Search

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 Alfv\'enic oscillations of the supercritical Earth's bow shock, detected by the MMS multi-spacecraft mission, is also discussed., Comment: 16 pages, 7 figures, accepted for publication in Plasma Physics and Controlled Fusion

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 modes grow in the simulation with no initial magnetic field. Their magnetic field diffuses across the 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 a 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., Comment: 18 pages, 9 figures, accepted for publication in Physica Scripta

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., Comment: 25 pages, 12 figures, accepted for publication in Physica Scripta

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 0.6$c$ 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., Comment: 25 pages, 12 figures, provisionally accepted for publication by the New Journal of Physics

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., Comment: Accepted for publication in Physics of Plasmas, 13 pages, 15 figures

Context. Relativistic jets are ubiquitous in astrophysics. High Mass Microquasars (HMMQs) are useful labs to study such jets, as they are relatively close and evolve over observable time scales. The ambient medium into which the jet propagates is, however, 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 use 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 in Cygnus X-3 case, and thus should be examined in more detail., Comment: 28 pages, 25 figures, 8 tables. Accepted for publication in A&A

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., Comment: 12 pages, 9 figures, Physics of Plasmas (in press)

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., Comment: 13 pages, 11 figures, accepted for publication in Physics of Plasmas

We examine with particle-in-cell (PIC) 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 increasing temperature of the escaping particles quench the beam instability. A larger thermal energy along than perpendicular to the magnetic field destabilizes the pair-Alfv\'en mode. In the rest frame of the upstream plasma, the group velocity of the growing pair-Alfv\'en waves is below that of the shock and the latter catches up with the waves. Accumulating pair-Alfv\'en waves gradually change the shock in the two-dimensional simulation from a Weibel-type shock into an Alfv\'enic shock with a Mach number that is about 6 for our initial conditions., Comment: 11 pages, 10 figures, accepted for publication in Physics of Plasmas

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 [J. Plasma Phys. (2016), vol. 82, 905820403], it was found implementing a toy model for the incoming particles trajectories in the filaments, that a strong enough external magnetic field $\mathbf{B}_0$ can prevent the filaments to block the flow if it is aligned with. Denoting $B_f$ the peak value of the field in the magnetic filaments, all test particles stream through them if $\alpha=B_0/B_f > 1/2$. Here, this result is extended to the case of an oblique external field $B_0$ making an angle $\theta$ with the flow. The result, numerically found, is simply $\alpha > \kappa(\theta)/\cos\theta$, where $\kappa(\theta)$ is of order unity. Noteworthily, test particles exhibit chaotic trajectories., Comment: 10 pages, 6 figures, to appear in Journal of Plasma Physics

We study the effect a guiding magnetic field has on the formation and structure of a pair jet that propagates through a collisionless electron-proton plasma at rest. We model with a PIC simulation a pair cloud with the temperature 400 keV and mean speed 0.9c. The cloud propagates through a spatially uniform, magnetized and cool ambient electron-proton plasma that is at rest. Its mean velocity vector is aligned with the background magnetic field. A jet forms in time. Its outer cocoon consists of jet-accelerated ambient plasma and is separated from the inner cocoon by an electromagnetic piston with a thickness that is comparable to the thermal gyroradius of jet particles. A supercritical fast magnetosonic shock will form between the pristine ambient plasma and the jet-accelerated one on a time scale that exceeds our simulation time by an order of magnitude. The inner cocoon is pair plasma that lost its directed flow energy while it swept out the background magnetic field. A beam of electrons and positrons moves along the jet spine at its initial speed. Its electrons are slowed down and some positrons are accelerated as they cross the jet's head. The latter escape upstream along the magnetic field, which yields an excess of MeV positrons ahead of the jet. Some of the protons, which were located behind the electromagnetic piston at the time it formed, are accelerated to MeV energies, Comment: 12 pages, 15 figures, accepted for publication by Astronomy and Astrophysics

