The evolution of a deformed subcritical fast magnetosonic shock front is compared between two two-dimensional PIC simulations with different orientations of the magnetic field relative to the simulation box. All other initial and simulation conditions are kept identical. Shock boundary oscillations are observed in the simulation where the magnetic field direction is resolved. This oscillation is caused by the reformation of the shock front. One part of the front acts as a shock, while the other functions as a magnetic piston, with both halves changing their states in antiphase. The oscillation period corresponds to the time required for one shock wave to grow as the other collapses. In contrast, the corrugated fast magnetosonic shock does not oscillate in the second simulation, where the magnetic field is oriented out of the simulation plane. This dependence on magnetic field orientation suggests that the shock oscillation is induced by magnetic tension, which is only effective in the first simulation. In both simulations, the shock perturbation does not grow over time, indicating that the shocks are stable. The potential relevance of these findings for the Alfvénic oscillations of the supercritical Earth's bow shock, detected by the MMS multi-spacecraft mission, is also discussed.

The role of thermal fluctuations on the stimulated Raman backscattering instability is investigated by means of Vlasov and particle-in-cell (PIC) simulations in a regime of strong linear Landau damping of the Langmuir wave. The instability is initially convective and amplifies thermal noise, leading to a low-amplitude back-scattered laser sideband. Linear Landau damping of the Langmuir sideband modifies and flattens the electron velocity distribution function at the resonant velocity, leading to a gradual decrease in the Landau damping rate and an increase in the convective amplification. The Langmuir wave traps electrons resulting in a rapid nonlinear absolute instability and large amplitude flashes of backscattered light off large amplitude Langmuir waves with trapped electrons, leading to the production of hot electrons. Conditions for simulating realistic thermal noise with Vlasov and PIC simulations are discussed and defined.

Ablating a target with an ultraintense laser pulse can create a cloud of collisionless plasma. A density ramp forms, in which the plasma density decreases and the ion's mean speed increases with distance from the plasma source. Its width increases with time. Electrons lose energy in the ion's expansion direction, which gives them a temperature anisotropy. We study with one-dimensional particle-in-cell simulations the expansion of a dense plasma into a dilute one, yielding a density ramp similar to that in laser-plasma experiments and a thermal-anisotropy-driven instability. Non-propagating Weibel-type wave modes grow in the simulation with no initial magnetic field. Their magnetic field diffuses across the shock and expands upstream. Circularly polarized propagating Whistler waves grow in a second simulation, in which a magnetic field is aligned with the ion expansion direction. Both wave modes are driven by non-resonant instabilities, they have similar exponential growth rates, and they can leave the density ramp and expand into the dilute plasma. Their large magnetic amplitude should make them detectable in experimental settings.

We use a two-dimensional particle-in-cell (PIC) simulation to study the propagation of subcritical fast magnetosonic shocks in electron-nitrogen plasma and their stability against an initial deformation. A slab of dense plasma launches two planar blast waves into a surrounding ambient plasma, which is permeated by a magnetic field that points out of the simulation box and is spatially uniform at the start of the simulation. One shock propagates into a spatially uniform ambient plasma. This reference shock has a Mach number of 1.75, and the heating of ions only along the shock normal compresses the ions that cross the shock to twice the upstream density. Drift instabilities lead to rapidly growing electron-cyclotron harmonic waves ahead of the location where the shock's density overshoot peaks, and to slowly growing lower-hybrid waves with a longer wavelength behind it. The second shock wave enters a perturbation layer that deforms it into a sine shape. Once the shock leaves the perturbation layer, the deformation is weakly damped and non-oscillatory, and the shock remains stable. Even without an external perturbation, and for the plasma parameters considered here, drift instabilities will cause ripples in the shock wave. These instabilities lead to a spatially and temporally varying compression of the plasma that crosses the shock.

