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
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.
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.
We study the influence of collisions on the dynamics of a cold non-relativistic plasma. It is shown that even a comparatively small collision frequency can significantly change the large amplitude wave solution. Published by AIP Publishing.
We derive two equations describing the coupling between electromagnetic and electrostaticoscillations in one-dimensional geometry in a magnetized cold and non-relativistic plasma. The nonlinear interaction between the wave modes is studied numerically. The effects of the external magnetic field strength and the initial electromagneticpolarization are of particular interest here. New results can, thus, be identified.
The resonant interaction between three waves in a uniform magnetized plasma is reconsidered. Starting from previous kinetic expressions, we limit our investigation to waves propagating perpendicularly to the external magnetic field. It is shown that reliable results can only be obtained in the two-dimensional case, i.e., when the wave vectors have both x and y components. (C) 2015 AIP Publishing LLC.
Observations by, for instance, the EISCAT Svalbard Radar (ESR) demonstrate that the symmetry of the naturally occurring ion line in the polar ionosphere can be broken by an enhanced, nonthermal, level of fluctuations (naturally enhanced ion-acoustic lines, NEIALs). It was in many cases found that the entire ion spectrum can be distorted, also with the appearance of a third line, corresponding to a propagation velocity significantly slower than the ion acoustic sound speed. It has been argued that selective decay of beam excited primary Langmuir waves can explain some phenomena similar to those observed. We consider a related model, suggesting that a primary nonlinear process can be an oscillating two-stream instability, generating a forced low frequency mode that does not obey any ion sound dispersion relation. At later times, the decay of Langmuir waves can give rise also to enhanced asymmetric ion lines. The analysis is based on numerical results, where the initial Langmuir waves are excited by a cold dilute electron beam. By this numerical approach, we can detect fine details of the physical processes, in particular, demonstrate a strong space-time intermittency of the electron waves in agreement with observations. Our code solves the full Vlasov equation for electrons and ions, with the dynamics coupled through the electrostatic field derived from Poissons equation. The analysis distinguishes the dynamics of the background and beam electrons. This distinction simplifies the analysis for the formulation of the weakly nonlinear analytical model for the oscillating two-stream instability. The results have general applications beyond their relevance for the ionospheric observations.
We study with a one-dimensional particle-in-cell simulation the expansion of a pair cloud into a magnetized electron–proton plasma as well as the formation and subsequent propagation of a tangential discontinuity that separates both plasmas. Its propagation speed takes the value that balances the magnetic pressure of the discontinuity against the thermal pressure of the pair cloud and the ram pressure of the protons. Protons are accelerated by the discontinuity to a speed that exceeds the fast magnetosonic speed by the factor of 10. A supercritical fast magnetosonic shock forms at the front of this beam. An increasing proton temperature downstream of the shock and ahead of the discontinuity leaves the latter intact. We create the discontinuity by injecting a pair cloud at a simulation boundary into a uniform electron–proton plasma, which is permeated by a perpendicular magnetic field. Collisionless tangential discontinuities in the relativistic pair jets of x-ray binaries (microquasars) are in permanent contact with the relativistic leptons of their inner cocoon, and they become the sources of radio synchrotron emissions.
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 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.
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.
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 is 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 collisionless 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.
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.
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].
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 which resemble their magnetohydrodynamic counterparts. The ambient plasma is composed of electrons with the temperature of 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.
We examine with particle-in-cell simulations how a parallel shock in pair plasma reacts to upstream waves, which are driven by escaping downstream particles. Initially, the shock is sustained in the two-dimensional simulation by a magnetic filamentation (beam-Weibel) instability. Escaping particles drive an electrostatic beam instability upstream. Modifications of the upstream plasma by these waves hardly affect the shock. In time, a decreasing density and an increasing temperature of the escaping particles quench the beam instability. A larger thermal energy along than perpendicular to the magnetic field destabilizes the pair-Alfvén mode. In the rest frame of the upstream plasma, the group velocity of the growing pair-Alfvén waves is below that of the shock and the latter catches up with the waves. Accumulating pair-Alfvén waves gradually change the shock in the two-dimensional simulation from a Weibel-type shock into an Alfvénic shock with a Mach number that is about 6 for our initial conditions.
