We report on the temporally and spatially resolved detection of the precursory stages that lead to the formation of an unmagnetized, supercritical collisionless shock in a laser-driven laboratory experiment. The measured evolution of the electrostatic potential associated with the shock unveils the transition from a current free double layer into a symmetric shock structure, stabilized by ion reflection at the shock front. Supported by a matching particle-in-cell simulation and theoretical considerations, we suggest that this process is analogous to ion reflection at supercritical collisionless shocks in supernova remnants.
We report on the experimental observation of the instability of a plasma shell, which formed during the expansion of a laser-ablated plasma into a rarefied ambient medium. By means of a proton radiography technique, the evolution of the instability is temporally and spatially resolved on a timescale much shorter than the hydrodynamic one. The density of the thin shell exceeds that of the surrounding plasma, which lets electrons diffuse outward. An ambipolar electric field grows on both sides of the thin shell that is antiparallel to the density gradient. Ripples in the thin shell result in a spatially varying balance between the thermal pressure force mediated by this field and the ram pressure force that is exerted on it by the inflowing plasma. This mismatch amplifies the ripples by the same mechanism that drives the hydrodynamic nonlinear thin-shell instability (NTSI). Our results thus constitute the first experimental verification that the NTSI can develop in colliding flows.
Proton radiography using laser-driven sources has been developed as a diagnostic since the beginning of the decade, and applied successfully to a range of experimental situations. Multi-MeV protons driven from thin foils via the Target Normal Sheath Acceleration mechanism, offer, under optimal conditions, the possibility of probing laser-plasma interactions, and detecting electric and magnetic fields as well as plasma density gradients with similar to ps temporal resolution and similar to 5-10 mu m spatial resolution. In view of these advantages, the use of proton radiography as a diagnostic in experiments of relevance to Inertial Confinement Fusion is currently considered in the main fusion laboratories. This paper will discuss recent advances in the application of laser-driven radiography to experiments of relevance to Inertial Confinement Fusion. In particular we will discuss radiography of hohlraum and gasbag targets following the interaction of intense ns pulses. These experiments were carried out at the HELEN laser facility at AWE (UK), and proved the suitability of this diagnostic for studying, with unprecedented detail, laser-plasma interaction mechanisms of high relevance to Inertial Confinement Fusion. Non-linear solitary structures of relevance to space physics, namely phase space electron holes, have also been highlighted by the measurements. These measurements are discussed and compared to existing models.
The hierarchy of unstable modes when two counter-streaming pair plasmas interact over a flow-aligned magnetic field has been recently investigated [Phys. Plasmas 23, 062122 (2016)]. The analysis is here extended to the case of an arbitrarily tilted magnetic field. The two plasma shells are initially cold and identical. For any angle θ ∈ [0, π/2] between the field and the initial flow, the hierarchy of unstable modes is numerically determined in terms of the initial Lorentz factor of the shells γ0, and the field strength as measured by a parameter denoted σ. For θ = 0, four different kinds of mode are likely to lead the linear phase. The hierarchy simplifies for larger θ's, partly because the Weibel instability can no longer be cancelled in this regime. For θ > 0.78 (44°) and in the relativistic regime, the Weibel instability always govern the interaction. In the non-relativistic regime, the hierarchy becomes θ-independent because the interaction turns to be field-independent. As a result, the two-stream instability becomes the dominant one, regardless of the field obliquity.
A relativistic fluid model is implemented to assess the role of the ions motion in the linear phase of relativistic beam plasma electromagnetic instabilities. The all unstable wave vector spectrum is investigated, allowing us to assess how ion motions modify the competition between every possible instability. Beam densities up to the plasma one are considered. Due to the fluid approach, the temperatures must remain small, i.e., nonrelativistic. In the cold limit, ions motion affect the most unstable mode when the beam gamma factor bM/mi, being the beam to plasma density ratio, i the ion charge, M their mass, and m the electrons. The return current plays an important role by prompting Buneman-type instabilities which remain in the nonrelativistic regime up to high beam densities. Nonrelativistic temperatures only slightly affect these conclusions, except in the diluted beam regime where they can stabilize the Buneman modes.
