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Register a new userMagnetic field amplification by the Weibel instability at planetary and astrophysical high-Mach-number shocks
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Collisionless shocks are ubiquitous in the Universe and often associated with strong magnetic field. Here we use large-scale particle-in-cell simulations of non-relativistic perpendicular shocks in the high-Mach-number regime to study the amplification of magnetic field within shocks. The magnetic field is amplified at the shock transition due to the ion-ion two-stream Weibel instability. The normalized magnetic-field strength strongly correlates with the Alfvenic Mach number. Mock spacecraft measurements derived from PIC simulations are fully consistent with those taken in-situ at Saturns bow shock by the Cassini spacecraft.
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Turbulent dynamo field amplification has often been invoked to explain the strong field strengths in thin rims in supernova shocks ($sim 100 , mu$G) and in radio relics in galaxy clusters ($sim mu$G). We present high resolution MHD simulations of the interaction between pre-shock turbulence, clumping and shocks, to quantify the conditions under which turbulent dynamo amplification can be significant. We demonstrate numerically converged field amplification which scales with Alfven Mach number, $B/B_0 propto {mathcal M}_{rm A}$, up to ${mathcal M}_{rm A} sim 150$. This implies that the post-shock field strength is relatively independent of the seed field. Amplification is dominated by compression at low ${mathcal M}_{rm A}$, and stretching (turbulent amplification) at high ${mathcal M}_{rm A}$. For high $mathcal{M}_{rm A}$, the $B$-field grows exponentially and saturates at equipartition with turbulence, while the vorticity jumps sharply at the shock and subsequently decays; the resulting field is orientated predominately along the shock normal (an effect only apparent in 3D and not 2D). This agrees with the radial field bias seen in supernova remnants. By contrast, for low $mathcal{M}_{rm A}$, field amplification is mostly compressional, relatively modest, and results in a predominantly perpendicular field. The latter is consistent with the polarization seen in radio relics. Our results are relatively robust to the assumed level of gas clumping. Our results imply that the turbulent dynamo may be important for supernovae, but is only consistent with the field strength, and not geometry, for cluster radio relics. For the latter, this implies strong pre-existing $B$-fields in the ambient cluster outskirts.
How electrons get accelerated to relativistic energies in a high-Mach-number quasi-perpendicular 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.
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 Alfven-ion-cyclotron (AIC), mirror, and Weibel instabilities, which are all driven unstable by the effective temperature anisotropy induced by the shock-reflected 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 Alfven Mach numbers tends to transition to the Weibel instability at higher Alfven 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 Alfven and sound Mach numbers both in excess of $sim 20{rm -}40$ 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.
Using large-scale fully-kinetic two-dimensional particle-in-cell simulations, we investigate the effects of shock rippling on electron acceleration at low-Mach-number shocks propagating in high-$beta$ plasmas, in application to merger shocks in galaxy clusters. We find that the electron acceleration rate increases considerably when the rippling modes appear. The main acceleration mechanism is stochastic shock-drift acceleration, in which electrons are confined at the shock by pitch-angle scattering off turbulence and gain energy from the motional electric field. The presence of multi-scale magnetic turbulence at the shock transition and the region immediately behind the main shock overshoot is essential for electron energization. Wide-energy non-thermal electron distributions are formed both upstream and downstream of the shock. The maximum energy of the electrons is sufficient for their injection into diffusive shock acceleration. We show for the first time that the downstream electron spectrum has a~power-law form with index $papprox 2.5$, in agreement with observations.
Plasma instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks may be responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated long-term particle acceleration associated with relativistic electron-ion or electron-positron jet fronts propagating into an unmagnetized ambient electron-ion or electron-positron plasma. These simulations have been performed with a longer simulation system than our previous simulations in order to investigate the nonlinear stage of the Weibel instability and its particle acceleration mechanism. The current channels generated by the Weibel instability are surrounded by toroidal magnetic fields and radial electric fields. This radial electric field is quasi stationary and accelerates particles which are then deflected by the magnetic field.
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