The filamentation instability occurring when a non relativistic electron beam passes through a quantum magnetized plasma is investigated by means of a cold quantum magnetohydrodynamic model. It is proved that the instability can be completely suppressed by quantum effects if and only if a finite magnetic field is present. A dimensionless parameter is identified which measures the strength of quantum effects. Strong quantum effects allow for a much smaller magnetic field to suppress the instability than in the classical regime.
The effects of the non-linearity of the medium on the growth rate of filamentation instability in a magnetized plasma interacting with an intense laser pulse, is investigated. The non-linearity of the medium, modeled by Kerr non-linearity, is an important factor, which determines the rate of instability growth. Sensitivity of the rate of filamentation growth, to the Kerr non-linear coefficient could be adjusted by the external magnetic field and laser intensity.
The filamentation instability of the electromagnetic (EM) beam in an underdense plasma with high level of degeneracy is examined by means of the momentum equation, continuity equation and Maxwell's equations. It has been demonstrated that the instability develops for weakly as well as strongly relativistic degenerate plasma and arbitrary strong amplitude of EM beams.
The growth rate of the filamentation instability triggered when a diluted cold electron beam passes through a cold plasma is evaluated using the quantum hydrodynamic equations. Compared with a cold fluid model, quantum effects reduce both the unstable wave vector domain and the maximum growth rate. Stabilization of large wave vector modes is always achieved, but significant reduction of the maximum growth rate depends on a dimensionless parameter that is provided. Although calculations are extended to the relativistic regime, they are mostly relevant to the non-relativistic one.
Dynamic mitigation is presented for filamentation instability and magnetic reconnection in a plasm driven by a wobbling electron sheet current. The wobbling current introduces an oscillating perturbation and smooths the perturbation. The sheet current creates an anti-parallel magnetic field in plasma. The initial small perturbation induces the electron beam filamentation and the magnetic reconnection. When the wobbling or oscillation motion is added to the sheet electron beam along the sheet current surface, the perturbation phase is mixed and consequently the instability growth is delayed rem…
A nonlinear Langmuir wave in the kinetic regime $kλ_D\gtrsim0.2$ may have a filamentation instability, where $k$ is the wavenumber and $λ_D$ is the Debye length. The nonlinear stage of that instability develops into the filamentation of Langmuir waves which in turn leads to the saturation of the stimulated Raman scattering in laser-plasma interaction experiments. Here we study the linear stage of the filamentation instability of the particular family \cite{RoseRussellPOP2001} of Bernstein-Greene-Kruskal (BGK) modes \cite{BernsteinGreeneKruskal1957} that is a bifurcation of the linear Langmuir …
A Langmuir wave (LW) model is constructed whose equilibria are consistent with stimulated Raman scatter optimization, with Hamiltonian dynamics and with rotational invariance. Linear instability analysis includes terms to all orders in wave amplitude and fluctuation wavenumber expansions, deltak. Resultant LW modulational instability is nonstandard: as the LW amplitude increases, unstable deltak range first expands and then shrinks to zero. Large amplitude wave model dynamics requires hyper-diffraction terms if k LambdaD < 0.45, lest artificially small length scales become unstable.
Filamentation due to the growth of a Weibel-type instability was observed in the interaction of a pair of counter-streaming, ablatively-driven plasma flows, in a supersonic, collisionless regime relevant to astrophysical collisionless shocks. The flows were created by irradiating a pair of opposing plastic (CH) foils with 1.8 kJ, 2-ns laser pulses on the OMEGA EP laser system. Ultrafast laser-driven proton radiography was used to image the Weibel-generated electromagnetic fields. The experimental observations are in good agreement with the analytical theory of the Weibel instability and with p…
The filamentation instability triggered when two counter streaming plasma shells overlap appears to be the main mechanism by which collisionless shocks are generated. It has been known for long that a flow aligned magnetic field can completely suppress this instability. In a recent paper [PHYSICS OF PLASMAS 18, 080706 (2011)], it was demonstrated in two dimensions that for the case of two cold, symmetric, relativistically colliding shells, such cancellation cannot occur if the field is not perfectly aligned. Here, this result is extended to the case of two asymmetric shells. The filamentation …
The filamentation instability of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell (PIC) simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases linearly in time. Currents orthogonal to the beam velocity vector are driven through the magnetic and electric fields in the simulation plane. The fields are tied to the filament boundaries and the scale size …
The filamentation instability (sometimes also referred to as "Weibel") is a key process in many astrophysical scenario. In the Fireball model for Gamma Ray Bursts, this instability is believed to mediate collisionless shock formation from the collision of two plasma shells. It has been known for long that a flow aligned magnetic field can completely cancel this instability. We show here that in the general case where there is an angle between the field and the flow, the filamentation instability can never be stabilized, regardless of the field strength. The presented model analyzes the stabili…
The quantum electromagnetic dielectric tensor for a multi species plasma is re-derived from the gauge invariant Wigner-Maxwell system and presented under a form very similar to the classical one. The resulting expression is then applied to a quantum kinetic theory of the electromagnetic filamentation instability. Comparison is made with the quantum fluid theory including a Bohm pressure term, and with the cold classical plasma result. A number of analytical expressions are derived for the cutoff wave vector, the largest growth rate and the most unstable wave vector.