The electromagnetic instabilities driven by a relativistic electron beam, which moves through a magnetized plasma, are analyzed with a cold two-fluid model. It allows for any angle B between the beam velocity vector and the magnetic field vector and considers any orientation of the wavevector in the two-dimensional plane spanned by these two vectors. If the magnetic field is strong, the two-stream instability dominates if B=0 and the oblique modes grow faster at larger B. A weaker magnetic field replaces the two-stream modes with oblique modes as the fastest-growing waves. The threshold value separating both magnetic regimes is estimated. A further dimensionless parameter is identified, which determines whether or not the wavevector of the most unstable wave is changed continuously, as B is varied from 0 to /2. The fastest growing modes are always found for a transverse propagation of the beam with B=/2, irrespective of the magnetic field strength. ©2008 American Institute of Physics
Instabilities driven by relativistic electron beams are being investigated due to their importance for plasma heating and electromagnetic field generation in astrophysical and laboratory plasmas. Particle-in-cell (PIC) simulations of initially unmagnetized colliding plasmas have demonstrated the generation of strong magnetic fields and a moderate electron acceleration. The inclusion of a flow-aligned magnetic field suppresses the electromagnetic filamentation instability and PIC simulations have shown that the plasma dynamics turns quasi-electrostatic. To quantify the impact of the magnetic field, we have analyzed numerically a magnetized multi-fluid model that includes a kinetic pressure term. This fluid model allows us to examine the beam-driven instability at all angles between the wavevector and the magnetic field vector. More accurate kinetic models typically focus only on the filamentation instability, due to the increased analytical complexity. We present here the fluid model and a growth rate map of the entire k-space for a beam Lorentz factor 4. We verify that the two-stream, mixed mode and filamentation instability belong to the same wave branch and that the magnetic field selects the fastest-growing mode. We estimate the magnetic fields required to suppress the filamentation and the mixed mode instabilities.
The temperature-dependent fluid model from Phys. Plasmas 13, 042106 (2006) is expanded in order to explore the oblique electromagnetic instabilities, which are driven by a hot relativistic electron beam that is interpenetrating a hot and magnetized plasma. The beam velocity vector is parallel to the magnetic-field direction. The results are restricted to nonrelativistic temperatures. The growth rates of all instabilities but the two-stream instability can be reduced by a strong magnetic field so that the distribution of unstable waves becomes almost one dimensional. For high beam densities, highly unstable oblique modes dominate the spectrum of unstable waves as long as omega(c)/omega(p)less than or similar to 2 gamma(3/2)(b), where omega(c) is the electron gyrofrequency, omega(p) is the electron plasma frequency, and gamma(b) is the relativistic factor of the beam. A uniform stabilization over the entire k space cannot be achieved.
Particle-in-cell 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 in 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.
Beam-plasma instabilities are a key physical process in many astrophysical phenomena. Within the fireball model of Gamma ray bursts, they first mediate a relativistic collisionless shock before they produce upstream the turbulence needed for the Fermi acceleration process. While non-relativistic systems are usually governed by flow-aligned unstable modes, relativistic ones are likely to be dominated by normally or even obliquely propagating waves. After reviewing the basis of the theory, results related to the relativistic kinetic regime of the poorly-known oblique unstable modes will be presented. Relevant systems besides the well-known electron beam-plasma interaction are presented, and it is shown how the concept of modes hierarchy yields a criterion to assess the proton to electron mass ratio in Particle in cell simulations.
The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.
In plasmas where the mean-free-path is much larger than the size of the system, shock waves can arise with a front much shorter than the mean-free path. These so-called "collisionless shocks" are mediated y collective plasma interactions. Studies conducted so far on these shocks found that although binary collisions are absent, the distribution functions are thermalized downstream by scattering on the fields, so that magnetohydrodynamic prescriptions may apply. Here we show a clear departure from this pattern in the case of Weibel shocks forming over a flow-aligned magnetic field. A micro-physical analysis of the particle motion in the Weibel filaments shows how they become unable to trap the flow in the presence of too strong a field, inhibiting the mechanism of shock formation. Particle-in-cell simulations confirm these results.