The expansion of a magnetized high-pressure plasma into a low-pressure ambient medium is examined with particle-in-cell simulations. The magnetic field points perpendicular to the plasmas expansion direction and binary collisions between particles are absent. The expanding plasma steepens into a quasi-electrostatic shock that is sustained by the lower-hybrid (LH) wave. The ambipolar electric field points in the expansion direction and it induces together with the background magnetic field a fast E cross B drift of electrons. The drifting electrons modify the background magnetic field, resulting in its pile-up by the LH shock. The magnetic pressure gradient force accelerates the ambient ions ahead of the LH shock, reducing the relative velocity between the ambient plasma and the LH shock to about the phase speed of the shocked LH wave, transforming the LH shock into a nonlinear LH wave. The oscillations of the electrostatic potential have a larger amplitude and wavelength in the magnetized plasma than in an unmagnetized one with otherwise identical conditions. The energy loss to the drifting electrons leads to a noticeable slowdown of the LH shock compared to that in an unmagnetized plasma. Published by AIP Publishing.
By modelling the expansion of a cloud of electrons and positrons with the temperature of 400 keV which propagates at the mean speed of 0.9c (c: speed of light) through an initially unmagnetized electron-proton plasma with a particle-in-cell simulation, we find a mechanism that collimates the pair cloud into a jet. A filamentation (beam-Weibel) instability develops. 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 of 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.
The interaction of electrons with strong electrostatic waves and an external magnetic field, which is oriented obliquely to the wave vector, leads to stochastic acceleration and acceleration by the cross-field transport of trapped electrons. This wave-particle interaction involves three velocity components of the electrons and, for a plane wave, one spatial position. The phase-space evolution is also affected by nonlinear oscillations in the amplitude of the saturated wave, and the system becomes explicitly time dependent. Here, the wave-particle interactions are investigated with a particle-in-cell simulation, and the results are visualized by examining orbits of individual electrons and also time-evolving phase-space structures. Two clearly distinct electron populations are identified, one due to cross-field transport and the other due to stochastic interactions, which are robust against growing secondary modes. © 2005 American Institute of Physics.
The ever increasing performance of supercomputers is now enabling kinetic simulations of extreme astrophysical and laser produced plasmas. Three-dimensional particle-in-cell (PIC) simulations of relativistic shocks have revealed highly filamented spatial structures and their ability to accelerate particles to ultrarelativistic speeds. However, these PIC simulations have not yet revealed mechanisms that could produce particles with tera-electron volt energies and beyond. In this work, PIC simulations in one dimension (1D) of the foreshock region of an internal shock in a gamma ray burst are performed to address this issue. The large spatiotemporal range accessible to a 1D simulation enables the self-consistent evolution of proton phase space structures that can accelerate particles to giga-electron volt energies in the jet frame of reference, and to tens of tera-electron volt in the Earth's frame of reference. One potential source of ultrahigh energy cosmic rays may thus be the thermalization of relativistically moving plasma.
Particle-in-cell simulations of jets of electrons and positrons in an ambient electron–proton plasma have revealed an acceleration of positrons at the expense of electron kinetic energy. We show that a filamentation instability, between an 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.
Nonrelativistic electrostatic unmagnetized shocks are frequently observed in laboratory plasmas and they are likely to exist in astrophysical plasmas. Their maximum speed, expressed in units of the ion acoustic speed far upstream of the shock, depends only on the electron-to-ion temperature ratio if binary collisions are absent. The formation and evolution of such shocks is examined here for a wide range of shock speeds with particle-in-cell simulations. The initial temperatures of the electrons and the 400 times heavier ions are equal. Shocks form on electron time scales at Mach numbers between 1.7 and 2.2. Shocks with Mach numbers up to 2.5 form after tens of inverse ion plasma frequencies. The density of the shock-reflected ion beam increases and the number of ions crossing the shock thus decreases with an increasing Mach number, causing a slower expansion of the downstream region in its rest frame. The interval occupied by this ion beam is on a positive potential relative to the far upstream. This potential pre-heats the electrons ahead of the shock even in the absence of beam instabilities and decouples the electron temperature in the foreshock ahead of the shock from the one in the far upstream plasma. The effective Mach number of the shock is reduced by this electron heating. This effect can potentially stabilize nonrelativistic electrostatic shocks moving as fast as supernova remnant shocks.