Generation of relativistic electron (RE) beams during ultraintense laser pulse interaction with plasma targets is studied by collisional particle-in-cell (PIC) simulations. Strong magnetic field with transverse scale length of several local plasma skin depths, associated with RE currents propagation in the target, is generated by filamentation instability (FI) in collisional plasmas, inducing a great enhancement of the divergence of REs compared to that of collisionless cases. Such effect is increased with laser intensity and target charge state, suggesting that the RE divergence might be impr…
The spatial-temporal evolution of the purely transverse current filamentation instability is analyzed by deriving a single partial differential equation for the instability and obtaining the analytical solutions for the spatially and temporally growing current filament mode. When the beam front always encounters fresh plasma, our analysis shows that the instability grows spatially from the beam front to the back up to a certain critical beam length; then the instability acquires a purely temporal growth. This critical beam length increases linearly with time and in the non-relativistic regime …
Density filamentation has been observed in many beam-plasma simulations and experiments. Because current filamentation is a pure transverse mode, charge density filamentation cannot be produced directly by the current filamentation process. To explain this phenomenon, several mechanisms are proposed such as the coupling of the Weibel instability to the two-stream instability, coupling to the Langmuir wave, differences in thermal velocities between the beam and return currents, the magnetic pressure gradient force, etc. In this paper, it is shown that the gradient of the Lorentz factor can, in …
At incident powers much higher than the threshold for filamentation a pulse from a high-power laser generates in the transversal plane a complex structure. It consists of randomly meandering stripes defining connected regions where the field intensity is high; and, the complementary regions dominated by diffusive plasma with defocusing property. The pattern is similar to an ensemble of clusters of various extensions. We provide evidence that there is a correlation between this filamentation and the {\it labyrinth} instability in reaction-diffusion systems. Besides the similarity of the spatial…
Current Filamentation Instability (CFI) is capable of generating strong magnetic fields relevant to explain radiation processes in astrophysical objects and lead to the onset of particle acceleration in collisionless shocks. Probing such extreme scenarios in the laboratory is still an open challenge. In this work, we investigate the possibility of using neutral $e^{-}$ $e^{+}$ beams to explore the CFI with realistic parameters, by performing 2D particle-in-cell simulations. We show that CFI can occur unless the rate at which the beam expands due to finite beam emittance is larger than the CFI …
I theoretically found eigenmodes and growth rates of relativistic current filamentation instability in collisional regimes, deriving a generalized dispersion relation from self-consistent beam-Maxwell equations. For symmetrically counterstreaming, fully relativistic electron currents, the collisional coupling between electrons and ions creates the unstable modes of growing oscillation and wave, which stand out for long-wavelength perturbations. In the stronger collisional regime, the growing oscillatory mode tends to be dominant for all wavelengths. In the collisionless limit, those modes vani…
Counterstreaming plasma structures are widely present in laboratory experiments and astrophysical systems, and they are investigated either to prevent unstable modes arising in beam-plasma experiments or to prove the existence of large scale magnetic fields in astrophysical objects. Filamentation instability arises in a counterstreaming plasma and is responsible for the magnetization of the plasma. Filamentationally unstable mode is described by assuming that each of the counterstreaming plasmas has an isotropic Lorentzian (kappa) distribution. In this case, the filamentation instability growt…
The physics of instabilities in the precursor of relativistic collisionless shocks is of broad importance in high energy astrophysics, because these instabilities build up the shock, control the particle acceleration process and generate the magnetic fields in which the accelerated particles radiate. Two crucial parameters control the micro-physics of these shocks: the magnetization of the ambient medium and the Lorentz factor of the shock front; as of today, much of this parameter space remains to be explored. In the present paper, we report on a new instability upstream of electron-positron …
The filamentation (Weibel) instability plays a key role in the formation of collisionless shocks which are thought to produce Gamma-Ray-Bursts and High-Energy-Cosmic-Rays in astrophysical environments. While it has been known for long that a flow-aligned magnetic field can completely quench the instability, it was recently proved in 2D that in the cold regime, such cancelation is possible if and only if the field is perfectly aligned. Here, this result is finally extended to a 3D geometry. Calculations are conducted for symmetric and asymmetric counter-streaming relativistic plasma shells. 2D …
We consider two kinds of pumped Langmuir waves (LWs) in the kinetic regime, $kλ_D\gtrsim0.2,$ where $k$ is the LW wavenumber and $λ_D$ is the Debye length. They are driven to finite amplitude by a coherent external potential whose amplitude is either weak or strong. These dynamically prepared nonlinear LWs develop a transverse (filamentation) instability whose nonlinear evolution destroys the LW's transverse coherence. Instability growth rates in the weakly pumped regime are the same as those of BGK modes considered in Part I, while strongly pumped LWs have higher filamentation grow rates.