Collisionless shocks are shocks in which the mean-free path is much larger than the shock front. They are ubiquitous in astrophysics and the object of much current attention as they are known to be excellent particle accelerators that could be the key to the cosmic rays enigma. While the scenario leading to the formation of a fluid shock is well known, less is known about the formation of a collisionless shock. We present theoretical and numerical results on the formation of such shocks when two relativistic and symmetric plasma shells (pair or electron/proton) collide. As the two shells start to interpenetrate, the overlapping region turns Weibel unstable. A key concept is the one of trapping time τ_{p}, which is the time when the turbulence in the central region has grown enough to trap the incoming flow. For the pair case, this time is simply the saturation time of the Weibel instability. For the electron/proton case, the filaments resulting from the growth of the electronic and protonic Weibel instabilities, need to grow further for the trapping time to be reached. In either case, the shock formation time is 2τ_{p} in two-dimensional (2D), and 3τ_{p} in 3D. Our results are successfully checked by particle-in-cell simulations and may help designing experiments aiming at producing such shocks in the laboratory.
In this article, we discuss the idea of a hierarchy of instabilities that can rapidly couple the disparate scales of a turbulent plasma system. First, at the largest scale of the system, L, current carrying flux ropes can undergo a kink instability. Second, a kink instability in adjacent flux ropes can rapidly bring together bundles of magnetic flux and drive reconnection, introducing a new scale of the current sheet width, ℓ, perhaps several ion inertial lengths (δ _{ i }) across. Finally, intense current sheets driven by reconnection electric fields can destabilize kinetic waves such as ion cyclotron waves as long as the drift speed of the electrons is large compared to the ion thermal speed, v _{ D }≫v _{ i }. Instabilities such as these can couple MHD scales to kinetic scales, as small as the proton Larmor radius, ρ _{ i }.
Magnetic confinement fusion science leads many other branches of plasma physics in its capacity to predict, interpret and understand the behaviour of energetic particle populations. The range of applications of this capability should be extended, for the mutual benefit of fusion research and of other branches of science. In this paper we review progress in applying fusion-derived techniques to one of the central questions of astrophysics: the origin of the cosmic ray population that is magnetically confined within our Galaxy. While it is widely believed that supernova remnant shocks provide the main acceleration sites for cosmic ray electrons and protons, the fundamental 'injection' problem remains. Namely, how particles are initially accelerated from ambient thermal to mildly relativistic energies, beyond which Fermi-type processes take over. The cosmic ray injection environment is magnetized and has many other physical resemblances to beam-heated and deuterium-tritium tokamak plasmas, in consequence, many of the same physical processes come into play. These include, for example, collective beam-plasma instability, resonant wave-particle coupling, and the stochasticization of particle orbits. A broad range of analytical and numerical techniques familiar in the fusion context has been successfully applied to the injection problem (see, for example, Dieckmann M.E. et al 2000 Astron. Astrophys. 356 377). Ideas from magnetic fusion have also been used to help design and interpret recent magnetized plasma experiments (Woolsey N.C. et al 2001 Phys. Plasmas 8 2439) using the high-power VULCAN laser, which address the cosmic ray injection problem from a new perspective.
The filamentation instability (FI) driven by beams of counter-propagating electrons is examined with one dimensional (1D) and two-dimensional (2D) particle-in-cell (PIC) simulations. The 1D simulation reveals the saturation mechanism of the FI. The magnetic pressure gradient displaces the electrons. The resulting electrostatic field inhibits together with the magnetic field a further growth of the filaments by suppressing the electron motion. The FI evolves into a stationary equilibrium in 1D, which shows a statistical distribution of the filament sizes that resembles a Gumbel distribution. The 2D PIC simulation allows the filaments to move around each other and filaments carrying currents of equal polarity can merge. The time-evolution of the characteristic size of the filaments in the 2D simulation is measured. It increases linearly with the time.