The expansion of a charge-neutral cloud of electrons and positrons with the temperature 1 MeV into an unmagnetized ambient plasma is examined with a 2D particle-in-cell simulation. The pair outflow drives solitary waves in the ambient protons. Their bipolar electric fields attract electrons of the outflowing pair cloud and repel positrons. These fields can reflect some of the protons, thereby accelerating them to almost an MeV. Ion acoustic solitary waves are thus an efficient means to couple energy from the pair cloud to protons. The scattering of the electrons and positrons by the electric field slows down their expansion to a nonrelativistic speed. Only a dilute pair outflow reaches the expansion speed expected from the cloud's thermal speed. Its positrons are more energetic than its electrons. In time, an instability grows at the front of the dense slow-moving part of the pair cloud, which magnetizes the plasma. The instability is driven by the interaction of the outflowing positrons with the protons. These results shed light on how magnetic fields are created and ions are accelerated in pair-loaded astrophysical jets and winds.
A pair of curved shocks in a collisionless plasma is examined with a two-dimensional particle-in-cell 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.
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.
Two^{ }counterpropagating cool and equally dense electron beams are modeled with^{ }particle-in-cell simulations. The electron beam filamentation instability is examined in^{ }one spatial dimension, which is an approximation for a quasiplanar^{ }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.
The growth of magnetic fields in the density gradient of a rarefaction wave has been observed in simulations and in laboratory experiments. The thermal anisotropy of the electrons, which gives rise to the magnetic instability, is maintained by the ambipolar electric field. This simple mechanism could be important for the magnetic field amplification in astrophysical jets or in the interstellar medium ahead of supernova remnant shocks. The acceleration of protons and the generation of a magnetic field by the rarefaction wave, which is fed by an expanding circular plasma cloud, is examined here in form of a 2D particle-in-cell simulation. The core of the plasma cloud is modeled by immobile charges, and the mobile protons form a small ring close to the cloud's surface. The number density of mobile protons is thus less than that of the electrons. The protons of the rarefaction wave are accelerated to 1/10 of the electron thermal speed, and the acceleration results in a thermal anisotropy of the electron distribution in the entire plasma cloud. The instability in the rarefaction wave is outrun by a TM wave, which grows in the dense core distribution, and its magnetic field expands into the rarefaction wave. This expansion drives a secondary TE wave.
The formation of unmagnetized electrostatic shock-like structures with a high Mach number is examined with one-and two-dimensional particle-in-cell (PIC) simulations. The structures are generated through the collision of two identical plasma clouds, which consist of equally hot electrons and ions with a mass ratio of 250. The Mach number of the collision speed with respect to the initial ion acoustic speed of the plasma is set to 4.6. This high Mach number delays the formation of such structures by tens of inverse ion plasma frequencies. A pair of stable shock-like structures is observed after this time in the 1D simulation, which gradually evolves into electrostatic shocks. The ion acoustic instability, which can develop in the 2D simulation but not in the 1D one, competes with the nonlinear process that gives rise to these structures. The oblique ion acoustic waves fragment their electric field. The transition layer, across which the bulk of the ions change their speed, widens and their speed change is reduced. Double layer-shock hybrid structures develop.
We use an ionization region model to explore the ionization processes in the high power impulse magnetron sputtering (HiPIMS) discharge in argon with a titanium target. In conventional dc magnetron sputtering (dcMS), stepwise ionization can be an important route for ionization of the argon gas. However, in the HiPIMS discharge stepwise ionization is found to be negligible during the breakdown phase of the HiPIMS pulse and becomes significant (but never dominating) only later in the pulse. For the sputtered species, Penning ionization can be a significant ionization mechanism in the dcMS discharges, while in the HiPIMS discharge Penning ionization is always negligible as compared to electron impact ionization. The main reasons for these differences are a higher plasma density in the HiPIMS discharge, and a higher electron temperature. Furthermore, we explore the ionization fraction and the ionized flux fraction of the sputtered vapor and compare with recent experimental work. (C) 2015 AIP Publishing LLC.