By modelling the expansion of a cloud of electrons and positrons with the temperature 400 keV that propagates at the mean speed 0.9c ($c:$ speed of light) through an initially unmagnetized electron-proton plasma with a particle-in-cell (PIC) simulation, we find a mechanism that collimates the pair cloud into a jet. A filamentation instability develops between the protons at rest and the moving positrons. Its magnetic field collimates the positrons and drives an electrostatic shock into the electron-proton plasma. The magnetic field acts as a discontinuity that separates the protons of the shocked ambient plasma, known as the outer cocoon, from the jet's interior region. The outer cocoon expands at the speed 0.15c along the jet axis and at 0.03c perpendicularly to it. The filamentation instability converts the jet's directed flow energy into magnetic energy in the inner cocoon. The magnetic discontinuity cannot separate the ambient electrons from the jet electrons. Both species rapidly mix and become indistinguishable. The spatial distribution of the positive charge carriers is in agreement with the distributions of the ambient material and the jet material predicted by a hydrodynamic model apart from a dilute positronic outflow that is accelerated by the electromagnetic field at the jet's head., Comment: Physics of Plasmas (in press), 12 pages, 10 figures

Recently a filamentation instability was observed when a laser-generated pair cloud interacted with an ambient plasma. The magnetic field it drove was strong enough to magnetize and accelerate the ambient electrons. It is of interest to determine if and how pair cloud-driven instabilities can accelerate ions in the laboratory or in astrophysical plasma. For this purpose, the expansion of a localized pair cloud with the temperature 400 keV into a cooler ambient electron-proton plasma is studied by means of one-dimensional particle-in-cell (PIC) simulations. The cloud's expansion triggers the formation of electron phase space holes that accelerate some protons to MeV energies. Forthcoming lasers might provide the energy needed to create a cloud that can accelerate protons., Comment: 5 pages 4 figures, accepted for publication in Physics of Plasmas

The expansion of a thermal pressure-driven radial blast shell into a dilute ambient plasma is examined with two-dimensional PIC simulations. The purpose is to determine if laminar shocks form in a collisionless plasma that resemble their magnetohydrodynamic counterparts. The ambient plasma is composed of electrons with the temperature 2 keV and cool fully ionized nitrogen ions. It is permeated by a spatially uniform magnetic field. A forward shock forms between the shocked ambient medium and the pristine ambient medium, which changes from an ion acoustic one through a slow magnetosonic one to a fast magnetosonic shock with increasing shock propagation angles relative to the magnetic field. The slow magnetosonic shock that propagates obliquely to the magnetic field changes into a tangential discontinuity for a perpendicular propagation direction, which is in line with the magnetohydrodynamic model. The expulsion of the magnetic field by the expanding blast shell triggers an electron-cyclotron drift instability., Comment: 10 pages and 11 figures. Accepted for publication in the Physics of Plasmas

A one-dimensional particle-in-cell (PIC) simulation tracks a fast magnetosonic shock over time scales comparable to an inverse ion gyrofrequency. The magnetic pressure is comparable to the thermal pressure upstream. The shock propagates across a uniform background magnetic field with a pressure that equals the thermal pressure upstream at the angle 85$^\circ$ at a speed that is 1.5 times the fast magnetosonic speed in the electromagnetic limit. Electrostatic contributions to the wave dispersion increase its phase speed at large wave numbers, which leads to a convex dispersion curve. A fast magnetosonic precursor forms ahead of the shock with a phase speed that exceeds the fast magnetosonic speed by about $\sim 30 \%$. The wave is slower than the shock and hence it is damped., Comment: 4 pages, 3 figures

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 that the two-stream instability outgrows the filamentation instability for this speed and is thus responsible for the shock formation. The incomplete thermalization of the upstream plasma by its quasi-electrostatic waves allows other instabilities to grow. A shock transition layer forms, in which a filamentation instability modulates the plasma far upstream of the shock. The inflowing upstream plasma is progressively heated by a two-stream instability closer to the shock and compressed to the expected downstream density by the Weibel instability. The strong magnetic field due to the latter is confined to a layer 10 electron skin depths wide., Comment: 12 pages, 14 figures, accepted for publication in MNRAS