The observation of ultra-relativistic plasma flow in the form of the collimated jets of active galactic nuclei and gamma ray bursts requires a better understanding of their relaxation. A description of the plasma thermalization requires, in principle, a kinetic model, e.g. in form of relativistic particle-in-cell simulations. The computational cost of such simulations imposes, however, strong limitations on the system size and geometry, which restricts the physical accuracy of the simulation, e.g. by reducing the proton-to-electron mass ratio or the plasma flow speed. Alternatively, one may attempt to subdivide the overall system into well-defined components, which can then be resolved at an appropriate resolution. This may provide qualitative insight into the plasma relaxation, which could be compared to experimental data. An important observation is the similarity of gamma ray bursts in terms of the emitted radiation. The gamma factor associated with the flow speed of gamma ray bursts is of the order 100-1000. A similar emission of gamma ray bursts, despite the large variations in their flow speeds, suggests plasma processes that do not strongly depend on the flow speed. We present one-dimensional particle-in-cell simulation studies of the ultrarelativistic two-stream instability. The instability is driven by two spatially homogeneous inter-penetrating plasma beams, which consist of electrons and protons. The simulation box is aligned with the plasma flow velocity vector. This system thus excludes the important Weibel and mixed mode instabilities, but it allows us to model the two-stream instability over a wide spatial interval. We find a universal behaviour of the instability that does not depend on the beam speed. We observe for flow gamma factors between 100-1000 the development of broadband electrostatic turbulence, which yields the relativistic Brownian motion of the electrons. This Brownian motion results in the development of a Jüttner-Synge electron momentum distribution that shows a linear scaling of the momentum spread with the initial beam gamma factor. The reaction of the proton component to the wave fields locally accelerates electrons to ultra-relativistic speeds, yielding a thin high energy tail in addition to the thermal bulk population.
A two-stream instability in an unmagnetized plasma is examined by a particle-in-cell simulation. Each beam initially consists of cold electrons and protons that stream at a relative Lorentz factor 100. This is representative for plasma close to the external shocks of gamma-ray bursts. An electrostatic wave develops which saturates by trapping electrons. This wave collapses and the resulting electrostatic turbulence gives an electron momentum distribution that resembles a power law with a spectral break. Some electrons reach Lorentz factors over 1000. © 2005 The American Physical Society.
The emission of energetic radiation by astrophysical sources, e.g. the accretion disks of micro-quasars and active galactic nuclei, and gamma ray bursts, requires efficient particle acceleration mechanisms. Previously, electron surfing acceleration (ESA) has been introduced as a process that may accelerate electrons to unlimited energies. The ESA mechanism requires a quasi-electrostatic wave that can, for example, be driven by a two-stream instability. The wave traps electrons and transports them across an ambient magnetic field that is oriented perpendicularly to the wave vector. For sufficiently strong waves, the electrons cannot de-trap, which is opening up the prospect of unlimited electron acceleration. Particle-in-cell simulations have, however, revealed an important limitation of ESA. The saturated wave is not stable and its collapse releases the electrons. For non-relativistic phase speeds, the electron energy is limited to keV-regimes. We have found with the help of particle-in-cell simulations that relativistic phase speeds of the wave stabilize the system. We discuss how the electrons can be trapped for a longer time while the relativistic phase speed implies a rapid electron acceleration. We show that the peak electron speed accessible to the ESA mechanism increases into relativistic regimes. Quasi-electrostatic waves with a phase speed of 0.6c, which we may find in the upstream region of mildly relativistic shocks in micro-quasar accretion disks, can accelerate electrons to gamma factors of a few. Increasing the phase speed of the waves to values between 0.9c and 0.99c, which we may find at the most energetic astrophysical objects, e.g. active galactic nuclei and gamma ray bursts, yields peak electron gamma factors above 100. We show how a new limit emerges,in form of a peak electron gamma factor that equals the proton-to electron mass ratio. Such electron flow speeds are comparable to the fastest observed plasma flow speeds associated with gamma ray burst jets and the collimated jets of active galactic nuclei. ESA may thus contribute to their generation.
We examine the saturation of electrostatic waves driven by proton beams moving at relativistic speeds through a plasma. We visualize the plasma phase space distribution after the saturation of the wave that has developed between the background electrons and the proton beams. A secondary instability grows between the background protons and a proton beam due to relativistic effects. We show how the saturated wave forms a proton phase space vortex that may generate cosmic ray electrons by its collapse. © 2005 IEEE.