The growth of nanoparticles (NPs) in plasmas is an attractive technique where improved theoretical understanding is needed for quantitative modeling. The variation of the work function W with size for small NPs, r(NP) amp;lt;= 5 nm, is a key quantity for modeling of three NP charging processes that become increasingly important at a smaller size: electron field emission, thermionic electron emission, and electron impact detachment. Here we report the theoretical values of the work function in this size range. Density functional theory is used to calculate the work functions for a set of NP charge numbers, sizes, and shapes, using copper for a case study. An analytical approximation is shown to give quite accurate work functions provided that r(NP) amp;gt; 0.4 nm, i.e., consisting of about amp;gt; 20 atoms, and provided also that the NPs have relaxed close to spherical shape. For smaller sizes, W deviates from the approximation, and also depends on the charge number. Some consequences of these results for nanoparticle charging are outlined. In particular, a decrease in W for NP radius below about 1 nm has fundamental consequences for their charge in a plasma environment, and thereby on the important processes of NP nucleation, early growth, and agglomeration. Published by AIP Publishing.
Expansion of the ion and electron fronts of a cold non-neutral plasma slab with a quasi-neutral core bounded by layers containing only ions is investigated analytically and exact solutions are obtained. It is found that on average, the plasma expansion time scales linearly with the initial inverse ion plasma frequency as well as the degree of charge imbalance, and no expansion occurs if the cold plasma slab is stationary and overall neutral. However, in both cases, there can exist prominent oscillations on the electron front.
Radial expansion of an ionizing gas or plasma cylinder into vacuum is investigated. An exact model for the evolution of the density and velocity fields of the electrons, ions, and neutrals, including the effect of photo and electron-impact ionization on the flow characteristics is developed and solutions obtained. A quasineutral nonlinear electrostatic mode involving rapid oscillations in the electron velocity but not in the density can occur in the expanding plasma. The mode turns out to be almost unaffected by weak ionization.
The paper presents the results of current measurements for the electron beam, propagating inside a drift tube filled in with a gas mixture (Ar and N-2). The experiments were performed using the TEA-500 pulsed electron accelerator. The main characteristics of electron beam were as follows: 60 ns pulse duration, up to 200 J energy, and 5 cm diameter. The electron beam propagated inside the drift tube assembled of three sections. Gas pressures inside the drift tube were 760 +/- 3, 300 +/- 3, and 50 +/- 1 Torr. The studies were performed in argon, nitrogen, and their mixtures of 33%, 50%, and 66% volume concentrations, respectively. (C) 2015 AIP Publishing LLC.
A one-dimensional particle-in-cell simulation tracks a fast magnetosonic shock over time scales comparable with 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° 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 ∼30%. The wave is slower than the shock, and hence, it is damped.
The evolution of the Buneman and two-stream instabilities driven by a cold dilute mildly relativistic electron beam is studied as a function of the ion-to-electron mass ratio. The growth rates of both instabilities are comparable for the selected parameters if the realistic ion-to-electron mass ratio is used and the Buneman instability outgrows the two-stream instability for an artificially reduced mass ratio. Particle-in-cell simulations show that both instabilities grow independently during their linear growth phase. The much lower saturation amplitude of the Buneman instability implies that it saturates first even if the linear growth rates of both instabilities are equal. The electron phase space holes it drives coalesce. Their spatial size increases in time and they start interacting with the two-stream mode, which results in the growth of electrostatic waves over a broad range of wave numbers. A reduced ion-to-electron mass ratio results in increased ion heating and in an increased energy loss of the relativistic electron beam compared to that in a simulation with the correct mass ratio.
A two-dimensional particle simulation models the collision of two electron-ion plasma clouds along a quasiparallel 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 the cross-section of the torus of a spheromak, which may provide the coherent magnetic fields in gamma-ray burst jets needed for their prompt emissions.
