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Register a new userMach number and plasma beta dependence of the ion temperature perpendicular to the external magnetic field in the transition region of perpendicular collisionless 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.
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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.
The existence and properties of low Mach-number ($M gtrsim 1$) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. Using this semi-analytical model, we study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum shock potential and Mach number. We find that even a small amount of impurities can influence the shock properties significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.
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.
Strong shocks in collisionless plasmas, such as supernovae shocks and shocks driven by coronal mass ejections, are known to be a primary source of energetic particles. Due to their different mass per charge ratio, the interaction of heavy ions with the shock layer differs from that of protons, and injection of these ions into acceleration processes is a challenge. Here we show the first direct observational evidence of magnetic reflection of alpha particles from a high Mach number quasi-perpendicular shock using in-situ spacecraft measurements. The intense magnetic amplification at the shock front associated with nonstationarity modulates the trajectory of alpha particles, some of which travel back upstream as they gyrate in the enhanced magnetic field and experience further acceleration in the upstream region. Our results in particular highlight the important role of high magnetic amplification in seeding heavy ions into the energization processes at nonstationary reforming shocks.
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