Quasi-parallel Collisionless Shocks Research Articles

Nonthermal Acceleration of Electrons, Positrons, and Protons at a Nonrelativistic Quasi-parallel Collisionless Shock

Energetic positrons have been observed in the interstellar medium, and high-energy positrons with relativistic energies up to approximately 1 TeV have been detected in Galactic cosmic rays. We conducted a study on the acceleration of particles, specifically positrons, in a nonrelativistic quasi-parallel collisionless shock induced by a plasma consisting of protons, electrons, and positrons. The positron-to-proton number density ratio in the plasma is 0.1. We focused on a representative shock with a sonic Mach number of 17.1 and an Alfvénic Mach number of 16.8 in the rest frame of the shock. To investigate the acceleration mechanisms of particles including positrons in the shock, we utilized 1D particle-in-cell simulations. It was found that all three species of particles in the shock can be accelerated and exhibit power-law spectra. At the shock front, a significant portion of incoming upstream particles are reflected and undergo significant energy increases, and these reflected particles can be efficiently injected into the process of diffusive shock acceleration (DSA). Moveover, the reflected positrons can be further accelerated by an electric field parallel to the magnetic field when they move along the magnetic field upstream of the shock. As a result, positrons can be preferentially accelerated to be injected in the DSA process compared to electrons.

Structure of a Quasi-parallel Shock Front

The aim of this study is to compare observations of the magnetic field structure of observed quasi-parallel collisionless shock fronts with the results obtained analytically. A two-fluid analytic model of the shock front structure was derived under the assumptions that the shock is stationary and planar. The ion and electron kinetic pressures were assumed to be scalar, and polytropic state equations were used. The results of this analytical approach show that the shock magnetic field has an oscillatory structure. Venus Express (VEX) observations of the Venusian bow shock have been used to validate these theoretical findings. The Venusian bow shock and corresponding foreshock are significantly smaller than those of Earth. Thus, observations of the underlying structure of the quasi-parallel shock at Venus are not masked by the presence of high-amplitude waves and nonlinear structures originating in the foreshock. It is shown that the structure of the shock front, as observed by VEX, has a very strong similarity to the structure obtained analytically.

On the distribution function of suprathermal particles at collisionless shocks

The departure of particle distributions from the Maxwellian is commonly observed in space plasmas. These non-Maxwellian distributions which are typical for plasmas that are not in thermal equilibrium, can be modeled with κ-distribution. Kinetic simulations of quasi-parallel collisionless shocks show that proton distribution is a composite of thermal, suprathermal, and non-thermal parts. By using particle-in-cell shock simulations, we show that κ-distribution adequately fits thermal and suprathermal parts together, as a single continuous distribution in early proton spectra. We derive suprathermal proton distribution directly from the generalized entropy of non-extensive statistical mechanics, and show that thermal and suprathermal populations are both naturally embedded in κ-distribution. We find that the index κ of the distribution increases with the distance from the shock, following the decrease in suprathermal part. The non-equilibrium plasma distribution which is continuously being enriched with suprathermal particles at the reforming shock barrier, reaches the thermal equilibrium in the far downstream. The suprathermal part completely fades there, and the shape of proton distribution becomes a Maxwellian from which directly emerges a power-law.

Simulation of Accelerated Particle Diffusion in Collisionless Shocks with an Admixture of Heavier-than-Hydrogen Ions

We report on the results of hybrid simulation of diffusive shock acceleration of ions with different charge-to-mass ratios in quasi-parallel collisionless shocks. We consider a hydrogen medium with dynamically insignificant admixtures of helium and carbon ions in various charge states. Spatial regions of applicability of the Bohm approximation as well as the quasi-linear diffusion theory are determined. The possibility of nondiffusive propagation in regions far ahead of the shock is considered.

