Yufei Hao

Formation of downstream high-speed jets by a rippled nonstationary quasi-parallel shock: 2-D hybrid simulations

Experimental observations from space missions (including more recently CLUSTER and THEMIS data) have clearly revealed the existence of high speed jets (HSJs) in the downstream region of the quasi-parallel terrestrial bow shock. Presently, two-dimensional (2-D) hybrid simulations are performed in order to investigate the formation of such HSJs through a rippled quasi-parallel shock front. The simulation results show that (i) such shock fronts are strongly nonstationary along the shock normal, and (ii) ripples are evidenced along the shock front as the upstream ULF waves (excited by interaction between incident and reflected ions) are convected back to the front by the solar wind and contribute to the rippling formation. Then, these ripples are inherent structures of a quasi-parallel shock. As a consequence, new incident solar wind ions interact differently at different locations along the shock surface, and the ion bulk velocity strongly differs locally as ions are transmitted downstream. Preliminary results show that (i) local bursty patterns of turbulent magnetic field may form within the rippled front and play the role of local secondary shock, (ii) some incident ion flows penetrate the front, suffer some deflection (instead of being decelerated) at the locations of these secondary shocks, and are at the origin of well structured (filamentary) HSJs downstream, and (iii) the spatial scales of HSJs are in a good agreement with experimental observations. Such downstream HSJs are shown to be generated by local curvature effects (front rippling) and the nonstationarity of the shock front itself.

ION DYNAMICS DURING THE PARAMETRIC INSTABILITIES OF A LEFT-HAND POLARIZED ALFVÉN WAVE IN A PROTON-ELECTRON-ALPHA PLASMA

The parametric instabilities of an Alfv´ en wave in a proton-electron plasma system are found to have great influence on proton dynamics, where part of the protons can be accelerated through the Landau resonance with the excited ion acoustic waves, and a beam component along the background magnetic field is formed. In this paper, with a one- dimensional hybrid simulation model, we investigate the evolution of the parametric instabilities of a monochromatic left-hand polarized Alfvwave in a proton-electron-alpha plasma with a low beta. When the drift velocity between the protons and alpha particles is sufficiently large, the wave numbers of the backward daughter Alfvwaves can be cascaded toward higher values due to the modulational instability during the nonlinear evolution of the parametric instabilities, and the alpha particles are resonantly heated in both the parallel and perpendicular direction by the backward waves. On the other hand, when the drift velocity of alpha particles is small, the alpha particles are heated in the linear growth stage of the parametric instabilities due to the Landau resonance with the excited ion acoustic waves. Therefore, the heating occurs only in the parallel direction, and there is no obvious heating in the perpendicular direction. The relevance of our results to the preferential heating of heavy ions observed in the solar wind within 0.3 AU is also discussed in this paper.

He2+ dynamics and ion cyclotron waves in the downstream of quasi-perpendicular shocks: 2-D hybrid simulations

The free energy provided by the ion temperature anisotropy is considered to be the source of ion cyclotron waves in the downstream of a quasi-perpendicular shock. Besides the proton cyclotron waves excited by the proton temperature anisotropy, He2 + is decelerated differentially from the protons by the shock due to its different charge-to-mass ratio and forms a bunched ring-like distribution in the immediate downstream of the quasi-perpendicular shock. However, how the helium cyclotron waves associated with the anisotropic distribution of He2 + are excited is still in debate. In this paper, with two-dimensional (2-D) hybrid simulations, we investigate He2 + dynamics and its role in the ion cyclotron waves downstream of quasi-perpendicular shocks (the proton plasma beta in the upstream is 0.4). A bunched ring-like distribution of He2 + is formed in the immediate downstream of the quasi-perpendicular shocks; then it evolves into a shell-like distribution. At last, a bi-Maxwellian distribution of He2 + is generated in the far downstream. In the medium and low Mach number shocks, besides the proton cyclotron waves excited near the shock front, there is another enhancement of the magnetic fluctuations in the downstream. The results show that the helium cyclotron waves can be driven directly by the bunched ring-like distribution of He2 + in a low or medium Mach number quasi-perpendicular shock. The relevance of our simulation results to the satellite observations is also discussed in this paper.

ION DYNAMICS AT A RIPPLED QUASI-PARALLEL SHOCK: 2D HYBRID SIMULATIONS

In this paper, two-dimensional (2-D) hybrid simulations are performed to investigate ion dynamics at a rippled quasi-parallel shock. The results show that the ripples around the shock front are inherent structures of a quasi-parallel shock, and the reformation of the shock is not synchronous along the surface of the shock front. By following the trajectories of the upstream ions, we find that these ions behave differently when they interact with the shock front at different positions along the shock surface. The upstream particles are easier to transmit through the upper part of a ripple, and the bulk velocity in the corresponding downstream is larger, where a high-speed jet is formed. In the lower part of the ripple, the upstream particles tend to be reflected by the shock. For the reflected ions by the shock, they may suffer multiple stage acceleration when moving along the shock surface, or trapped between the upstream waves and the shock front. At last, these ions may escape to the further upstream or enter the downstream, therefore, the superthermal ions can be found in both the upstream and downstream.

