The theoretical model by Sorasio et al. (2006) for the steady state Mach number of electrostatic shocks formed in the interaction of two plasma slabs of arbitrary density and temperature is generalized for relativistic electron and non-relativistic ion temperatures. We find that the relativistic correction leads to lower Mach numbers, and as a consequence, ions are reflected with lower energies. The steady state bulk velocity of the downstream population is introduced as an additional parameter to describe the transition between the minimum and maximum Mach numbers in dependence of the initial density and temperature ratios. In order to transform the soliton-like solution in the upstream region into a shock, a population of reflected ions is considered and differences to a zero-ion temperature model are discussed.
The head-on collision between electrostatic shocks is studied via multi-dimensional Particle-In-Cell simulations. It is found that the shock velocities drop significantly and a strong magnetic field is generated after the interaction. This transverse magnetic field is due to the Weibel instability caused by pressure anisotropies due to longitudinal electron heating while the shocks approach each other. Finally, it is shown that this phenomenon can be explored in the laboratory with current laser facilities within a significant parameter range.
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 s…
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 pha…
The emergence of a density bump at the front of a collisionless electrostatic shock wave have been observed experimentally during the ablation of an aluminium foil by a femtosecond laser pulse. We have performed numerical simulations of the dynamics of this phenomena developing alongside the generation of a package of ion-acoustic waves, exposed to a continual flow of energetic electrons, in a collisionless plasma. We present the physical interpretation of the observed effects and show that the bump consists of transit particles, namely, the accelerated ions from the dense plasma layer, and th…
Over the last few decades, different types of plasma waves (e.g., the ion acoustic waves (IAWs), electrostatic solitary waves (ESWs), upper/lower hybrid waves, the Langmuir waves etc.) have been observed in the upstream, downstream and ramp regions of the collisionless interplanetary (IP) shocks. These waves appear as short duration (only a few milliseconds at 1 au) electric field signatures in the in-situ measurements, with typical frequencies $\sim1-10$ kHz. A number of IAW features at the IP shocks seem to be unexplained by kinetic models and requires a new modeling effort. Thus, this paper…
A rigorous theoretical investigation has been made on the nonlinear propagation of dust-ion-acoustic shock waves in a multi-component magnetized pair-ion plasma having inertial warm positive and negative ions, inertialess non-thermal electrons and positrons, and static negatively charged massive dust grains. The Burgers' equation is derived by employing reductive perturbation method. The plasma model supports both positive and negative shock structures in the presence of static negatively charged massive dust grains. It is found that the steepness of both positive and negative shock profiles d…
A numerical study on ion acceleration in electrostatic shock waves is presented, with the aim of determining the best plasma configuration to achieve quasi-monoenergetic ion beams in laser-driven systems. It was recently shown that tailored near-critical density plasmas characterized by a long-scale decreasing rear density profile lead to beams with low energy spread [F. Fiúza et al., Physical Review Letters 109, 215001 (2012)]. In this work, a detailed parameter scan investigating different plasma scale lengths is carried out. As result, the optimal plasma spatial scale length that allows for…
Electrostatic two-stream instabilities play essential roles in an electrostatic collisionless shock formation. They are a key dissipation mechanism and result in ion heating and acceleration. Since the number and energy of the shock-accelerated ions depend on the instabilities, precise identification of the active instabilities is important. Two-dimensional particle-in-cell simulations in a multicomponent plasma reveal ion reflection and acceleration at the shock front, excitation of a longitudinally propagating electrostatic instability due to a non-oscillating component of the electrostatic …
We numerically investigate the impact of Coulomb collisions on the ion dynamics in high-$Z$, solid density caesium hydride and copper targets, irradiated by high-intensity ($I\approx2{-}5\times10^{20}{\rm\,Wcm^{-2}}$), ultrashort (${\sim}10{\rm\,fs}$), circularly polarized laser pulses, using particle-in-cell simulations. Collisions significantly enhance electron heating, thereby strongly increasing the speed of a shock wave launched in the laser-plasma interaction. In the caesium hydride target, collisions between the two ion species heat the protons to ${\sim}100{-}1000{\rm\,eV}$ temperature…
Laser-driven collisonless 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 importan…
We present analysis of more than one hundred large-amplitude bipolar electrostatic structures in a quasi-perpendicular supercritical Earth's bow shock crossing, measured by the Magnetospheric Multiscale spacecraft. The occurrence of the bipolar structures is shown to be tightly correlated with magnetic field gradients in the shock transition region. The bipolar structures have negative electrostatic potentials and spatial scales of a few Debye lengths. The bipolar structures propagate highly oblique to the shock normal with velocities (in the plasma rest frame) of the order of the ion-acoustic…