The expansion of a dense plasma into a dilute plasma across an initially uniform perpendicular magnetic field is followed with a one-dimensional particle-in-cell (PIC) simulation over MHD time scales. The dense plasma expands in the form of a fast rarefaction wave. The accelerated dilute plasma becomes separated from the dense plasma by a tangential discontinuity at its back. A fast magnetosonic shock with the Mach number 1.5 forms at its front. Our simulation demonstrates how wave dispersion widens the shock transition layer into a train of nonlinear fast magnetosonic waves., Comment: 5 pages, 4 figures, accepted for publication in Physics of Plasmas

The expansion of a radial blast shell into an ambient plasma is modeled with a particle-in-cell (PIC) simulation. The unmagnetized plasma consists of electrons and protons. The formation and evolution of an electrostatic shock is observed, which is trailed by ion-acoustic solitary waves that grow on the beam of the blast shell ions in the post-shock plasma. In spite of the initially radially symmetric outflow, the solitary waves become twisted and entangled and, hence, they break the radial symmetry of the flow. The waves and their interaction with the shocked ambient ions slows down the blast shell protons and brings the post-shock plasma closer to an equilibrium., Comment: 5 pages, 4 figures, accepted by Physics of Plasmas

We report on the first experimental observation of a current-driven instability developing in a quasi-neutral matter-antimatter beam. Strong magnetic fields ($\geq$ 1 T) are measured, via means of a proton radiography technique, after the propagation of a neutral electron-positron beam through a background electron-ion plasma.The experimentally determined equipartition parameter of $\epsilon_B \approx 10^{-3}$, is typical of values inferred from models of astrophysical gamma-ray bursts, in which the relativistic flows are also expected to be pair dominated. The data, supported by Particle-In-Cell simulations and simple analytical estimates, indicate that these magnetic fields persist in the background plasma for thousands of inverse plasma frequencies. The existence of such long-lived magnetic fields can be related to analog astrophysical systems, such as those prevalent in lepton-dominated jets.

The thin-shell instability has been named as one process, which can generate entangled structures in astrophysical plasma on collisional (fluid) scales. It is driven by a spatially varying imbalance between the ram pressure of the inflowing upstream plasma and the downstream's thermal pressure at a non-planar shock. Here we show by means of a particle-in-cell (PIC) simulation that an analogue process can destabilize a thin shell formed by two interpenetrating, unmagnetized and collisionless plasma clouds. The amplitude of the shell's spatial modulation grows and saturates after about ten inverse proton plasma frequencies, when the shell consists of connected piecewise linear patches., Comment: 5 pages, 6 figures

A pair of curved shocks in a collisionless plasma is examined with a two-dimensional particle-in-cell (PIC) simulation. The shocks are created by the collision of two electron-ion clouds at a speed that exceeds everywhere the threshold speed for shock formation. A variation of the collision speed along the initially planar collision boundary, which is comparable to the ion acoustic speed, yields a curvature of the shock that increases with time. The spatially varying Mach number of the shocks results in a variation of the downstream density in the direction along the shock boundary. This variation is eventually equilibrated by the thermal diffusion of ions. The pair of shocks is stable for tens of inverse ion plasma frequencies. The angle between the mean flow velocity vector of the inflowing upstream plasma and the shock's electrostatic field increases steadily during this time. The disalignment of both vectors gives rise to a rotational electron flow, which yields the growth of magnetic field patches that are coherent over tens of electron skin depths., Comment: 10 pages, 10 figures accepted for publication in Physics of Plasmas