Recent particle-in-cell (PIC) simulation studies have addressed particle acceleration and magnetic field generation in relativistic astrophysical flows by plasma phase space structures. We discuss the astrophysical environments such as the jets of compact objects, and we give an overview of the global PIC simulations of shocks. These reveal several types of phase space structures, which are relevant for the energy dissipation. These structures are typically coupled in shocks, but we choose to consider them here in an isolated form. Three structures are reviewed. (1) Simulations of interpenetrating or colliding plasma clouds can trigger filamentation instabilities, while simulations of thermally anisotropic plasmas observe the Weibel instability. Both transform a spatially uniform plasma into current filaments. These filament structures cause the growth of the magnetic fields. (2) The development of a modified two-stream instability is discussed. It saturates first by the formation of electron phase space holes. The relativistic electron clouds modulate the ion beam and a secondary, spatially localized electrostatic instability grows, which saturates by forming a relativistic ion phase space hole. It accelerates electrons to ultra-relativistic speeds. ( 3) A simulation is also revised, in which two clouds of an electron-ion plasma collide at the speed 0.9c. The inequal densities of both clouds and a magnetic field that is oblique to the collision velocity vector result in waves with a mixed electrostatic and electromagnetic polarity. The waves give rise to growing corkscrew distributions in the electrons and ions that establish an equipartition between the electron, the ion and the magnetic energy. The filament-, phase space hole- and corkscrew structures are discussed with respect to electron acceleration and magnetic field generation.
Thin-shell instability is 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 downstreams thermal pressure at a nonplanar shock. Here we show by means of a particle-in-cell simulation that an analog process can destabilize a thin shell formed by two interpenetrating, unmagnetized, and collisionless plasma clouds. The amplitude of the shells spatial modulation grows and saturates after about ten inverse proton plasma frequencies, when the shell consists of connected piecewise linear patches.
Energetic electromagnetic emissions by astrophysical jets like those that are launched during the collapse of a massive star and trigger gamma-ray bursts 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 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.
Two charge- and current-neutral plasma beams are modeled with a one-dimensional particle-in-cell 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 the other of protons and negatively charged oxygen (dust). All species have the temperature 9.1 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 acousticwaves, which trap the protons of the second beam. Astructure similar to a proton phase-space hole develops, which grows through its interaction with the oxygen and the heated electrons into a rarefaction pulse. This pulse drives a 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 (SNR) shocks. This double layer is thus potentially relevant for the electron acceleration (injection) into the diffusive shock acceleration by SNR shocks.
Electron surfing acceleration (ESA) is based on the trapping of electrons by a wave and the transport of the trapped electrons across a perpendicular magnetic field. ESA can accelerate electrons to relativistic speeds and it may thus produce hot electrons in plasmas supporting fast ion beams, like close to astrophysical shocks. One-dimensional (1D) particle-in-cell (PIC) simulations have demonstrated that trapped electron structures (phase space holes) are stabilized by relativistic phase speeds of the waves, by which ESA can accelerate electrons to ultrarelativistic speeds. The 2(1/2)D electromagnetic and relativistic PIC simulations performed in the present paper model proton beam driven instabilities in the presence of a magnetic field perpendicular to the simulation plane. This configuration represents the partially electromagnetic mixed modes and the filamentation modes, in addition to the Buneman waves. The waves are found to become predominantly electromagnetic and nonplanar for beam speeds that would result in stable trapped electron structures. The relativistic boost of ESA reported previously is cancelled by this effect. For proton beam speeds of 0.6 and 0.8c, the electrons reach only million electron volt energies. The system with the slower beam is followed sufficiently long in time to reveal the development of a secondary filamentation instability. The instability forms a channel in the simulation domain that is void of any magnetic field. Proton beams may thereby cross perpendicular magnetic fields for distances beyond their gyroradius.