The evolution of the filamentation instability produced by two counter-streaming pair plasmas is studied with particle-in-cell (PIC) simulations in both one (1D) and two (2D) spatial dimensions. Radiation friction effects on particles are taken into account. After an exponential growth of both the magnetic field and the current density, a nonlinear quasi-stationary phase sets up characterized by filaments of opposite currents. During the nonlinear stage, a strong broadening of the particle energy spectrum occurs accompanied by the formation of a peak at twice their initial energy. A simple the…
Two counter-propagating cool and equally dense electron beams are modelled with particle-in-cell (PIC) simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasi-planar filament boundary. It is confirmed, that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. Th…
The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their nonrelativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated, that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small co…
Particle-in-cell (PIC) simulations of collisionless jets of electrons and positrons in an ambient electron-proton plasma have revealed an acceleration of positrons at the expense of electron kinetic energy. The dominant instability within the jet was a filamentation instability between electrons, protons and positrons. In this work we show that a filamentation instability, between an initially unmagnetized ambient electron-proton plasma at rest and a beam of pair plasma that moves through it at a non-relativistic speed, indeed results in preferential positron acceleration. Filaments form that …
When a relativistic intensity laser interacts with the surface of a solid density target, suprathermal electron currents are subject to Weibel instability filamentation when propagating through the thermal population of the bulk target. We present time resolved shadowgraphy of radial ionization front expansion and Weibel instability filamentation within a thin, sub-micron, sheet initiated by irradiation with a short pulse, high intensity laser. High temporal (100 fs) and spatial (1 $μ$m) resolution shadowgraphy of the interaction reveals a relativistic expansion of the ionization front within …
We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particle-in-cell …
We show that the Weibel or currente filamentation instability can lead to the emission of circularly polarized radiation. Using particle-in-cell (PIC) simulations and a radiation post-processing numerical algorithm, we demonstrate that the level of circular polarization increases with the initial plasma magnetization, saturating at ~13% when the magnetization, given by the ratio of magnetic energy density to the electron kinetic energy density, is larger than 0.05. Furthermore, we show that this effect requires an ion-electron mass ratio greater than unity. These findings, which could also be …
Two counter-propagating cool and equally dense electron beams are modelled with particle-in-cell (PIC) simulations. The electron beam filamentation instability is examined in one spatial dimension. The box length resolves one pair of current filaments. A small, a medium-sized and a large filament are considered and compared. The magnetic field amplitude at the saturation time of the filamentation instability is proportional to the filament size. It is demonstrated, that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, …
The current filamentation instability, which generically arises in the counterstreaming of supersonic plasma flows, is known for its ability to convert the free energy associated with anisotropic momentum distributions into kinetic-scale magnetic fields. The saturation of this instability has been extensively studied in symmetric configurations where the interpenetrating plasmas share the same properties (velocity, density, temperature). In many physical settings, however, the most common configuration is that of asymmetric plasma flows. For instance, the precursor of relativistic collisionles…
We present experimental measurements of the femtosecond time-scale generation of strong magnetic-field fluctuations during the interaction of ultrashort, moderately relativistic laser pulses with solid targets. These fields were probed using low-emittance, highly relativistic electron bunches from a laser wakefield accelerator, and a line-integrated $B$-field of $2.70 \pm 0.39\,\rm kT\,μm$ was measured. Three-dimensional, fully relativistic particle-in-cell simulations indicate that such fluctuations originate from a Weibel-type current filamentation instability developing at submicron scales …
Beam filamentation instability drives deuterium-tritium fusion with polarized neutron emission
State Key Laboratory of Nuclear Physics and Technology, Peking University（北京大学核物理与技术国家重点实验室）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；College of Physics, Sichuan University（四川大学物理学院）；Beijing Laser Acceleration Innovation Center（北京激光聚变创新中心）
The linear instability that induces a relativistic electron beam passing through a return plasma current to filament transversely is often related to some filamentation mode with wave vector normal to the beam or confused with Weibel modes. We show that these modes may not be relevant in this matter and identify the most unstable mode on the two-stream/filamentation branch as the main trigger for filamentation. This sets both the characteristic transverse and longitudinal filamentation scales in the non-resistive initial stage.