The jets of compact accreting objects are composed of electrons and a mixture of positrons and ions. These outflows impinge on the interstellar or intergalactic medium and both plasmas interact via collisionless processes. Filamentation (beam-Weibel) instabilities give rise to the growth of strong electromagnetic fields. These fields thermalize the interpenetrating plasmas. Hitherto, the effects imposed by a spatial non-uniformity on filamentation instabilities have remained unexplored. We examine the interaction between spatially uniform background electrons and a minuscule cloud of electrons and positrons. A square micro-cloud of equally dense electrons and positrons impinges in our particle-in-cell (PIC) simulation on a spatially uniform plasma at rest. The mean speed of the micro-cloud corresponds to a relativistic factor of 15, which is relevant for laboratory experiments and for relativistic astrophysical outflows. The spatial distributions of the leptons and of the electromagnetic fields are examined at several times. A filamentation instability develops between the magnetic field carried by the micro-cloud and the background electrons. The electromagnetic fields, which grow from noise levels, redistribute the electrons and positrons within the cloud, which boosts the peak magnetic field amplitude. The current density and the moduli of the electromagnetic fields grow aperiodically in time and steadily along the direction that is anti-parallel to the cloud's velocity vector. The micro-cloud remains conjoined during the simulation. The instability induces an electrostatic wakefield in the background plasma., Comment: 10 pages, 13 figures, Astronomy and Astrophysics (in press)

The generation of ultra-relativistic positron beams with short duration ($\tau_{e^+} \leq 30$ fs), small divergence ($\theta_{e^+} \simeq 3$ mrad), and high density ($n_{e^+} \simeq 10^{14} - 10^{15}$ cm$^{-3}$) from a fully optical setup is reported. The detected positron beam propagates with a high-density electron beam and $\gamma$-rays of similar spectral shape and peak energy, thus closely resembling the structure of an astrophysical leptonic jet. It is envisaged that this experimental evidence, besides the intrinsic relevance to laser-driven particle acceleration, may open the pathway for the small-scale study of astrophysical leptonic jets in the laboratory.

The dynamics of magnetic fields with amplitude of several tens of Megagauss, generated at both sides of a solid target irradiated with a high intensity (? 1019W/cm2) picosecond laser pulse, has been spatially and temporally resolved using a proton imaging technique. The amplitude of the magnetic fields is sufficiently large to have a constraining effect on the radial expansion of the plasma sheath at the target surfaces. These results, supported by numerical simulations and simple analytical modeling, may have implications for ion acceleration driven by the plasma sheath at the rear side of the target as well as for the laboratory study of self-collimated high-energy plasma jets., Comment: Accepted for publication in Physical Review Letters

The growth and saturation of Buneman-type instabilities is examined with a particle-in-cell (PIC) simulation for parameters that are representative for the foreshock region of fast supernova remnant (SNR) shocks. A dense ion beam and the electrons correspond to the upstream plasma and a fast ion beam to the shock-reflected ions. The purpose of the 2D simulation is to identify the nonlinear saturation mechanisms, the electron heating and potential secondary instabilities that arise from anisotropic electron heating and result in the growth of magnetic fields. We confirm that the instabilities between both ion beams and the electrons saturate by the formation of phase space holes by the beam-aligned modes. The slower oblique modes accelerate some electrons, but they can not heat up the electrons significantly before they are trapped by the faster beam-aligned modes. Two circular electron velocity distributions develop, which are centred around the velocity of each ion beam. They develop due to the scattering of the electrons by the electrostatic wave potentials. The growth of magnetic fields is observed, but their amplitude remains low., Comment: 18 pages, 11 figures, accepted for publication in Plasma Physics and Controlled Fusion

The expansion of an initially unmagnetized planar rarefaction wave has recently been shown to trigger a thermal anisotropy-driven Weibel instability (TAWI), which can generate magnetic fields from noise levels. It is examined here if the TAWI can also grow in a curved rarefaction wave. The expansion of an initially unmagnetized circular plasma cloud, which consists of protons and hot electrons, into a vacuum is modelled for this purpose with a two-dimensional particle-in-cell (PIC) simulation. It is shown that the momentum transfer from the electrons to the radially accelerating protons can indeed trigger a TAWI. Radial current channels form and the aperiodic growth of a magnetowave is observed, which has a magnetic field that is oriented orthogonal to the simulation plane. The induced electric field implies that the electron density gradient is no longer parallel to the electric field. Evidence is presented here for that this electric field modification triggers a second magnetic instability, which results in a rotational low-frequency magnetowave. The relevance of the TAWI is discussed for the growth of small-scale magnetic fields in astrophysical environments, which are needed to explain the electromagnetic emissions by astrophysical jets. It is outlined how this instability could be examined experimentally.