We study with a 3D PIC simulation discontinuities between an electron-positron pair plasma and magnetized electrons and protons. A pair plasma is injected at one simulation boundary with a speed 0.6c along its normal. It expands into an electron-proton plasma and a magnetic field that points orthogonally to the injection direction. Diamagnetic currents expel the magnetic field from within the pair plasma and pile it up in front of it. It pushes electrons, which induces an electric field pulse ahead of the magnetic one. This initial electromagnetic pulse (EMP) confines the pair plasma magnetically and accelerates protons electrically. The fast flow of the injected pair plasma across the protons behind the initial EMP triggers the filamentation instability. Some electrons and positrons cross the injection boundary and build up a second EMP. Electron-cyclotron drift instabilities perturb the plasma ahead of both EMPs seeding a Rayleigh-Taylor-type instability. Despite equally strong perturbations ahead of both EMPs, the second EMP is much more stable than the initial one. We attribute the rapid collapse of the initial EMP to the filamentation instability, which perturbed the plasma behind it. The Rayleigh-Taylor-type instability transforms the planar EMPs into transition layers, in which magnetic flux ropes and electrostatic forces due to uneven numbers of electrons and positrons slow down and compress the pair plasma and accelerate protons. In our simulation, the expansion speed of the pair cloud decreased by about an order of magnitude and its density increased by the same factor. Its small thickness implies that it is capable of separating a relativistic pair outflow from an electron-proton plasma, which is essential for collimating relativistic jets of pair plasma in collisionless astrophysical plasma.

We study with particle-in-cell (PIC) simulations the stability of fast magnetosonic shocks. They expand across a collisionless plasma and an orthogonal magnetic field that is aligned with one of the directions resolved by the 2D simulations. The shock speed is 1.6 times the fast magnetosonic speed when it enters a layer with a reduced density of mobile ions, which decreases the shock speed by up to 15% in 1D simulations. In the 2D simulations, the density of mobile ions in the layer varies sinusoidally perpendicularly to the shock normal. We resolve one sine period. This variation only leads to small changes in the shock speed evidencing a restoring force that opposes a shock deformation. As the shock propagates through the layer, the ion density becomes increasingly spatially modulated along the shock front and the magnetic field bulges out where the mobile ion density is lowest. The perturbed shock eventually reaches a steady state. Once it leaves the layer, the perturbations of the ion density and magnetic field oscillate along its front at a frequency close to the lower-hybrid frequency; the shock is mediated by a standing wave composed of obliquely propagating lower-hybrid waves. We perform three 2D simulations with different box lengths along the shock front. The shock front oscillations are aperiodically damped in the smallest box with the fastest variation of the ion density, strongly damped in the intermediate one, and weakly damped in the largest box. The shock front oscillations perturb the magnetic field in a spatial interval that extends by several electron skin depths upstream and downstream of the shock front and could give rise to Whistler waves that propagate along the shock's magnetic field overshoot. Similar waves were observed in hybrid and PIC simulations and by the MMS satellite mission.

Context. Relativistic jets are ubiquitous in astrophysics. High-mass microquasars (HMMQs) are useful laboratories for studying these jets because they are relatively close and evolve over observable timescales. The ambient medium into which the jet propagates, however, is far from homogeneous. Corresponding simulation studies to date consider various forms of a wind-shaped ambient medium, but typically neglect radiative cooling and relativistic effects. Aims. We investigate the dynamical and structural effects of radiative losses and system parameters on relativistic jets in HMMQs, from the jet launch to its propagation over several tens of orbital separations. Methods. We used 3D relativistic hydrodynamical simulations including parameterized radiative cooling derived from relativistic thermal plasma distribution to carry out parameter studies around two fiducial cases inspired by Cygnus X-1 and Cygnus X-3. Results. Radiative losses are found to be more relevant in Cygnus X-3 than Cygnus X-1. Varying jet power, jet temperature, or the wind of the donor star tends to have a larger impact at early times, when the jet forms and instabilities initially develop, than at later times when the jet has reached a turbulent state. Conclusions. Radiative losses may be dynamically and structurally relevant at least for Cygnus X-3 and thus should be examined in more detail.