THE ROLE OF LARGE AMPLITUDE UPSTREAM LOW-FREQUENCY WAVES IN THE GENERATION OF SUPERTHERMAL IONS AT A QUASI-PARALLEL COLLISIONLESS SHOCK: CLUSTER OBSERVATIONS

The superthermal ions at a quasi-parallel collisionless shock are considered to be generated during the reformation of the shock. Recently, hybrid simulations of a quasi-parallel shock have shown that during the reformation of a quasi-parallel shock the large-amplitude upstream low-frequency waves can trap the reflected ions at the shock front when they try to move upstream, and then these reflected ions can be accelerated several times to become superthermal ions. In this paper, with the Cluster observations of a quasi-parallel shock event, the relevance between the large-amplitude upstream low-frequency waves and the superthermal ions (about several keV) have been studied. The observations clearly show that the differential energy flux of superthermal ions in the upstream region is modulated by the upstream low-frequency waves, and the maxima of the differential energy flux are usually located between the peaks of these waves (including the shock front and the peak of the upstream wave just in front of the shock front). These superthermal ions are considered to originate from the reflected ions at the shock front, and the modulation is caused due to the trapping of the reflected ions between the upstream waves or the upstream waves and the shock front when these reflected ions try to travel upstream. It verifies the results from hybrid simulations, where the upstream waves play an important role in the generation of superthermal ions in a quasi-parallel shock.

Reformation of rippled quasi‐parallel shocks: 2‐D hybrid simulations

One-dimensional (1-D) hybrid simulations have demonstrated that a quasi-parallel shock is non-stationary and undergoes a reformation process. Recently, two-dimensional (2-D) hybrid simulations have revealed that ripples along the shock front is an inherent property of a quasi-parallel shock. In this paper, we investigate reformation process of a rippled quasi-parallel shock with a 2-D hybrid simulation model. The simulation results show that at a rippled shock, incident particles behave differently and just can be partially reflected at some specific locations along the rippled shock front, and the reflected particles will form an ion beam that moves back to the upstream along the magnetic field. Then, the beam locally interacts with upstream waves, and the waves are enhanced and finally steepen into a new shock front. As the upstream incident plasma moves to the shock front, the new shock front will approach and merge with the old shock front. Such a process occurs only before these locations along the shock front, and after the merging of the new shock front and old shock front is finished, a relatively plane shock front is formed. Subsequently, a new rippled shock front is again generated due to its interaction with the upstream waves, and it will repeat the previous process. In this pattern, the shock reforms itself quasi-periodically, at the same time, ripples can shift along the shock front. The simulations present a more complete view of reformation for quasi-parallel shocks.

Effects of alpha beam on the parametric decay of a parallel propagating circularly polarized Alfven wave: Hybrid simulations

Alfven waves with a finite amplitude are found to be unstable to a parametric decay in low beta plasmas. In this paper, the parametric decay of a circularly polarized Alfven wave in a proton-electron-alpha plasma system is investigated with one-dimensional (1-D) hybrid simulations. In cases without alpha particles, with the increase of the wave number of the pump Alfven wave, the growth rate of the decay instability increases and the saturation amplitude of the density fluctuations slightly decrease. However, when alpha particles with a sufficiently large bulk velocity along the ambient magnetic field are included, at a definite range of the wave numbers of the pump wave, both the growth rate and the saturation amplitude of the parametric decay become much smaller and the parametric decay is heavily suppressed. At these wave numbers, the resonant condition between the alpha particles and the daughter Alfven waves is satisfied, therefore, their resonant interactions might play an important role in the supp...

Two-dimensional Hybrid Simulations of Filamentary Structures and Kinetic Slow Waves Downstream of a Quasi-parallel Shock

In this paper, with two-dimensional (2-D) hybrid simulations, we study the generation mechanism of filamentary structures downstream of a quasi-parallel shock. The results show that in the downstream both the amplitude of magnetic field and number density exhibit obvious filamentary structures, and the magnetic field and number density are anticorrelated. Detailed analysis find that these downstream compressive waves propagate almost perpendicular to the magnetic field, and the dominant wave number is around the inverse of ion kinetic scale. Their parallel and perpendicular components roughly satisfies(where and represent the parallel and in-plane perpendicular components of magnetic field, is the wave number in the perpendicular direction, and in the ion gyroradius), and their Alfven ratio also roughly agree with the analytical relation (where and indicate the Alfven ratio and plasma beta), while the corresponding cross helicity and compressibility show good agreement with previous theoretical calculations. All these properties are consistent with those of kinetic slow waves (KSWs). Therefore, we conclude that the filamentary structures in the downstream of a quasi-parallel shock are produced due to the excitation of KSWs.

Parametric decay of oblique whistler waves in the Earth's magnetosphere: 2-D PIC simulations

Whistler mode waves in the Earths magnetosphere have already been widely investigated in the linear or quasi-linear regime, but there is still lack of research on nonlinear physical processes. In this paper, with a 2-D PIC simulation model, we have studied the parametric decay of oblique whistler waves for the first time. The parametric decay of an oblique whistler wave first occurs along its propagating direction, which involves a backward daughter whistler wave and a forward ion acoustic mode. This is quite similar to the parametric decay of parallel whistler waves in 1-D simulations. Interestingly, the parametric decay will then take place along the perpendicular direction, which can generate a family of daughter whistler waves along the perpendicular direction with the nearly same parallel wave number. Meanwhile, the highly oblique whistler waves will also be excited during this perpendicular decay, whose wave normal angle can even reach up to the resonant cone angle. Moreover, the parametric decay tends to be stronger for the pump whistler wave with a larger frequency or larger amplitude. But the growth rate of the parametric decay has little change when the wave normal angle of the pump whistler wave varies within a limited range. Interestingly, parallel whistler waves can also experience the similar decay process, which may suggest that the parametric decay of whistler waves should be a multi-dimensional process in nature. During the decay process, the generated ion acoustic waves can accelerate a part of protons through the Landau resonance. Our simulation results not only uncover the evolution pattern of whistler waves during the parametric decay in a two-dimensional regime but also propose a potential nonlinear physical process related to whistler waves in the Earths magnetosphere.