The expansion of a dense plasma through a more rarefied ionised medium is a phenomenon of interest in various physics environments ranging from astrophysics to high energy density laser- matter laboratory experiments. Here this situation is modeled via a 1D Particle-In-Cell simulation; a jump in the plasma density of a factor of 100 is introduced in the middle of an otherwise equally dense electron-proton plasma with an uniform proton and electron temperature of 10eV and 1keV respectively. The diffusion of the dense plasma, through the rarified one, triggers the onset of different nonlinear phenomena such as a strong ion-acoustic shock wave and a rarefaction wave. Secondary structures are detected, some of which are driven by a drift instability of the rarefaction wave. Efficient proton acceleration occurs ahead of the shock, bringing the maximum proton velocity up to 60 times the initial ion thermal speed.

An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe in accordance with previous works the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not accounted for by the linearized theory. A single-fluid-based theory is used to determine the source of this nonlinear electric field. It is demonstrated that the magnetic stress tensor, which vanishes in a 1D geometry, is more important in this 2-dimensional model used here. The electric field grows to an amplitude, which yields a force on the electrons that is comparable to the magnetic one. The peak energy density of each magnetic field component in the simulation plane agrees with previous estimates. Eddy currents develop, which let the amplitude of the third magnetic field component grow, which is not observed in a 1D simulation., Comment: accepted by Plasma Physics and Controlled Fusion

A 2D particle simulation models the collision of two electron-ion plasma clouds along a quasi-parallel magnetic field. The collision speed is 0.9c and the density ratio 10. A current sheet forms at the front of the dense cloud, in which the electrons and the magnetic field reach energy equipartition with the ions. A structure composed of a solenoidal and a toroidal magnetic field grows in this sheet. It resembles that in the cross-section of the torus of a force-free spheromak, which may provide the coherent magnetic fields in gamma-ray burst (GRB) jets needed for their prompt emissions., Comment: 4 pages

Particle-in-cell (PIC) simulations are widely used as a tool to investigate instabilities that develop between a collisionless plasma and beams of charged particles. However, even on contemporary supercomputers, it is not always possible to resolve the ion dynamics in more than one spatial dimension with such simulations. The ion mass is thus reduced below 1836 electron masses, which can affect the plasma dynamics during the initial exponential growth phase of the instability and during the subsequent nonlinear saturation. The goal of this article is to assess how far the electron to ion mass ratio can be increased, without changing qualitatively the physics. It is first demonstrated that there can be no exact similarity law, which balances a change of the mass ratio with that of another plasma parameter, leaving the physics unchanged. Restricting then the analysis to the linear phase, a criterion allowing to define a maximum ratio is explicated in terms of the hierarchy of the linear unstable modes. The criterion is applied to the case of a relativistic electron beam crossing an unmagnetized electron-ion plasma., Comment: To appear in Physics of Plasmas

The localized deposition of the energy of a laser pulse, as it ablates a solid target, introduces high thermal pressure gradients in the plasma. The thermal expansion of this laser-heated plasma into the ambient medium (ionized residual gas) triggers the formation of non-linear structures in the collision-less plasma. Here an electron-proton plasma is modelled with a particle-in-cell (PIC) simulation to reproduce aspects of this plasma expansion. A jump is introduced in the thermal pressure of the plasma, across which the otherwise spatially uniform temperature and density change by the factor 100. The electrons from the hot plasma expand into the cool one and the charge imbalance drags a beam of cool electrons into the hot plasma. This double layer reduces the electron temperature gradient. The presence of the low-pressure plasma modifies the proton dynamics compared to the plasma expansion into a vacuum. The jump in the thermal pressure develops into a primary shock. The fast protons, which move from the hot into the cold plasma in form of a beam, give rise to the formation of phase space holes in the electron and proton distributions. The proton phase space holes develop into a secondary shock that thermalizes the beam., Comment: 17 pages, 9 Figures, accepted for publication in plasma physics and controlled fusion

