Collisionless shock in a laser-produced ablating plasma

The Earth’s bow shock is the best-known collisionless shock in space. Although much is known about the bow shock, the mechanisms of heating and thermalization processes still remain poorly understood. Collisionless shocks are different from ordinary fluid shocks, because a fraction of the incident solar wind is reflected from the bow shock and the transmitted particles are not immediately thermalized. The reflected particles interact with the incident solar wind producing waves and instabilities that can heat and accelerate particles to high energies. Some of the waves can grow to large amplitudes such as Short Large Amplitude Magnetic Structures. Other upstream nonlinear structures include hot flow anomalies and density holes. The upstream nonlinear structures subsequently convect Earthward with the SW and could impact the structure and dynamics of the bow shock. These observations have clearly indicated that the upstream dynamics are an integral part of the bow shock system. Although much has been learned about the behavior of Earth’s bow shock dynamics from the existing data, many fundamental questions remain not answered. This article will review observations of ion dynamics of Earth’s bow shock system, what we have learned from recent and past observations. We provide new perspectives from multi-spacecraft Cluster observations about the spatial and temporal variations including the fundamental shock heating, acceleration, and entropy generation processes.

In strictly collisionless electrostatic shocks, the ion distribution function can develop discontinuities along phase-space separatrices, due to partial reflection of the ion population. In this paper, we depart from the strictly collisionless regime and present a semi-analytical model for weakly collisional kinetic shocks. The model is used to study the effect of small but finite collisionalities on electrostatic shocks, and they are found to smooth out these discontinuities into growing boundary layers. More importantly, ions diffuse into and accumulate in the previously empty regions of phase space, and, by upsetting the charge balance, lead to growing downstream oscillations of the electrostatic potential. We find that the collisional age of the shock is the more relevant measure of the collisional effects than the collisionality, where the former can become significant during the lifetime of the shock, even for weak collisionalities.

Collisionless shocks are considered as one of the most efficient phenomena for the electron acceleration in space and astrophysical plasmas, yet the detailed acceleration process and heating mechanism remain unsolved. Various acceleration and heating mechanisms have so far been proposed and discussed to explain the spacecraft measurements in situ at Earth’s bow shock, involving the large-scale electromagnetic fields, plasma turbulence, and wave-particle interactions. A key element of the acceleration and heatingmechanisms is the spatial scale of the shock transition with respect to the gyro-radius of the electrons [1]. In the simplest picture, since the shock transition occurs on a spatial scale of ion gyro-radius, the electrons behave as magnetized at the shock transition. The cross-shock potential (electrostatic potential drop across the shock transition) plays two distinct roles in electron dynamics [2]. First, the cross-shock potential reduces a certain amount of the upstream flow kinetic energy (mostly carried by the ions due to their mass); Second, the kinetic energy is used to heat the electrons (DC heating). On the other hand, the electrons can also be scattered (or demagnetized) by high-amplitude, randomly-oscillating electromagnetic fields such as turbulence or strong inhomogeneities (AC heating). Space turbulence can potentially scatter the electrons randomly leaving upstream or downstream of the shock ramp region. For a quasiperpendicular shock, the electrons become scattered in a non-adiabatic sense perpendicular to the mean magnetic field (Figure 1). In this paper, the adiabaticity in collisionless shocks is addressed to the studies based on particlein-cell-simulation (PIC). Two important parameters enter a PIC simulation carried out for the study of a collisionless shock: the mass ratio mp/me between ions and electrons and the ratio of the electron plasma frequency to gyrofrequency ωpe/ce, see e.g., [3]. Due to the computational limitations, the usage of the realistic values for the both parameters is not yet possible. The common way to overcome this problem is to find a compromise for the two parameters that can mostly optimize the purpose of the study. The impact of using low frequency ratio of the electron plasma frequency to gyrofrequency in numerical simulations has been discussed in Krasnoselskikh et al. [4]: the electric field is considerably overestimated than it should be for a comparison with the Earth bow shock. Here, I address the question, “What is the consequence of using a smaller frequency ratio upon the adiabatic motion of the electrons”?