Population densities of excited states of argon atoms in a high power impulse magnetron sputtering (HiPIMS) discharge are examined using a global discharge model and a collisional-radiative model. Here, the ionization region model (IRM) and the Orsay Boltzmann equation for electrons coupled with ionization and excited states kinetics (OBELIX) model are combined to obtain the population densities of the excited levels of the argon atom in a HiPIMS discharge. The IRM is a global plasma chemistry model based on particle and energy conservation of HiPIMS discharges. OBELIX is a collisional-radiative model where the electron energy distribution is calculated self-consistently from an isotropic Boltzmann equation. The collisional model constitutes 65 individual and effective excited levels of the argon atom. We demonstrate that the reduced population density of high-lying excited argon states scales with (p*)(-6), where p * is the effective quantum number, indicating the presence of a multistep ladder-like excitation scheme, also called an excitation saturation. The reason for this is the dominance of electron impact processes in the population and de-population of high-lying argon states in combination with a negligible electron-ion recombination.
The^{ }direct observation and full characterization of a phase space electron^{ }hole (EH) generated during laser-matter interaction is presented. This structure,^{ }propagating in a tenuous, nonmagnetized plasma, has been detected via^{ }proton radiography during the irradiation with a ns laser pulse^{ }(I^{2}10^{14} W/cm^{2}) of a gold hohlraum. This technique has allowed the^{ }simultaneous detection of propagation velocity, potential, and electron density spatial^{ }profile across the EH with fine spatial and temporal resolution^{ }allowing a detailed comparison with theoretical and numerical models.
The expansion of a dense plasma through a more rarefied ionized 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 one-dimensional 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 10 eV and 1 keV, respectively. The diffusion of the dense plasma, through the rarefied 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.
[No abstract available]
It is shown that a relative drift between the ions and the charged dust particles in a magnetized quantum dusty plasma can produce an oscillatory instability in a quantum dust acousticlike wave. The threshold and growth rate of the instability are presented. The result may explain the origin of low-frequency electrostatic fluctuations in semiconductors quantum wells. (C) 2008 American Institute of Physics.
We present an investigation of the nonlinear propagation of high-frequency coherent electromagnetic waves in a uniform quantum magnetoplasma. Specifically, we consider nonlinear couplings of right-hand circularly polarized electromagnetic-electron-cyclotron (CPEM-EC) waves with dispersive shear Alfven (DSA) and dispersive compressional Alfven (DCA) perturbations in plasmas composed of degenerate electron fluids and non-degenerate ion fluids. Such interactions lead to amplitude modulation of the CPEM-EC wave packets, the dynamics of which is governed by a three-dimensional nonlinear Schrodinger equation (NLSE) with the frequency shift arising from the relativistic electron mass increase in the CPEM-EC fields and density perturbations associated with the DSA and DCA perturbations. Accounting for the electromagnetic and quantum forces, we derive the evolution equation for the DSA and DCA waves in the presence of the magnetic field-aligned ponderomotive force of the CPEM-EC waves. The NLSE and the driven DSA and DCA equations are then used to investigate the modulational instability. The relevance of our investigation to laser-plasma interaction experiments and the cores of white dwarf stars is pointed out.
The nonlinear interaction between two laser beams in a plasma is investigated in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schrödinger equations that are coupled with the slow plasma density response. A nonlinear dispersion relation is derived and used to 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.
The nonlinear propagation of a circularly polarized electromagnetic (CPEM) wave in a strongly magnetized electron-positron-ion plasma is investigated. Two coupled equations describing the interaction between a high-frequency CPEM wave and the low-frequency electrostatic wake field are derived. It is found that the generation of the wake fields partly depends on the presence of the ion species and the external magnetic field. The wake field generation in turn leads to deceleration and frequency down conversion of the electromagnetic pulse.
The amplitude modulation of compressional dispersive Alfven (CDA) waves in a low-beta plasma is considered. It is shown that the dynamics of modulated CDA waves is governed by a cubic nonlinear Schrodinger equation, which depicts the formation of a dark/grey envelope CDA soliton.
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