PIC Simulation of a quasi-parallel collisionless shock: Interaction between upstream waves and backstreaming ions

We perform a one-dimensional full particle-in-cell (PIC) simulation of a quasi-parallel collisionless shock with the Alfvén Mach number 6.6 and a shock angle of 20 degrees between the upstream magnetic field and the shock normal direction. The backstreaming ions are self-consistently generated by reflections of the incoming ions at the shock. They generate the Alfvénic electromagnetic wave via the right-handed resonant ion-ion instability, as the ions travel toward the upstream region. The energy distribution of the backstreaming ions far upstream splits into two populations as it approaches the shock. The energy threshold of the populations is approximately the energy gained by a single specular reflection at the shock. The maximum energy of the backstreaming ions near the shock is about 10 times larger than the specularly reflected ion energy. Nonlinear phase bunches of the high-energy backstreaming ions and the background ions are found near the shock, due to the resonant and non-resonant trappings by the excited waves, respectively.

Resonant micro-instabilities at quasi-parallel collisionless shocks: Cause or consequence of shock (re)formation

A case of two interpenetrating, cold and quasi-neutral ion-electron plasmas is investigated with the multi-fluid approach. We consider that one plasma flows quasi-parallel to the lines of a background magnetic field embedded in another static plasma. If the flow turns super-Alfvénic, we show that parallel R/L-modes and perpendicular X/O-modes become unstable and grow in amplitude. Within the linear theory, we find that the growth rate curve of an unstable mode has a maximum at some wavenumber specific to each mode. If we consider a shock-like plasma configuration, we find that the fastest growing mode is the resonant one (with k∼rgi−1) which strongly interacts with ions. In Particle-In-Cell (PIC) simulations, we observe that a resonant wave with the same properties is excited during the early phases of shock formation. Once the wave becomes non-linear, it efficiently scatters ions and triggers the initial shock formation. This implies that the typical compression ratio of ∼4 could naturally arise as a consequence of a highly resonant micro-physical process. We model the interaction of ions reflected from the reforming shock barrier in a weak-beam case, and we show that the upstream wave now matches the instability we expect from the equations. By using PIC simulations, we explain how the strong-beam resonant instability triggers shock formation in the non-linear stage, and how the weak-beam instability reforms and transmits the shock afterwards. The micro-instabilities that we study here could largely contribute to shock triggering as well as to the reformation and transmission of the shock itself.

The Acceleration of Thermal Ions at a Strong, Quasi-Parallel Interplanetary Shock: A Hybrid Simulation

Using a self-consistent hybrid simulation, with kinetic protons and fluid electrons, we investigate the acceleration of thermal protons and minor ions (alphas, 3He++, and C5+) by a quasi-parallel collisionless shock. The results are compared to spacecraft observations of a strong interplanetary shock seen by the Advanced Composition Explorer on DOY 94, 2001, which was associated with significant increases in the flux of > 50 keV/nuc ions. Our simulation uses similar plasma and shock parameters to those observed. The densities of minor ions for two of the species (alphas and C5+) were based on observations at thermal energies for this shock, and we used a nominal value for the density of 3He++, since no observations at thermal energies was available to us. Acceleration of the ions by the shock leads to a high-energy tail in the distribution in the post-shock plasma for all ion species. We find that by extrapolating the simulated tails to the higher energies measured by ACE/EPAM and ACE/ULEIS, the intensity matches well the observations for protons, alphas, and carbon. This suggests that thermal solar wind, accelerated directly at the shock, is a significant source of the observed high-energy protons and these minor ions.

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

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.

Observations of energetic particles in the upstream of a quasi-parallel collisionless shock

通过Cluster卫星在2005年3月16日观测到的一个准平行激波观测事例，研究了准平行激波上游低频等离子体波动与能量离子之间的关系.卫星观测结果表明，在准平行激波上游，离子微分能通量受到了非线性波动的调制.在磁场强度较小区域，离子微分能通量较高.产生这种现象的可能原因是准平行激波上游的非线性波动可以捕获离子，被捕获的离子在波动中来回弹跳并被电场加速，从而导致磁场强度较小区域离子微分能通量较高.这一观测结果与已有的混合模拟结果相吻合.