This thesis presents an experimental investigation carried out to study penetration and fragmentation of liquid injected into Mach 6 hypersonic cross flow. Flow topology, shock and vortex systems, fragmentation and atomization mechanisms are investigated using high-speed photography, Schlieren photography, flow visualization and Phase Doppler Interferometry techniques. All experiments are conducted at the H-3 Mach 6 wind tunnel facility of the von Karman Institute. Water is used for all tests. Freestream conditions of air flow are kept constant. The variation of the injector geometry and the effect of momentum flux ratio are studied throughout the experimental campaign. Droplet size measurements are analyzed and treated to characterize the atomization process of the liquid jet. The Sauter Mean Diameter and the standard deviation of the droplet size distribution are calculated and presented as a function of location and momentum flux ratio. The obtained Sauter Mean Diameter distribution is compared with the theory available in the literature for lower cross flow speed cases. The whipping phenomenon observed for the low momentum flux ratio liquid injections is explained by frequency maps, which allow one to see the flow domains with similar frequency content. This analysis proposes that the penetration of liquid jet determines the shape of the bow shock, which determines the location and angle of the separation shock. The separation shock is observed to penetrate into liquid phase, playing an important role in fragmentation of liquid, thus changing the penetration height and the shape of the bow shock. A continuous interaction between the liquid penetration, bow shock, separation shock and liquid fragmentation is believed to be the mechanism responsible of the whipping phenomenon. The fragmentation of liquid exposed to Mach 6 air flow is also investigated. Experiments are conducted using water-filled balloons mounted on sharp and blunt leading edge supports. The water-filled balloons are exposed to Mach 6 air flow and high speed camera measurements are taken during the bursting of the balloon, to study the fragmentation of water. Shock patterns and flow topology are visualized by Schlieren photography.

A thorough understanding of collisionless shocks requires knowledge of how different ion species are accelerated across the shock. We investigate a bow shock crossing using the Magnetospheric Multiscale spacecraft after a coronal mass ejection crossed Earth, which led to solar wind consisting of protons, alpha particles, and singly charged helium ions. The three species are resolved upstream of the shock. The low Mach number of the bow shock enabled the ions to be partly distinguished downstream of the shock due to the relatively low ion heating. Some of the protons are specularly reflected and produce quasi‐periodic fine structures in the velocity distribution functions downstream of the shock. Heavier ions are shown to transit the shock without reflection. However, the gyromotion of the heavier ions partially obscures the fine structure of proton distributions. Additionally, the calculated proton moments are unreliable when the different ion species are not distinguished by the particle detector. The need for high time‐resolution mass‐resolving ion detectors when investigating collisionless shocks is discussed.

Using test particle trajectories in a simplified model of a supercritical, oblique, collisionless shock, we investigate the interaction of solar wind thermal ions with the earth's bow shock. We present results for shocks with shock angle (θBn) between 35° and 60° and show that their velocity space signatures are consistent with observations of many upstream ion events, particularly gyrating ions and field‐aligned ion beams. The shock is modeled as a finite, planar discontinuity in the magnetic field and in the electrostatic potential, which is also given an overshoot at the shock. We find that the shock can produce backstreaming ions by reflecting a small fraction of the incident distribution. The reflected particle trajectories are of three types: specularly reflected, multiple traversal, and multiple bounce. All backstreaming reflected ions are found to suffer specular reflection on their first encounter with the shock surface; their subsequent behavior is determined by the angle θBn and their initial conditions.

We present a statistical analysis of large-amplitude bipolar electrostatic structures measured by the Magnetospheric Multiscale spacecraft in the Earth's bow shock. The analysis is based on 371 large-amplitude bipolar structures collected in nine supercritical quasi-perpendicular Earth's bow shock crossings. We have found that 361 of the bipolar structures have negative electrostatic potentials, and only 10 structures (> 1, a parameter range typical of collisionless shocks in the heliosphere and various astrophysical environments. This analysis indicates that the original mechanism of electron surfing acceleration involving electron phase space holes is not likely to be efficient in realistic collisionless shocks.

The possibility of a collisionless shock in a plasma not subject to electrostatic instabilities nor immersed in a permanent magnetic field is investigated. The equations governing a steady shock in an electron-ion plasma are deduced and their limitations are discussed. Attention is given to the fact that the velocity distribution in a collisionless plasma may not be Maxwellian. This yields a parameter which is a measure of high-energy particle density. It is found that almost always no steady shock exists. The inverse of the electron plasma wave-number k0=ωp/c provides a scale length for the shock, though the dampening effect of the ions indicates a shock thickness much in excess of . It is concluded that the mechanism for such shocks may be important in a gas such as the solar wind.

Collisionless shock acceleration, which transfers localized particle energies to nonthermal energetic particles via electromagnetic potential, is ubiquitous in space plasma. We investigate dynamics of collisionless electrostatic shocks that appear at the interface of two plasma slabs with different pressures using one-dimensional particle-in-cell (PIC) simulations and find that the shock structure transforms to a double-layer structure at the high density gradient. The threshold condition of the structure transformation is identified as density ratio of the two plasma slabs Γ∼40 regardless of the temperature ratio between them. We then update the collisionless shock model that takes into account density expansion effects caused by a rarefaction wave to improve the prediction of the critical Mach numbers. These critical Mach numbers are benchmarked by PIC simulations for a wide range of Γ. Furthermore, we introduce a semianalytical approach to forecast the shock velocity just from the initial conditions based on a concept of the accelerated fraction α.