By means of a particle-in-cell (PIC) simulation, we study the interaction between a uniform magnetized ambient electron–proton plasma at rest and an unmagnetized pair plasma, which we inject at one simulation boundary with a mildly relativistic mean speed and temperature. The magnetic field points out of the simulation plane. The injected pair plasma expels the magnetic field and piles it up at its front. It traps ambient electrons and drags them across the protons. An electric field grows, which accelerates protons into the pair cloud's expansion direction. This electromagnetic pulse separates the pair cloud from the ambient plasma. Electrons and positrons, which drift in the pulse's nonuniform field, trigger an instability that disrupts the current sheet ahead of the pulse. The wave vector of the growing perturbation is orthogonal to the magnetic field direction and magnetic tension cannot stabilize it. The electromagnetic pulse becomes permeable for pair plasma, which forms new electromagnetic pulses ahead of the initial one. A transition layer develops with a thickness of a few proton skin depths, in which protons and positrons are accelerated by strong electromagnetic fields. Protons form dense clumps surrounded by a strong magnetic field. The thickness of the transition layer grows less rapidly than we would expect from the typical speeds of the pair plasma particles and the latter transfer momentum to protons; hence, the transition layer acts as a discontinuity, separating the pair plasma from the ambient plasma. Such a discontinuity is an important building block for astrophysical pair plasma jets.

We examine with particle-in-cell simulations how a parallel shock in pair plasma reacts to upstream waves, which are driven by escaping downstream particles. Initially, the shock is sustained in the two-dimensional simulation by a magnetic filamentation (beam-Weibel) instability. Escaping particles drive an electrostatic beam instability upstream. Modifications of the upstream plasma by these waves hardly affect the shock. In time, a decreasing density and an increasing temperature of the escaping particles quench the beam instability. A larger thermal energy along than perpendicular to the magnetic field destabilizes the pair-Alfvén mode. In the rest frame of the upstream plasma, the group velocity of the growing pair-Alfvén waves is below that of the shock and the latter catches up with the waves. Accumulating pair-Alfvén waves gradually change the shock in the two-dimensional simulation from a Weibel-type shock into an Alfvénic shock with a Mach number that is about 6 for our initial conditions.

We study with 1D PIC simulations the expansion of a dense plasma into a dilute one for density ratios 2.5 <= alpha <= 20. Both are unmagnetized and consist of electrons and protons. Shocks form in all cases. We determine how alpha affects the speed of the shock, that of the trailing velocity plateau and the proton beam instabilities in its upstream region. The speed of the velocity plateau relative to the upstream plasma increases significantly with alpha. Faster shocks reflect more upstream protons and fewer protons make it downstream, which slows down the shock in the downstream frame. This slow-down reduces noticably the increase with alpha of the shock speed in the upstream frame. All simulations demonstrate that an ion acoustic instability develops between the shock-reflected proton beam and the ambient protons. We solve the linear dispersion relation for ion acoustic waves that have wave vectors which are parallel to the beam velocity vector. Upstream conditions, for which their growth rate is largest, lead to the most unstable upstream plasmas also in the simulation. Even though linear theory predicts the growth of sine waves, which reach a small amplitude in the simulations, solitary waves become the dominant ones upstream of the shock. They enforce the formation of new shocks and ion phase space vortices. We discuss the relevance of our findings to laser-plasma experiments.

We study with a one-dimensional particle-in-cell simulation the expansion of a pair cloud into a magnetized electron–proton plasma as well as the formation and subsequent propagation of a tangential discontinuity that separates both plasmas. Its propagation speed takes the value that balances the magnetic pressure of the discontinuity against the thermal pressure of the pair cloud and the ram pressure of the protons. Protons are accelerated by the discontinuity to a speed that exceeds the fast magnetosonic speed by the factor of 10. A supercritical fast magnetosonic shock forms at the front of this beam. An increasing proton temperature downstream of the shock and ahead of the discontinuity leaves the latter intact. We create the discontinuity by injecting a pair cloud at a simulation boundary into a uniform electron–proton plasma, which is permeated by a perpendicular magnetic field. Collisionless tangential discontinuities in the relativistic pair jets of x-ray binaries (microquasars) are in permanent contact with the relativistic leptons of their inner cocoon, and they become the sources of radio synchrotron emissions.

