δ y$ ). The energy increase rate from the motional electric field is indicated by the red dashed line. (c) The first adiabatic invariant of the energetic particles in $0 \leq x \leq 4$ as a function of $Δ y$ normalized to the upstream value using the bulk speed $V_{up}$ and the magnetic field strength $B_{0}$ . (d) Time evolution of the tracer particles’ energy distribution. The colors of the lines correspond to times in the color bar.
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Figure 4
(a) Electron phase space density in the upstream and downstream regions at $T = 7.8$ . The color and the ordinate axis of the lower energy part ( $γ - 1 < 1$ ) are in logarithmic scales. Normalized magnetic field fluctuation $⟨ | δ B | ⟩ / ⟨ | B | ⟩$ is also plotted with the red solid line referring to the right ordinate axis. Here $⟨ ⟩$ denotes the average in the $y − z$ plane and $δ B = B - ⟨ B ⟩$ . [(b) and (c)] Results from 2D simulations for the in-plane and out-of-plane upstream magnetic field cases, respectively. (d) Energy distributions in the downstream region ( $- 5.0 < x < - 4.5$ ) from the 3D (magenta line), 2D in-plane (gray line), and 2D out-of-plane (black solid line) runs. The black dashed line indicates a power-law distribution with the index of $- 3.5$ .
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