Magnetic Field Amplification by the Weibel Instability at Planetary and Astrophysical Shocks with High Mach Number

Bohdan, Artem; Pohl, M.; Niemiec, J.; Morris, Paul; Matsumoto, Yosuke; Amano, Takanobu; Hoshino, Masahiro; Sulaiman, A. H.

doi:10.1103/physrevlett.126.095101

Cited by 36 publications

(27 citation statements)

References 43 publications

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“…Perhaps, a larger growth rate driven by the unmagnetized non-gyrotropic beam will push the system into the filament merging phase before the ions behave magnetized Ω i t 1. The nonlinear evolution then becomes essentially the same as the unmagnetized plasma case, in which the magnetic field may be amplified to reach essentially the Alfvén current limit 26,27,30 . On the other hand, the saturation in most of our simulations presented in this paper occurs typically at Ω i t ∼ 1, beyond which the ions start to behave magnetized.…”

Section: Discussionmentioning

confidence: 96%

“…Oscillatory features observed in the terrestrial bow shock are sometimes attributed to the rippling mode 24,25 . More recent PIC simulations for high Mach number non-relativistic perpendicular shocks, relevant to young supernova remnant (SNR) shock, suggested that the electromagnetic fluctuations at the ion scale driven by the reflected ions are instead generated by the Weibel instability [26][27][28][29][30] . In contrast to the rippling mode, in which fluctuating magnetic field amplitudes are of the same order of the background field, the Weibel instability amplifies the magnetic field to a level much larger than the background field.…”

Section: Introductionmentioning

confidence: 99%

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Mach Number Dependence of Ion-scale Kinetic Instability at Collisionless Perpendicular Shock: Condition for Weibel-dominated Shock

Nishigai,

Amano

2021

Preprint

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We investigate ion-scale kinetic plasma instabilities at the collisionless shock using linear theory and nonlinear Particle-in-Cell (PIC) simulations. We focus on the Alfvén-ion-cyclotron (AIC), mirror, and Weibel instabilities, which are all driven unstable by the effective temperature anisotropy induced by the shockreflected ions within the transition layer of a strictly perpendicular shock. We conduct linear dispersion analysis with a homogeneous plasma model to mimic the shock transition layer by adopting a ring distribution with finite thermal spread to represent the velocity distribution of the reflected ions. We find that, for wave propagation parallel to the ambient magnetic field, the AIC instability at lower Alfvén Mach numbers tends to transition to the Weibel instability at higher Alfvén Mach numbers. The instability property is, however, also strongly affected by the sound Mach number. We conclude that the instability at a strong shock with Alfvén and sound Mach numbers both in excess of ∼ 20−40 may be considered as Weibel-like in the sense that the reflected ions behave essentially unmagnetized. Two-dimensional PIC simulations confirm the linear theory and find that, with typical parameters of young supernova remnant shocks, the ring distribution model produces magnetic fluctuations of the order of the background magnetic field, which is smaller than those observed in previous PIC simulations for Weibel-dominated shocks. This indicates that the assumption of the gyrotropic reflected ion distribution may not be adequate to quantitatively predict nonlinear behaviors of the dynamics in high Mach number shocks.

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Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Mach Number Dependence of Ion-scale Kinetic Instability at Collisionless Perpendicular Shock: Condition for Weibel-dominated Shock

Nishigai,

Amano

2021

Preprint

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“…Particle positions are updated using the Vay solver (Vay 2008). When applied to perpendicular shocks, the data from these simulations have proven to accurately reproduce the fundamental physical processes present in larger and computationally more expensive full 3D simulations (e.g., Bohdan et al 2017;Matsumoto et al 2017) and measured in situ (Bohdan et al 2020a(Bohdan et al , 2021. This version of the code also permits the tracing of individual particles, where we can track the components of their velocities and local fields, allowing for a detailed analysis of the underlying physical processes.…”