Particle-in-cell (PIC) simulations of collisionless jets of electrons and positrons in an ambient electron-proton plasma have revealed an acceleration of positrons at the expense of electron kinetic energy. The dominant instability within the jet was a filamentation instability between electrons, protons and positrons. In this work we show that a filamentation instability, between an initially unmagnetized ambient electron-proton plasma at rest and a beam of pair plasma that moves through it at a non-relativistic speed, indeed results in preferential positron acceleration. Filaments form that are filled predominantly with particles with the same direction of their electric current vector. Positron filaments are separated by electromagnetic fields from beam electron filaments. Some particles can cross the field boundary and enter the filament of the other species. Positron filaments can neutralize their net charge by collecting the electrons of the ambient plasma while protons cannot easily follow the beam electron filaments. Positron filaments can thus be compressed to a higher density and temperature than the beam electron filaments. Filament mergers, which take place after the exponential growth phase of the instability has ended, lead to an expansion of the beam electron filaments, which amplifies the magnetic field they generate and induces an electric field in this filament. Beam electrons lose a substantial fraction of their kinetic energy to the electric field. Some positrons in the beam electron filament are accelerated by the induced electric field to almost twice their initial speed. The simulations show that a weaker electric field is induced in the positron filament and particles in this filament hardly change their speed.

We present the results from a particle-in-cell (PIC) simulation that models the interaction between a spatially localized electron-positron cloud and an electron-ion plasma. The latter is permeated by a magnetic field that is initially spatially uniform and aligned with the mean velocity vector of the pair cloud. The pair cloud expels the magnetic field and piles it up into an electromagnetic piston. Its electromagnetic field is strong enough to separate the pair cloud from the ambient plasma in the direction that is perpendicular to the cloud propagation direction. The piston propagates away from the spine of the injected pair cloud and it accelerates the protons to a high nonrelativistic speed. The accelerated protons form an outer cocoon that will eventually become separated from the unperturbed ambient plasma by a fast magnetosonic shock. No electromagnetic piston forms at the front of the cloud and a shock is mediated here by the filamentation instability. The final plasma distribution resembles that of a hydrodynamic jet. Collisionless plasma jets may form in the coronal plasma of accreting black holes and the interaction between the strong magnetic field of the piston and the hot pair cloud may contribute to radio emissions by such objects.

We study with a two-dimensional particle-in-cell simulation the stability of a discontinuity or piston, which separates an electron-positron cloud from a cooler electron-proton plasma. Such a piston might be present in the relativistic jets of accreting black holes separating the jet material from the surrounding ambient plasma and when pair clouds form during an X-ray flare and expand into the plasma of the accretion disk corona. We inject a pair plasma at a simulation boundary with a mildly relativistic temperature and mean speed. It flows across a spatially uniform electron-proton plasma, which is permeated by a background magnetic field. The magnetic field is aligned with one simulation direction and oriented orthogonally to the mean velocity vector of the pair cloud. The expanding pair cloud expels the magnetic field and piles it up at its front. It is amplified to a value large enough to trap ambient electrons. The current of the trapped electrons, which are carried with the expanding cloud front, drives an electric field that accelerates protons. A solitary wave grows and changes into a piston after it saturated. Our simulations show that this piston undergoes a collision-less instability similar to a Rayleigh-Taylor instability. The undular mode grows and we observe fingers in the proton density distribution. The effect of the instability is to deform the piston but it cannot destroy it.

When two collisionless plasma shells collide, they interpenetrate and the overlapping region may turn Weibel unstable for some values of the collision parameters. This instability grows magnetic filaments which, at saturation, have to block the incoming flow if a Weibel shock is to form. In a recent paper (Bret, J. Plasma Phys., vol. 82, 2016b, 905820403), it was found by implementing a toy model for the incoming particle trajectories in the filaments, that a strong enough external magnetic field $\unicode[STIX]{x1D63D}_{0}$ can prevent the filaments blocking the flow if it is aligned with them. Denoting by $B_{f}$ the peak value of the field in the magnetic filaments, all test particles stream through them if $\unicode[STIX]{x1D6FC}=B_{0}/B_{f}>1/2$. Here, this result is extended to the case of an oblique external field $B_{0}$ making an angle $\unicode[STIX]{x1D703}$ with the flow. The result, numerically found, is simply $\unicode[STIX]{x1D6FC}>\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})/\cos \unicode[STIX]{x1D703}$, where $\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})$ is of order unity. Noteworthily, test particles exhibit chaotic trajectories.