High-energy Nd:glass laser facility for collisionless laboratory astrophysics

A kilojoule-class laser (Raptor) has recently been activated at the Phoenix-laser-facility at the University of California Los Angeles (UCLA) for an experimental program on laboratory astrophysics in conjunction with the Large Plasma Device (LAPD). The unique combination of a high-energy laser system and the 18 meter long, highly-magnetized but current-free plasmawill support a new class of plasma physics experiments, including the first laboratory simulations of quasi-parallel collisionless shocks, experiments on magnetic reconnection, or advanced laser-based diagnostics of basic plasmas. Here we present the parameter space accessible with this new instrument, results from a laser-driven magnetic piston experiment at reduced power, and a detailed description of the laser system and its performance.

Hemispherical transport equation: modeling of quasiparallel collisionless shocks

Using a so-called hemispherical model we derive a general transport equation for cosmic ray and thermal particles scattered in pitch angle by magnetic inhomogeneities in a moving collisionless plasma. The weak scattering through 90 degrees results in isotropic particle distributions in each hemisphere. The consideration is not limited by small anisotropies and by the condition that particle velocities are higher than characteristic flow velocity differences. For high velocities and small anisotropies the standard cosmic ray transport equation is recovered. We apply the equations derived for investigation of injection and acceleration of particles by collisionless shocks.

Wave-Number Spectra and Intermittency in the Terrestrial Foreshock Region

Wave-number spectra of magnetic field fluctuations are directly determined in the terrestrial foreshock region (upstream of a quasiparallel collisionless shock wave) using four-point Cluster spacecraft measurements. The spectral curve is characterized by three ranges reminiscent of turbulence: energy injection, inertial, and dissipation range. The spectral index for the inertial range spectrum is close to Kolmogorov's slope, -5/3. On the other hand, the fluctuations are highly anisotropic and intermittent perpendicular to the mean magnetic field direction. These results suggest that the foreshock is in a weakly turbulent and intermittent state in which parallel propagating Alfvén waves interact with one another, resulting in the phase coherence or the intermittency.

Excited Low Frequency Waves by Beam Plasma in Upstream of Collisionless Shock and Their Effect on Dissipation of Shock

由于很大一部分来自激波上游的粒子被激波面所反射,因此在准平行无碰撞激波的上游存在着等离子体束流.通过一维混合模拟方法,计算了束流密度较小(nb/n0=0.02)和较大(nb/n0=0.2)两种不同情形下的等离子体束流不稳定性.结果表明,在束流密度较小时,束流激发的主要是平行于背景磁场方向传播的右旋波,此波动只能对束流粒子产生影响,包括减速和加热.在束流密度较大时,束流可同时激发平行和反平行于背景磁场方向传播的右旋波,除能对束流粒子产生影响外,还可通过非共振作用加速和加热背景粒子.文中对准平行无碰撞激波耗散机制的影响也进行了讨论.

On ion injection at quasiparallel shocks

A large number of numerical experiments has been performed in order to study the interaction of interstellar pickup protons and helium ions with quasiparallel collisionless shocks. The shocks are modeled by a one-dimensional hybrid simulation method which treats the ions as macroparticles and the electrons as a massless fluid. Solar wind alpha particles and pickup protons are included self-consistently. In addition, the particle splitting method is used for the solar wind ions so that the distribution function can be followed over more than 10 orders of magnitude. A large part of the pickup ion distribution is reflected; the reflection efficiency is very high, and can reach in cases where the pickup ion density is low as much as 50%–60%. The reflection efficiency is almost independent of magnetic field–shock normal angle. This indicates that magnetic mirroring is unimportant and does not lead to larger reflection efficiencies. The reflection efficiency of pickup protons rapidly decreases when the pickup ion density exceeds a few percent of the solar wind density. An addition of 25% pickup protons decreases the reflection coefficient for these ions to ∼10%. This represents the fact that a quasiparallel shock cannot be considered as being uncoupled from the upstream region: at high additions of pickup ions the shock structure is changed in such a way as to reflect less pickup ions. The intensity of diffuse ions upstream of a quasiparallel shock does not depend on the temperature of the core distribution. Within the framework of the present model even solar wind distributions with a hard power law tail do not produce higher intensities of diffuse ions. It is argued that this can be understood by the fact that the intrinsic self-consistency between the processes in the upstream region and at the shock transition determines the injection and reflection properties of the core solar wind distribution.