An electrostatic instability driven by counter-propagating tenuous proton beams that traverse a bulk plasma consisting of electrons and protons is considered. The system is spatially homogeneous and is evolved in time with a one-dimensional particle-in-cell simulation, which allows for a good statistical plasma representation. Mildly and highly relativistic beam speeds are modeled. The proton beams with a speed of 0.9c result in waves that saturate by the trapping of electrons. The collapse of the phase space holes in the electron distribution scatters these to a flat-top momentum distribution. The final electric fields are weak and the proton beams are weakly modulated. No secondary instabilities are likely to form that could thermalize the proton beams. The proton beams moving with 0.99c initially heat the bulk plasma through a three-wave interaction. Coalescing phase space holes in the bulk proton distribution arising from the saturation of ion acoustic waves transport wave energy to low wavenumbers. Highly relativistic phase space holes form in the electron distribution, which are not spatially homogeneous. The spatial envelope of these electron phase space holes interacts with the fluctuations driven by the phase space holes in the bulk protons, triggering a modulational instability. A Langmuir wave condensate forms that gives rise to strong and long electrostatic wave packets, as well as to a substantial modulation of the proton beams. The final state of the system with the highly relativistic proton beams is thus more unstable to further secondary instabilities that may transfer a larger beam energy fraction to the electrons and thermalize the proton beams more rapidly
A sounder measures the density of plasmas in various parts of the solar system. The sounder emits wave pulses into the ambient plasma and listens to the response. Intensity peaks in the wave response are typically related to two mechanisms. One is provided by waves that are reflected off plasma inhomogeneities and propagate back to the emitting antenna, where they are then detected. The second is provided by waves propagating with the same group velocity as that of the receiving antenna. In the second case the waves stay close to the antenna and thus yield a long-lasting response. Response peaks to sounding at the upper hybrid (UH) frequency have, in most cases, been related to reflected waves. In this work we examine if accompanying waves can give rise to the UH response peak. We examine quantitatively how the plasma response to sounding at the UH frequency depends on the plasma density, on the electron temperature, and on the emission amplitude. For the first two parameters this is done by solving the linear dispersion relation. The well-known property of the UH waves to change from having a zero group velocity to propagating waves, depending on how the electron density compares to the electron cyclotron frequency, is applied to Alouette sounder data. It is discussed how the change in the group velocity may affect the spectral profile of the UH resonance. We present results from numerical particle in cell (PIC) simulations which show that in the case of nonpropagating UH waves, energy can be coupled into the plasma even though the vanishing group velocity of the UH waves should not allow this. The PIC simulations and sounder data from the Alouette mission show that in the case of propagating UH waves the response duration to sounding may be used to determine the electron temperature. Emission amplitudes that are typical for plasma sounders are also shown to suppress the generation of certain electron cyclotron harmonic waves.
Contemporary lasers allow us to create shocks in the laboratory that propagate at a speed that matches that of energetic astrophysical shocks like those that ensheath supernova blast shells. The rapid growth time of the shocks and the spatio-temporal resolution, with which they can be sampled, allow us to identify the processes that are involved in their formation and evolution. Some laser-generated unmagnetized shocks are mediated by collective electrostatic forces and effects caused by binary collisions between particles can be neglected. Hydrodynamic models, which are valid for many large-scale astrophysical shocks, assume that collisions enforce a local thermodynamic equilibrium in the medium; laser-generated shocks are thus not always representative for astrophysical shocks. Laboratory studies of shocks can improve the understanding of their astrophysical counterparts if we can identify processes that affect electrostatic shocks and hydrodynamic shocks alike. An example is the nonlinear thin-shell instability (NTSI). We show that the NTSI destabilises collisionless and collisional shocks by the same physical mechanism.
The expansion of a radial blast shell into an ambient plasma is modeled with a particle-in-cell 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 radial 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 slow down the blast shell protons and bring the post-shock plasma closer to equilibrium.
Electrons can be accelerated by their interaction with nonlinearly saturated electrostatic waves up to speeds with which they can undergo diffusive acceleration across supernova remnant shocks. Here, we model this wave-electron interaction by particle-in-cell and Vlasov simulations. We find that the lifetime of the saturated wave is considerably longer in the Vlasov simulation, due to differences in how these simulation methods approximate the plasma. Electron surfing acceleration which requires a stable saturated wave may thus be more important for electron acceleration at shocks than previously thought. For beam speeds above a critical value, which we estimate here, both simulation codes exclude surfing acceleration due to a rapid wave collapse.
Electrons that are trapped by a quasi-electrostatic wave move, on average, with the phase speed of the wave. In the presence of a magnetic field B, the trapped electrons could, in principle, be accelerated to cosmic ray energies through cross-field transport. We model this cross-field transport with a particle-in-cell (PIC) simulation for an oblique B. The electron energies at the simulation's end exceed 5 MeV for all pitch angles and they can reach GeV energies along the wavevector. We discuss environments, in which such conditions may exist and for which such an acceleration would be relevant.