Received 25 July 2019Accepted 8 April 2020DOI:https://doi.org/10.1103/PhysRevLett.124.179502© 2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasHigh intensity laser-plasma interactionsLaser driven ion accelerationPhotonuclear reactionsPhysical SystemsAstrophysical jetsLasersAccelerators & BeamsPlasma Physics

We compare with one-dimensional particle-in-cell simulations the aperiodically growing instabilities driven by a bi-Maxwellian velocity distribution in unmagnetized electron plasma (Weibel instability) and in pair plasma. The simulation box is aligned with the cool direction. The waves in both simulations evolve towards a circularly polarized non-propagating magnetic structure. Its current and magnetic field are aligned and the structure is in a force-free state. We examine how a background magnetic field B-0, which is parallel to the simulation direction, affects the waves in the pair plasma. A weak B-0 cannot inhibit the growth of the aperiodically growing instability but it prevents it from reaching the force-free stable state. The mode collapses and seeds a pair Alfven waves. An intermediate B-0 couples the thermal anisotropy to the pair Alfven mode and propagating magnetowaves grow. The phase speed of the pair of Alfven waves is increased by the thermal anisotropy. Its growth is suppressed when B-0 is set to the value that stabilizes the mirror mode.

In this paper, we investigate nonrelativistic, kinetic, linear phase of the filamentation instability when an external magnetic field is present in the direction of the counterstreaming electron beams using Vlasov simulations in 1D-3V space. We first investigate the growth rate of instability. In the linear growth regime, our results correspond to the previous conclusions that with the increase in strength of the ambient magnetic field, there is a suppression of instability. Interestingly, we established that at a critical / threshold magnetic field, Vlasov simulations and particle-in-cell (PIC) simulations differ in their instability behaviour. At this particular magnetic field, there is a complete suppression of the growth of instability in Vlasov results compared to PIC simulations, where a strong growth of instability is shown. It is believed that thermal noise in the PIC leads to the growth. However, Vlasov simulations show wave–wave coupling which stabilises the modes. In this work, our focus is to demonstrate the difference in this behaviour and to thoroughly analyse the spectra and wave generation for the same.

We study with a 1D particle-in-cell (PIC) simulation the evolution of a subcritical perpendicular fast magnetosonic shock. The shock propagates at 1.5 times the fast magnetosonic speed. Some upstream protons are reflected by the shock's electric potential. They form a beam which carries less energy than those that are reflected magnetically by super-critical shocks. The beam triggers the growth of a fast magnetosonic solitary wave upstream of the shock, which reflects the beam protons back to the shock. Extracting the momentum and energy of this beam allows the solitary wave to grow into a proto-shock that is trailed by a short downstream region. Protons from the shock-reflected proton beam increase the density of the plasma between the shock and the proto-shock reducing its potential difference relative to both surrounding structures. Bulk protons, which cross the proto-shock, react to the decreased potential jump. The plasma behind the proto-shock accelerates and so does the shock. The trailing end of the proto-shock speeds up in order to continue reflecting the beam protons and eventually it catches up with its front; the proto-shock collapses and the self-reformation fails. A more energetic proton beam could decrease the potential jump across the shock, let it collapse and replace it with the proto-shock.

The evolution of the Buneman and two-stream instabilities driven by a cold dilute mildly relativistic electron beam is studied as a function of the ion\'\s charge-to-mass ratio. The growth rates of both instabilities are comparable for the selected parameters if the charge-to-mass ratio of protons is used and the Buneman instability outgrows the two-stream instability for a larger ratio. Particle-in-cell (PIC) simulations show that both instabilities grow independently during their linear growth phase. The much lower saturation amplitude of the Buneman instability implies that it saturates first even if the linear growth rates of both instabilities are equal. The electron phase space holes it drives coalesce. Their spatial size increases in time and they start interacting with the two-stream mode, which triggers the onset of electrostatic turbulence. A reduced charge-to-mass ratio results in stronger turbulence and ion heating and in an increased energy loss of the relativistic electron beam compared to that in a simulation with the correct ratio.