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Register a new userMach Number Dependence of Ion-scale Kinetic Instability at Collisionless Perpendicular Shock: Condition for Weibel-dominated Shock
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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 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.
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Ion temperature anisotropy is a common feature for (quasi-)perpendicular collisionless shocks. By using two-dimensional full particle simulations, it is shown, that the ion temperature component perpendicular to the shock magnetic field at the shock foot region is proportional to the square of the Alfven Mach number divided by the plasma beta. This result is also explained by a simple analytical argument, in which the reflected ions get energy from upstream plasma flow. By comparing our analytic and numerical results, it is also confirmed that the fraction of the reflected ions hardly depends on the plasma beta and the Alfven Mach number when the square of the Alfven Mach number divided by the plasma beta is larger than about 20.
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.
Large-scale two-dimensional (2D) full particle-in-cell simulations are carried out for studying the relationship between the dynamics of a perpendicular shock and microinstabilities generated at the shock foot. The structure and dynamics of collisionless shocks are generally determined by Alfven Mach number and plasma beta, while microinstabilities at the shock foot are controlled by the ratio of the upstream bulk velocity to the electron thermal velocity and the ratio of the plasma-to-cyclotron frequency. With a fixed Alfven Mach number and plasma beta, the ratio of the upstream bulk velocity to the electron thermal velocity is given as a function of the ion-to-electron mass ratio. The present 2D full PIC simulations with a relatively low Alfven Mach number (M_A ~ 6) show that the modified two-stream instability is dominant with higher ion-to-electron mass ratios. It is also confirmed that waves propagating downstream are more enhanced at the shock foot near the shock ramp as the mass ratio becomes higher. The result suggests that these waves play a role in the modification of the dynamics of collisionless shocks through the interaction with shock front ripples.
The nature of the magnetic structure arising from ion specular reflection in shock compression studies is examined by means of 1d particle in cell simulations. Propagation speed, field profiles and supporting currents for this magnetic structure are shown to be consistent with a magnetosonic soliton. Coincidentally, this structure and its evolution are typical of foot structures observed in perpendicular shock reformation. To reconcile these two observations, we propose, for the first time, that shock reformation can be explained as the result of the formation, growth and subsequent transition to a super-critical shock of a magnetosonic soliton. This argument is further supported by the remarkable agreement found between the period of the soliton evolution cycle and classical reformation results. This new result suggests that the unique properties of solitons can be used to shed new light on the long-standing issue of shock non-stationarity and its role on particle acceleration.
Shock parameters at Earths bow shock in rare instances can approach the Mach numbers predicted at supernova remnants. We present our analysis of a high Alfven Mach number ($M_A= 27$) shock utilizing multipoint measurements from the Magnetospheric Multiscale (MMS) spacecraft during a crossing of Earths quasi-perpendicular bow shock. We find that the shock dynamics are mostly driven by reflected ions, perturbations that they generate, and nonlinear amplification of the perturbations. Our analyses show that reflected ions create modest magnetic enhancements upstream of the shock which evolve in a nonlinear manner as they traverse the shock foot. They can transform into proto-shocks that propagate at small angles to the magnetic field and towards the bow shock. The nonstationary bow shock shows signatures of both reformation and surface ripples. Our observations indicate that although shock reformation occurs, the main shock layer never disappears. These observations are at high plasma $beta$, a parameter regime which has not been well explored by numerical models.
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