The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their nonrelativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated, that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied, that the electrostatic field performed undamped oscillations around a background electric field. Here we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF., Comment: 14 pages, 10 plots, accepted for publication in Physica Scripta

Plasma processes close to SNR shocks result in the amplification of magnetic fields and in the acceleration of electrons, injecting them into the diffusive acceleration mechanism. The acceleration of electrons and the B field amplification by the collision of two plasma clouds, each consisting of electrons and ions, at a speed of 0.5c is investigated. A quasi-parallel guiding magnetic field, a cloud density ratio of 10 and a plasma temperature of 25 keV are considered. A quasi-planar shock forms at the front of the dense plasma cloud. It is mediated by a circularly left-hand polarized electromagnetic wave with an electric field component along the guiding magnetic field. Its propagation direction is close to that of the guiding field and orthogonal to the collision boundary. It has a low frequency and a wavelength that equals several times the ion inertial length, which would be indicative of a dispersive Alfven wave close to the ion cyclotron resonance frequency of the left-handed mode (ion whistler), provided that the frequency is appropriate. However, it moves with the super-alfvenic plasma collision speed, suggesting that it is an Alfven precursor or a nonlinear MHD wave such as a Short Large-Amplitude Magnetic Structure (SLAMS). The growth of the magnetic amplitude of this wave to values well in excess of those of the quasi-parallel guiding field and of the filamentation modes results in a quasi-perpendicular shock. We present evidence for the instability of this mode to a four wave interaction. The waves developing upstream of the dense cloud give rise to electron acceleration ahead of the collision boundary. Energy equipartition between the ions and the electrons is established at the shock and the electrons are accelerated to relativistic speeds., Comment: 16 pages, 18 figures, Accepted for publication by Astron & Astrophys

The filamentation instability of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell (PIC) simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases linearly in time. Currents orthogonal to the beam velocity vector are driven through the magnetic and electric fields in the simulation plane. The fields are tied to the filament boundaries and the scale size of the flow-aligned and the perpendicular currents are thus equal. It is confirmed that the electrostatic and the magnetic forces are equally important, when the filamentation instability saturates in 1D. Their balance is apparently the saturation mechanism of the filamentation instability for our initial conditions. The electric force is relatively weaker but not negligible in the 2D simulation, where the electron temperature is set higher to reduce the computational cost. The magnetic pressure gradient is the principal source of the electrostatic field, when and after the instability saturates in the 1D simulation and in the 2D simulation., Comment: 10 pages, 6 figures, accepted by the Plasma Physics and Controlled Fusion (Special Issue EPS 2009)

The direct observation and full characterization of a Phase Space Electron Hole (EH) generated by laser-matter interaction is presented. This structure has been detected via proton radiography during the interaction between an intense laser pulse (t=1ns temporally flat-top, I= 10^14W/cm^2) and a gold 26 micron thick hohlraum. This technique has allowed us the simultaneous detection of propagation velocity, potential and electron density spatial profile across the EH with fine spatial and temporal resolution providing an unprecedentedly detailed experimental characterization.

Two counter-propagating cool and equally dense electron beams are modelled with particle-in-cell (PIC) simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasi-planar filament boundary. It is confirmed, that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction., Comment: 4 pages, 5 figures, accepted for publication in Physics of Plasmas

The Weibel instability is investigated with PIC simulations of an initially unmagnetized and spatially uniform electron plasma. This instability, which is driven by the thermally anisotropic electron distribution, generates electromagnetic waves with wave vectors perpendicular to the direction of the higher temperature. Two simulations are performed: A 2D simulation, with a simulation plane that includes the direction of higher temperature, demonstrates that the wave spectrum is initially confined to one dimension. The electric field components in the simulation plane generated by the instability equalize at the end of the simulation through a secondary instability. A 1D PIC simulation with a high resolution, where the simulation box is aligned with the wave vectors of the growing waves, reveals details of the electron phase space distribution and permits a comparison of the magnetic and electric fields when the instability saturates. It is shown that the electrostatic field is driven by the magnetic pressure gradient and that it and the magnetic field redistribute the electrons in space., Comment: Plasma Phys Controll Fusion, in press (to appear in june 2009)