Section: Simulation Setupmentioning

confidence: 99%

Preacceleration in the Electron Foreshock. I. Electron Acoustic Waves

Morris

Bohdan

Weidl

et al. 2022

ApJ

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To undergo diffusive shock acceleration, electrons need to be preaccelerated to increase their energies by several orders of magnitude, else their gyroradii will be smaller than the finite width of the shock. In oblique shocks, where the upstream magnetic field orientation is neither parallel nor perpendicular to the shock normal, electrons can escape to the shock upstream, modifying the shock foot to a region called the electron foreshock. To determine the preacceleration in this region, we undertake particle-in-cell simulations of oblique shocks while varying the obliquity and in-plane angles. We show that while the proportion of reflected electrons is negligible for θ Bn = 74.°3, it increases to R ∼ 5% for θ Bn = 30°, and that, via the electron acoustic instability, these electrons power electrostatic waves upstream with energy density proportional to R 0.6 and a wavelength ≈2λ se, where λ se is the electron skin length. While the initial reflection mechanism is typically a combination of shock-surfing acceleration and magnetic mirroring, we show that once the electrostatic waves have been generated upstream, they themselves can increase the momenta of upstream electrons parallel to the magnetic field. In ≲1% of cases, upstream electrons are prematurely turned away from the shock and never injected downstream. In contrast, a similar fraction is rescattered back toward the shock after reflection, reinteracts with the shock with energies much greater than thermal, and crosses into the downstream.

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“…The fully kinetic Particle-in-Cell (PIC) simulation has been the most powerful tool for the purpose. Starting from early simulations in one dimension (1D) (e.g., Shimada & Hoshino 2000;Hoshino & Shimada 2002;Scholer et al 2003), recent simulations have been performed routinely in two dimensions (2D) (e.g., Amano & Hoshino 2009;Umeda et al 2012a;Tran & Sironi 2020;Bohdan et al 2021) and sometimes even in three dimensions (3D) (Matsumoto et al 2017). Similarly, in-situ measurements by spacecraft, in particular at Earth's bow shock, have been used to study the electron dynamics at collisionless shocks (Feldman et al 1982(Feldman et al , 1983Thomsen et al 1987b;Scudder et al 1986;Schwartz et al 1988).…”

Section: Introductionmentioning

confidence: 99%

Theory of Electron Injection at Oblique Shock of Finite Thickness

Amano,

Hoshino

2022

Preprint

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A theory of electron injection into diffusive shock acceleration (DSA) for the generation of cosmic-ray electrons at collisionless shocks is presented. We consider a recently proposed particle acceleration mechanism called stochastic shock drift acceleration (SSDA). We find that SSDA may be understood as a diffusive particle acceleration mechanism at an oblique shock of finite thickness. More specifically, it is described by a solution to the diffusion-convection equation for particles with the characteristic diffusion length comparable to the shock thickness. On the other hand, the same equation yields the standard DSA if the diffusion length is much longer than the thickness. Although SSDA predicts, in general, a spectral index steeper than DSA, it is much more efficient for low-energy electron acceleration and is favorable for injection. The injection threshold energy corresponds to the transition energy between the two different regimes. It is of the order of 0.1-1 MeV in typical interstellar and interplanetary conditions if the dissipation scale of turbulence around the shock is determined by the ion inertial length. The electron injection is more efficient at high M A / cos θ Bn where M A and θ Bn are the Alfvén Mach number and the shock obliquity. The theory suggests that efficient acceleration of electrons to ultra-relativistic energies will be more easily realized at high-Mach-number young supernova remnant shocks, but not at weak or moderate shocks in the heliosphere unless the upstream magnetic field is nearly perpendicular to the shock normal.

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Magnetic Field Amplification by the Weibel Instability at Planetary and Astrophysical Shocks with High Mach Number

Cited by 36 publications

References 43 publications

Mach Number Dependence of Ion-scale Kinetic Instability at Collisionless Perpendicular Shock: Condition for Weibel-dominated Shock

Mach Number Dependence of Ion-scale Kinetic Instability at Collisionless Perpendicular Shock: Condition for Weibel-dominated Shock

Preacceleration in the Electron Foreshock. I. Electron Acoustic Waves

Theory of Electron Injection at Oblique Shock of Finite Thickness

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