Energetic electromagnetic emissions by astrophysical jets like those that are launched during the collapse of a massive star and trigger gamma-ray bursts (GRBs) are partially attributed to relativistic internal shocks. The shocks are mediated in the collisionless plasma of such jets by the filamentation instability of counterstreaming particle beams. The filamentation instability grows fastest only if the beams move at a relativistic relative speed. We model here with a particle-in-cell (PIC) simulation the collision of two cold pair clouds at the speed c/2 (c: speed of light). We demonstrate …
We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed c/5 and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing…
The electron beam Weibel instability in the electrostatic collisionless shock is studied via particle in cell simulation. When the non-relativistic incoming plasmas collide with cold dilute plasmas, an electrostatic shock forms near the interface. Following that, a filamentary out-of-plane magnetic field is formed as a result of the Weibel instability. It is demonstrated that the anisotropy of incoming hot electrons is insufficient to trigger the Weibel instability. And the Weibel instability is excited by cold electrons in dilute plasmas. After being accelerated to relativistic velocities by …
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 f…
We present a statistical analysis of more than two thousand bipolar electrostatic solitary waves (ESW) collected from ten quasi-perpendicular Earth's bow shock crossings by Magnetospheric Multiscale spacecraft. We developed and implemented a correction procedure for reconstruction of actual electric fields, velocities, and other properties of ESW from measurements, whose spatial scales are typically comparable with or smaller than spatial distance between voltage-sensitive probes. We determined the optimal ratio between frequency response factors of axial and spin plane antennas to be around 1…
Solar Wind Reflected Ion Properties at Earth's Bow Shock: Dependence on Upstream Conditions and Shock Geometry
University of California, Los Angeles（加州大学洛杉矶分校）；Shandong University（山东大学）；Embry-Riddle Aeronautical University（埃默里·莱德航空大学）；University of Potsdam（波茨坦大学）
Intense laser-plasma interactions are an essential tool for the laboratory study of ion acceleration at a collisionless shock. With two-dimensional particle-in-cell calculations of a multicomponent plasma we observe two electrostatic collisionless shocks at two distinct longitudinal positions when driven with a linearly-polarized laser at normalized laser vector potential a0 that exceeds 10. Moreover, these shocks, associated with protons and carbon ions, show a power-law dependence on a0 and accelerate ions to different velocities in an expanding upstream with higher flux than in a single-com…
We present a Vlasov, i.e. a kinetic Eulerian simulation study of nonlinear collisionless ion-acoustic shocks and solitons excited by an intense laser interacting with an overdense plasma. The use of the Vlasov code avoids problems with low particle statistics and allows a validation of particle-in-cell results. A simple original correction to the splitting method for the numerical integration of the Vlasov equation has been implemented in order to ensure the charge conservation in the relativistic regime. We show that the ion distribution is affected by the development of a turbulence driven b…
Unmagnetized collisionless plasma system consisting of positive- and negative ions, and electrons are considered to study the head-on collision of ion-acoustic shock waves (IASWs) and its effects on the formation of shock (monotonic and oscillatory) waves and phase shift. The soliton solution is derived from the two-sided Korteweg-de Vries Burger (KdVB) equations. The KdVB equations are obtained using extend Poincare-Lighthill-Kuo (ePLK) method. It is assumed that the negative ions are immobile and the electrons follow the Boltzmann energy distribution in the plasma. The effects of plasma para…
A theoretical investigation has been carried out to examine the ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system containing inertialess ultra-relativistically degenerate electrons, and inertial non-relativistic positively charged heavy and light ions. The Burgers' equation is derived by employing reductive perturbation method. It can be seen that under consideration of non-relativistic positively charged heavy and light ions, the plasma model supports only positive electrostatic shock structure. It is also observed that the charge state and number density of t…
This paper overviews experimental and numerical results on acceleration of narrow energy spread ion beams by an electrostatic collisionless shockwave driven by 1 um (Omega EP) and 10 um (UCLA Neptune Laboratory) lasers in near critical density CH and He plasmas, respectively. Shock waves in CH targets produced high-energy 50 MeV protons (energy spread of <30%) and 314 MeV C6+ ions (energy spread of <10%). Observation of acceleration of both protons and carbon ions to similar velocities is consistent with reflection of particles off the moving potential of a shock front. For shocks driven by CO…
Mildly relativistic shocks in magnetized electron-ion plasmas are investigated with 2D kinetic particle-in-cell simulations of unprecedentedly high resolution and large scale for conditions that may be found at internal shocks in blazar cores. Ion-scale effects cause corrugations along the shock surface whose properties somewhat depend on the configuration of the mean perpendicular magnetic field, that is either in or out of the simulation plane. We show that the synchrotron maser instability persists to operate in mildly relativistic shocks in agreement with theoretical predictions and produc…