Initially, inhomogeneous plasma jets, ejected by active galactic nuclei and associated with gamma-ray bursts, are thermalized by the formation of internal shocks. Jet subpopulations can hereby collide at Lorentz factors of a few. As the resulting relativistic shock expands into the upstream plasma, a significant fraction of the upstream ions is reflected. These ions, together with downstream ions that leak through the shock, form relativistic beams of ions that outrun the shock. The thermalization of these beams via the two-stream instability is thought to contribute significantly to plasma heating and particle acceleration by the shock. Here, the capability of a two-stream instability to generate relativistic field-aligned and cross-field electron flow, is examined for a magnetized plasma by means of a particle-in-cell (PIC) simulation. The electrons interact with the developing quasi-electrostatic waves and oblique magnetic fields. The simulation results bring forward evidence that such waves, by their non-linear interactions with the plasma, produce a highly relativistic field-aligned electron flow and electron energies, which could contribute to the radio synchrotron emissions from astrophysical jets, to ultrarelativistic leptonic subpopulations propagating with the jet and to the halo particles surrounding the accretion disc of the black hole.
Plasmas collide at relativistic speeds in many astrophysical and high energy density laboratory environments. The collision boundaries are not well understood. In the absence of a magnetic field B0 that is parallel to the flow velocity vector vb the boundaries are filamentary, since waves grow with wavevectors k that are not parallel to vb. Modelling such boundaries requires large 3D particle-in-cell (PIC) simulations. A flow-aligned B0 can suppress wave modes other than k parallel to vb, as multi-dimensional PIC simulations show. We select a vb, a plasma temperature T and B0, for which the growth rate of the two-stream instability exceeds that of all other instabilities. We exploit this planarity to resort to a 1D simulation, that lets two identical electron-proton plasma slabs collide with a relativistic speed and a Mach number of over 400. The developing electrostatic turbulent boundary dissipates its energy via electron phase space holes that accelerate electrons to relativistic speeds and increase significantly the speed of some protons. The results are important in the context of a dynamic accretion disc and microquasar jets. The accelerated electrons may feed the disc wind and the relativistic leptonic jets, and possibly contribute to the hard radiation component of the accretion disc.
Shocks play a key role in plasma thermalization and particle acceleration in the near Earth space plasma, in astrophysical plasma and in laser plasma interactions. An accurate understanding of the physics of plasma shocks is thus of immense importance. We give an overview over some recent developments in particle-in-cell simulations of plasma shocks and foreshock dynamics. We focus on ion reflection by shocks and on the two-stream instabilities these beams can drive, and these are placed in the context of experimental observations, e.g. by the Cluster mission. We discuss how we may expand the insight gained from the observation of proton beam driven instabilities at near Earth plasma shocks to better understand their astrophysical counterparts, such as ion beam instabilities triggered by internal and external shocks in the relativistic jets of gamma ray bursts, shocks in the accretion discs of micro-quasars and supernova remnant shocks. It is discussed how and why the peak energy that can be reached by particles that are accelerated by two-stream instabilities increases from keV energies to GeV energies and beyond, as we increase the streaming speed to relativistic values, and why the particle energy spectrum sometimes resembles power law distributions.
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 simulation over magnetohydrodynamics 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.
Particle-in-cell simulations confirm here that a mixed plasma mode is the fastest growing when a highly relativistic tenuous electron-proton beam interacts with an unmagnetized plasma. The mixed modes grow faster than the filamentation and two-stream modes in simulations with beam Lorentz factors Gamma of 4, 16, and 256, and are responsible for thermalizing the electrons. The mixed modes are followed to their saturation for the case of Gamma=4 and electron phase space holes are shown to form in the bulk plasma, while the electron beam becomes filamentary. The initial saturation is electrostatic in nature in the considered one- and two-dimensional geometries. Simulations performed with two different particle-in-cell simulation codes evidence that a finite grid instability couples energy into high-frequency electromagnetic waves, imposing simulation constraints.
Instabilities driven by two electron beams that stream at the relativistic relative velocity vb are important as a plasma thermalization and magnetic field generation mechanism in astrophysics and in inertial confinement fusion. The time-evolution of such instabilities, which are subdivided into the two-stream, mixed mode and filamentation (beam-Weibel) instability, is multi-dimensional and nonlinear and the instabilities are usually modelled with particle-in-cell (PIC) simulations. We examine the wave spectrum we obtain, if both beams have a density ratio 9 and (1-vb^2/c^2)^(-1/2)=4. The mixed mode dominates and grows fastest for highly relativistic vb. An electromagnetic finite grid instability is shown to generate artificial magnetic fields, imposing a simulation constraint.