The filamentation instability driven by two spatially uniform and counter-streaming beams of charged particles in plasmas is modelled by a particle-in-cell (PIC) simulation. Each beam consists of the electrons and positrons. The four species are equally dense and they have the same temperature. The one-dimensional simulation direction is orthogonal to the beam velocity vector. The magnetic field grows spontaneously and rearranges the particles in space, such that the distributions of the electrons of one beam and the positrons of the second beam match. The simulation demonstrates that as a result no electrostatic field is generated by the magnetic field through its magnetic pressure gradient prior to its saturation. This electrostatic field would be repulsive at the centres of the filaments and limit the maximum charge and current density. The filaments of electrons and positrons in this simulation reach higher charge and current densities than in one with no positrons. The oscillations of the magnetic field strength induced by the magnetically trapped particles result in an oscillatory magnetic pressure gradient force. The latter interplays with the statistical fluctuations in the particle density and it probably enforces a charge separation, by which electrostatic waves grow after the filamentation instability has saturated., Comment: 13 pages, 8 figures

Two charge- and current neutral plasma beams are modelled with a one-dimensional PIC simulation. The beams are uniform and unbounded. The relative speed between both beams is 0.4c. One beam is composed of electrons and protons and one out of protons and negatively charged oxygen (dust). All species have the temperature 9 keV. A Buneman instability develops between the electrons of the first beam and the protons of the second beam. The wave traps the electrons, which form plasmons. The plasmons couple energy into the ion acoustic waves, which trap the protons of the second beam. A proton phase space hole grows, which develops through its interaction with the oxygen and the heated electrons into a rarefaction pulse. This pulse drives a strong ion acoustic double layer, which accelerates a beam of electrons to about 50 MeV, which is comparable to the proton kinetic energy. The proton distribution eventually evolves into an electrostatic shock. Beams of charged particles moving at such speeds may occur in the foreshock of supernova remnant shocks. This double layer is thus potentially relevant for the electron acceleration (injection) into the diffusive shock acceleration by supernova remnants shocks.

Two counter-propagating cool and equally dense electron beams are modelled with particle-in-cell (PIC) simulations. The electron beam filamentation instability is examined in one spatial dimension. The box length resolves one pair of current filaments. A small, a medium-sized and a large filament are considered and compared. The magnetic field amplitude at the saturation time of the filamentation instability is proportional to the filament size. It is demonstrated, that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away. The confining potential is not sinusoidal, as assumed by the magnetic trapping model, and it permits an overlap of current filaments (plasmons) with an opposite flow direction. The scaling of the saturation amplitude of the magnetic field with the filament size observed here thus differs from that expected from the magnetic trapping model. The latter nevertheless gives a good estimate for the magnetic saturation amplitude. The increase of the peak electrostatic and magnetic field amplitudes with the filament size implies, that the electrons heat up more and that the spatial modulation of their mean speed along the beam flow direction increases with the filament size., Comment: 19 pages, 11 figures

Supernova remnant (SNR) blast shells can reach the flow speed $v_s = 0.1 c$ and shocks form at its front. Instabilities driven by shock-reflected ion beams heat the plasma in the foreshock, which may inject particles into diffusive acceleration. The ion beams can have the speed $v_b \approx v_s$. For $v_b \ll v_s$ the Buneman or upper-hybrid instabilities dominate, while for $v_b \gg v_s$ the filamentation and mixed modes grow faster. Here the relevant waves for $v_b \approx v_s$ are examined and how they interact nonlinearly with the particles. The collision of two plasma clouds at the speed $v_s$ is modelled with particle-in-cell (PIC) simulations, which convect with them magnetic fields oriented perpendicular to their flow velocity vector. One simulation models equally dense clouds and the other one uses a density ratio of 2. Both simulations show upper-hybrid waves that are planar over large spatial intervals and that accelerate electrons to $\sim$ 10 keV. The symmetric collision yields only short oscillatory wave pulses, while the asymmetric collision also produces large-scale electric fields, probably through a magnetic pressure gradient. The large-scale fields destroy the electron phase space holes and they accelerate the ions, which facilitates the formation of a precursor shock., Comment: 15 pages, 11 figures, accepted for publication in Plasma Physics and Controlled Fusion