Laser-driven collisionless electrostatic shock formation and the subsequent ion acceleration have been studied in near critical density plasmas. Particle-in-cell simulations show that both the speed of laser-driven collisionless electrostatic shock and the energies of shock-accelerated ions can be greatly enhanced due to fast laser propagation in near critical density plasmas. However, a response time longer than tens of laser wave cycles is required before the shock formation in a near critical density plasma, in contrast to the quick shock formation in a highly overdense target. More important, we find that some ions can be reflected by the collisionless shock even if the electrostatic potential jump across the shock is smaller than the ion kinetic energy in the shock frame, which seems against the conventional ion-reflection condition. These anomalous ion reflections are attributed to the strong time-oscillating electric field accompanying the laser-driven collisionless shock in a near critical density plasma.

The present conference on heliospheric collisionless shocks considers such macrostructure-, microstructure-, and particle acceleration-related topics as interplanetary shock phenomena near and within 1 AU, as well as beyond, planetary bow shocks, shock formation and evolution in the solar atmosphere, MHD and gasdynamic theories for planetary bow waves, and subcritical collisionless shock waves. Also discussed are ion reflection, gyration, and dissipation at supercritical shocks, the numerical simulation of quasi-perpendicular collisionless shocks, electron distributions near collisionless shocks, the microtheory of collisionless shock current layers, plasma waves and instabilities, the electron foreshock, upstream suprathermal ions, and both diffusive and shock drift acceleration.

In collisionless magnetosonic shock waves, ions are commonly thought to be decelerated by a dc electrostatic cross‐shock electric field along the shock normal , where γ is the effective polytrope index for electrons. By observation this ratio is ∼1/10 at the earth’s bow shock. When viewed in the de Hoffman‐Teller frame, corresponding changes in the ion kinematics occur. Since the e[ϕ*HT] is an order of magnitude smaller than the ion energy, the ions are not significantly affected by the electrostatic force. They are instead primarily retarded in this frame by the magnetic force. Since this latter force is proportional to the component of B out of the coplanarity plane, infinitesimally thin shock models may not be realistic for the study of the ion and electron dynamics in the de Hoffman‐Teller frame.

The electron heating at collisionless shocks in near‐Earth space is normally found to be relatively small. We report here on two sets of bow shock crossings observed by the ISEE 1 and ISEE 2 spacecraft in which very large electron temperature increases were found. The two sets of shocks are part of a larger set of 52 bow shock crossings compiled from the ISEE data set. When the shocks with the large electron heating are compared to the rest of the shocks in the compiled set, it is found that the only upstream parameter which is out of the ordinary is the upstream solar wind flow speed Vu. Indeed, for the entire shock set the only upstream parameters which correlate well with the electron heating are the solar wind speed and quantities derived from it. The best correlation among those tested is between the temperature increase (Ted ‐ Teu) and the difference in the square of the bulk flow speed (Vu² ‐ Vd²) across the shock, which is proportional to the total amount of bulk flow energy dissipated by the shock. A subsequent search for bow shock crossings which occur during intervals of high solar wind speed confirms that the electron heating is very large under high‐speed conditions. The first‐order dependence of the electron temperature increase on the available bulk flow energy is consistent with a heating process which is dominated by the macroscopic cross‐shock electrostatic potential jump. This study suggests that the temperature difference is the appropriate measure of electron heating at shocks (rather than the ratio Ted/Teu) and that the first‐order dependence on (Vu² ‐ Vd²) should be normalized out in future studies of electron heating at space shocks.

This paper provides a brief synthesis of certain aspects of the electric and magnetic field structure of a collisionless shock in the solar wind and outlines how electron heating and acceleration at the shock is related to that structure. Emphasis is on measurements obtained in the vicinity of Earth’s bow shock, although the results should have broad applicability to other shocks in the heliosphere.

The electronic attenuation, \ensuremath{\alpha}(\ensuremath{\infty}), the longitudinal ultrasound in aluminum along the [110] axis has been measured as a function of temperature for four directions of a high transverse magnetic field. We find \ensuremath{\alpha}(\ensuremath{\infty})=${B}_{q}^{H}$${q}^{2}$l where ${B}_{q}^{H}$ is a parameter that depends on the sound and field directions, q is the ultrasound wave number, and l is an average electron mean free path. Extrapolation of ${q}^{2}$/\ensuremath{\alpha}(\ensuremath{\infty}) to T=0 K yields ${B}_{q}^{H}$ when ${l}_{0}$ is isotropic and field independent. The temperature dependence of l demonstrates the anisotropy in the electron-phonon scattering rate. An inversion procedure is described where the relaxation time over the Fermi surface can be obtained from the angular variation of \ensuremath{\alpha}(\ensuremath{\infty}).