Injection and acceleration of H<sup>+</sup> and He<sup>2+</sup> at Earth's bow shock

Abstract. We have performed a number of one-dimensional hybrid simulations (particle ions, massless electron fluid) of quasi-parallel collisionless shocks in order to investigate the injection and subsequent acceleration of part of the solar wind ions at the Earth's bow shock. The shocks propagate into a medium containing magnetic fluctuations, which are initially superimposed on the background field, as well as generated or enhanced by the electromagnetic ion/ion beam instability between the solar wind and backstreaming ions. In order to study the mass (M) and charge (Q) dependence of the acceleration process He2+ is included self-consistently. The upstream differential intensity spectra of H+ and He2+ can be well represented by exponentials in energy. The e-folding energy Ec is a function of time: Ec increases with time. Furthermore the e-folding energy (normalized to the shock ramming energy Ep) increases with increasing Alfvén Mach number of the shock and with increasing fluctuation level of the initially superimposed turbulence. When backstreaming ions leave the shock after their first encounter they exhibit already a spectrum which extends to more than ten times the shock ramming energy and which is ordered in energy per charge. From the injection spectrum it is concluded that leakage of heated downstream particles does not contribute to ion injection. Acceleration models that permit thermal particles to scatter like the non-thermal population do not describe the correct physics.Key words. Interplanetary physics (planetary bow shocks) · Space plasma physics (charged particle motion and acceleration; numerical simulation studies)

Waves associated with quasi-parallel shocks: Generation, mode conversion and implications

Ions that are energized at quasi-parallel collisionless shocks and move back upstream generate low-frequency waves, largely on the fast/magnetosonic branch. At sufficient Mach number, the waves are convected back into the shock, lead to shock re-formation, and are mode-converted into downstream (magnetosheath) Alfvénic turbulence. Other waves are generated more locally at the interface of the incoming solar wind and the partially thermalized plasma. This paper reviews how recent simulation studies of collisionless shocks in conjunction with linear kinetic theory and proper wave diagnostics have aided in our understanding of the upstream and magnetosheath waves.

Shock waves in the solar corona and their radio emission

In the solar corona shock waves can be generated by coronal mass ejections and/or solar flares. They manifest themselves in solar type II radio bursts. A sample of 25 such radio bursts is investigated concerning their spectral features. Assuming that the type II burst radiation is generated in the vicinity of the transition region of coronal shock waves as indicated by plasma wave measurements at interplanetary shock waves the instantaneous bandwidth reflects the density jump of the shock. Comparing the observational results with the evaluation of the Rankine-Hugoniot relations of MHD shock waves solar type II bursts should be regarded as being generated by weak supercritical, quasi-parallel fast magnetosonic shock waves in the solar corona. As well-known from Earth's bow shock, quasi-parallel collisionless shocks are associated by strong magnetic field turbulence, e.g., in form of short large amplitude magnetic field structures (SLAMS). Assuming that these features also appear at quasi-parallel shock waves in the solar corona, electrons can be accelerated at such shock waves due to drift acceleration within SLAMS up to suprathermal energies. These electrons are able to excite Langmuir waves which can convert into radio waves observed as solar type II bursts.