We model relativistically colliding plasma by PIC simulations in one and two spatial dimensions, taking an ion-to-electron mass ratio of 400. Energy dissipation by a wave precursor of mixed polarity and different densities of the colliding plasma slabs results in a relativistic forward shock forming on millisecond timescales. The forward shock accelerates electrons to ultrarelativistic energies and reflects upstream ions, which drag the electrons along to preserve the plasma quasi-neutrality. No reverse shock forms. The shock may be representative for internal gamma ray burst shocks.

We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations., Comment: 18 pages, 8 figures

The collective production of electron-positron pairs by electrostatic waves in quantum plasmas is investigated. In particular, a semi-classical governing set of equation for a self-consistent treatment of pair creation by the Schwinger mechanism in a quantum plasma is derived., Comment: 4 pages, 3 figures, to appear in JETP Letters

We investigate the acceleration of electrons via their interaction with electrostatic waves, driven by the relativistic Buneman instability, in a system dominated by counter-propagating proton beams. We observe the growth of these waves and their subsequent saturation via electron trapping for a range of proton beam velocities, from 0.15c to 0.9c. We can report a reduced stability of the electrostatic wave (ESW) with increasing non-relativistic beam velocities and an improved wave stability for increasing relativistic beam velocities, both in accordance with previous findings. At the highest beam speeds, we find the system to be stable again for a period of ~160 plasma periods. Furthermore we observe a, to our knowledge, previously unreported secondary electron acceleration mechanism at low beam speeds. We believe that it is the result of parametric couplings to produce high phase velocity ESW's which then trap electrons, accelerating them to higher energies. This allows electrons in our simulation study to achieve the injection energy required for Fermi acceleration, for beam speeds as low as 0.15c in unmagnetised plasma.

Particle acceleration by means of non-linear plasma wave interactions is of great topical interest. Accordingly, in this paper we focus on the electron surfing process. Self-consistent kinetic simulations, using both relativistic Vlasov and PIC (Particle In Cell) approaches, show here that electrons can be accelerated to highly relativistic energies (up to 100 m_e c^2) if the phase speed of the electrostatic wave is mildly relativistic (0.6c to 0.9c for the magnetic field strengths considered). The acceleration is strong because of relativistic stabilisation of the nonlinearly saturated electrostatic wave, seen in both relativistic Vlasov and PIC simulations. An inverse power law momentum distribution can arise for the most strongly accelerated electrons. These results are of relevance to observed rapid changes in the radio synchrotron emission intensities from microquasars, gamma ray bursts and other astrophysical objects that require rapid acceleration mechanisms for electrons., Comment: 22 pages, 19 figures. Two MPEG movies available on demand to support some observations

Observations of synchrotron radiation across a wide range of wavelengths provide clear evidence that electrons are accelerated to relativistic energies in supernova remnants (SNRs). However, a viable mechanism for the pre-acceleration of such electrons to mildly relativistic energies has not yet been established. In this paper an electromagnetic particle-in-cell (PIC) code is used to simulate acceleration of electrons from background energies to tens of keV at perpendicular collisionless shocks associated with SNRs. Free energy for electron energization is provided by ions reflected from the shock front, with speeds greater than the upstream electron thermal speed. The PIC simulation results contain several new features, including: the acceleration, rather than heating, of electrons via the Buneman instability; the acceleration of electrons to speeds exceeding those of the shock-reflected ions producing the instability; and strong acceleration of electrons perpendicular to the magnetic field. Electron energization takes place through a variety of resonant and non-resonant processes, of which the strongest involves stochastic wave-particle interactions. In SNRs the diffusive shock process could then supply the final step required for the production of fully relativistic electrons. The mechanisms identified in this paper thus provide a possible solution to the electron pre-acceleration problem., Comment: 36 pages, 13 figures