The filamentation instability (FI) is an aperiodically growing instability driven by counterpropagating electron beams. Its ability to generate magnetic fields is important for the energetic plasmas in gamma ray burst jets and inertial confinement fusion plasmas. The FI has been examined both analytically and with particle-in-cell (PIC) simulations. We perform PIC simulations and follow the FI through its nonlinear saturation. The power spectrum of the flow-aligned current component is self-similar during the linear phase. We show that the perpendicular current distribution is self-similar during the nonlinear evolution and that the filament size increases linearly with time. We demonstrate that, at least for warm plasmas, the current filaments can't be described by simple flux tubes. Instead, the filaments merge by magnetic reconnection to form larger, partially overlapping current sheets. In the filament overlap region the electrons are accelerated.
Colliding plasmas can form current filaments that are magnetically confined and interact through electromagnetic fields during the nonlinear evolution of this filamentation instability. A nonrelativistic and a relativistic electron flow are examined. Two-dimensional (2D) particle-in-cell (PIC) simulations evolve the instability in a plane orthogonal to the flow vector and confirm that the current filaments move, merge through magnetic reconnection and evolve into current sheets and large flux tubes. The current filaments overlap over limited spatial intervals. Electrons accelerate in the overlap region and their final energy distribution decreases faster than exponential. The spatial power spectrum of the filaments in the flow-aligned current component can be approximated by a power-law during the linear growth phase. This may reflect a phase transition. The power spectrum of the current component perpendicular to the flow direction shows a power-law also during the nonlinear phase, possibly due to preferential attachment. The power-law distributed power spectra evidence self-similarity over a limited scale size and the wavenumber of the maximum of the spatial power spectrum of the filament distribution decreases linearly in time. Power-law correlations of velocity fields, which could be connected to the current filaments, may imply super-diffusion.
Collisionless quasiperpendicular shocks with magnetoacoustic Mach numbers exceeding a certain threshold are known to reflect a fraction of the upstream ion population. These reflected ions drive instabilities which, in a magnetized plasma, can give rise to electron acceleration. In the case of shocks associated with supernova remnants (SNRs), electrons energized in this way may provide a seed population for subsequent acceleration to highly relativistic energies. If the plasma is weakly magnetized, in the sense that the electron cyclotron frequency is much smaller than the electron plasma frequency omega (p), a Buneman instability occurs at omega (p). The nonlinear evolution of this instability is examined using particle-in-cell simulations, with initial parameters which are representative of SNR shocks. For simplicity, the magnetic field is taken to be strictly zero. It is shown that the instability saturates as a result of electrons being trapped by the wave potential. Subsequent evolution of the waves depends on the temperature of the background protons T-i and the size of the simulation box L. If T-i is comparable to the initial electron temperature T-e, and L is equal to one Buneman wavelength lambda (0), the wave partially collapses into low frequency waves and backscattered waves at around omega (p). If, on the other hand, T-i much greater thanT(e) and L = lambda (0), two high frequency waves remain in the plasma. One of these waves, excited at a frequency slightly lower than omega (p), may be a Bernstein-Greene-Kruskal mode. The other wave, excited at a frequency well above omega (p), is driven by the relative streaming of trapped and untrapped electrons. In a simulation with L = 4 lambda (0), the Buneman wave collapses on a time scale consistent with the excitation of sideband instabilities. Highly energetic electrons were not observed in any of these simulations, suggesting that the Buneman instability can only produce strong electron acceleration in a magnetized plasma. [S1070-664X(00)02712-9].
We examine wave-particle interactions in a magnetized plasma. We present snapshots of an animation of the three-dimensional electron phase space distribution produced by an electrostatic wave propagating across a magnetic field. The distribution function has been evolved by a particle in cell simulation. The electron phase space has been visualized by distributing the simulation electrons over an array representing phase space density and by volume rendering this array. The results are, due to the choice of initial plasma and wave parameters, of relevance for electron acceleration at astrophysical shocks.