2D hybrid simulations of short large-amplitude magnetic structures (SLAMS) upstream of quasi-parallel collisionless shocks

The development of turbulence under the energy feed of diffuse backstreaming ions upstream of quasi-parallel (QP) shocks is investigated using two-dimensional (2D) hybrid simulations involving the injection of a very hot ion beam against a cold incident ion flow. The waves attempt to propagate upstream but are convected back toward the shock by the incident flow and strongly grow in amplitude as they encounter larger beam densities. Pulsations are formed which are very similar to the short large amplitude magnetic structures (SLAMS) observed upstream of the Earth's bow shock. It is shown that SLAMS induce slowing and heating of the incident flow and play an active role in the shock transition.

On the origin of short large‐amplitude magnetic structures upstream of quasi‐parallel collisionless shocks

In order to model the development of the turbulence upstream of quasi‐parallel shocks, one‐dimensional hybrid simulations have been performed of the injection of a very hot ion population into a cold incident flow. ULF electromagnetic waves are initially generated in the right‐hand resonant ion beam mode. As these waves are convected to the injection source and encounter larger beam densities, they grow in amplitude and scatter the beam ions. Beam ion clumps characterized by distributions with a significant fraction of ions having velocities antiparallel to the beam bulk velocity are generated, and destabilize the left‐hand resonant ion beam mode. This process enables the formation of enhanced magnetic field structures which, like the short large‐amplitude magnetic structures (SLAMS) observed upstream of the quasi‐parallel Earth's bow shock, show scale lengths smaller than the ULF waves wavelength, have magnetic amplitudes up to a few times the ambient magnetic field, are left‐hand polarized in the plasma rest frame, and often possess attached whistler waves.

Upstream waves, shocklets, short large‐amplitude magnetic structures and the cyclic behavior of oblique quasi‐parallel collisionless shocks

The re‐formation process of more oblique quasi‐parallel shocks is investigated using one‐dimensional hybrid simulations. Several types of simulations have been performed. The simulation of a shock with a magnetic field‐shock normal angle of 30° shows that a more oblique quasi‐parallel shock exhibits reformation cycles with a larger length scale, that is of about 20 ion inertial lengths. This is considerably larger than the distance specularly reflected ions are able to propagate upstream before they are deflected so that their velocity in the shock normal direction is close to zero. These cycles are due to steepening and growth of upstream waves into pulsationlike structures when they are convected into the region of strongly increasing diffuse ion density immediately upstream of the shock. When the steepening wave packet crashes into the shock, the shock ramp dispersively radiates whistler waves into the region between the shock ramp and the approaching wave, while the steepening of the pulsation leads to phase standing whistler waves on the upstream side. Entropy production occurs either at the shock ramp or at the upstream edge of the pulsation when the steepening process has produced a large kink in the magnetic field and is due to nonadiabatic motion of the incident solar wind ions. In order to analyze the wave steepening, upstream waves have been isolated, and their subsequent interaction with a hot, tenuous ion beam representing the diffuse backstreaming ions has been studied. When an upstream wave is convected into or a region with increasing hot beam density, the wave steepens and becomes a pulsationlike wave packet. In order for the wave to grow to a pulsationlike structure the characteristic scale length of the density increase has to be of the same order as the wavelength of the original magnetosonic wave. Similar results are obtained when counterstreaming beam of hot ions is injected into a solar wind which does not initially contain a wave field. In this case the polarization of the pulsations depends on the hot beam temperature. The strong density increase of hot beam ions in these simulations is due to the steady injection of beam ions in a solar wind with an embedded field which is inclined relative to the solar wind direction. In the shock simulation the shock itself is the steady source of the hot backstreaming ions. These simulations suggest that upstream waves, shocklets, and short large‐amplitude magnetic structures are all the same entity in different stages of their development and play a crucial role in re‐forming oblique quasi‐parallel shocks.