Energetic electromagnetic emissions by astrophysical jets like those that are launched during the collapse of a massive star and trigger gamma-ray bursts (GRBs) are partially attributed to relativistic internal shocks. The shocks are mediated in the collisionless plasma of such jets by the filamentation instability of counterstreaming particle beams. The filamentation instability grows fastest only if the beams move at a relativistic relative speed. We model here with a particle-in-cell (PIC) simulation the collision of two cold pair clouds at the speed c/2 (c: speed of light). We demonstrate …
The filamentation instability driven by two spatially uniform and counter-streaming beams of charged particles in plasmas is modelled by a particle-in-cell (PIC) simulation. Each beam consists of the electrons and positrons. The four species are equally dense and they have the same temperature. The one-dimensional simulation direction is orthogonal to the beam velocity vector. The magnetic field grows spontaneously and rearranges the particles in space, such that the distributions of the electrons of one beam and the positrons of the second beam match. The simulation demonstrates that as a res…
Counterstreaming plasmas exhibits an electromagnetic unstable mode of filamentation type, which is responsible for the magnetization of plasma system. It is shown that filamentation instability becomes significantly faster when plasma is hotter in the streaming direction. This is relevant for astrophysical sources, where strong magnetic fields are expected to exist and explain the nothermal emission observed.
In this work, we derive a dispersion equation that describes the excitation of the oblique (or Alfvén) firehose instability in a plasma that contains both electron and ion species modelled by bi-kappa velocity distribution functions. The equation is obtained with the assumptions of low-frequency waves and moderate to large values of the parallel (respective to the ambient magnetic field) plasma beta parameter, but it is valid for any direction of propagation and for any value of the particle gyroradius (or Larmor radius). Considering values for the physical parameters typical to those found in…
The equations governing the interaction between incoherent light and electron-acoustic waves are presented. The modulational instability properties of the system are studied, and the effect of partially coherent light is discussed. It is shown that partial coherence of the light suppresses the modulational instability. However, short wavelength perturbations are less affected, and will therefore dominate in, e.g. pulse filamentation. The results may be of importance to space plasmas and laser-plasma systems.
Low frequency longitudinal wave instability in magnetized high correlation dusty plasmas is investigated. The dust charging relaxation is taken into account. It is found that the instablity of wave is determined significantly by the frequency of wave, the dust charging relaxation, the shear viscosity and viscoelastic relaxation time, the coupling parameter of high correlation of dust as well the strength of magnetic field.
Temporal evolution of the inhomogeneous energy density driven instability (IEDDI) is examined in presence of a nonuniform transverse dc electric field in collisional magnetized plasma cylinder. Using experimentally known parameters relevant to IEDDI, we have estimated the growth rate for $ν$=1, 2 and 3 nonlocal eigenmodes.
It is shown that the transport in low temperature, collisional, bounded plasma is enhanced by instabilities at high magnetic field. While the magnetic field confines the electrons in a stable plasma, the instability completely destroys the confinement such that the transport becomes independent of the magnetic field in the highly magnetized limit. An analytical expression of the instability-enhanced collision frequency is proposed, based on a magnetic field independent edge-to-center density ratio.
Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it and their influence on the resulting electrostatic waves are shown.
The nonlinear evolution of the Kelvin Helmholtz instability in a magnetized plasma with a perpendicular flow close to, or in, the supermagnetosonic regime can produce a significant parallel-to-perpendicular pressure anisotropy. This anisotropy, localized inside the flow shear region, can make the configuration unstable either to the mirror or to the firehose instability and, in general, can affect the development of the KHI. The interface between the solar wind and the Earth's magnetospheric plasma at the magnetospheric equatorial flanks provides a relevant setting for the development of this …
Ab initio simulations of the propagation in a plasma of a soon to be available relativistic electron-positron beam or fireball beam provide an effective mean for the study of microphysics relevant to astrophysical scenarios. We show that the current filamentation instability associated with some of these scenarios reaches saturation after only 10 cm of propagation in a typical laboratory plasma with a density 10^17/cc. The different regimes of the instability, from the purely transverse to the mixed mode filamentation, can be accessed by varying the background plasma density. The instability g…
The Jeans instability is analyzed for dense magnetohydrodynamic plasmas with intrinsic magnetization, the latter due to collective electron spin effects. Furthermore, effects of electron tunneling as well as the Fermi pressure are included. It is found that the intrinsic magnetization of the plasma will enhance the Jeans instability, and can significantly modify the structure of the instability spectra. Implications and limitations of our results are discussed, as well as possible generalizations.
A recent experimental observation has shown efficient transport of Mega Ampere of electron currents through aligned carbon nanotube arrays [Phys. Rev Letts. 108, 235005 (2012)]. The result was subsequently interpreted on the basis of suppression of the filamentation instability in an inhomogeneous plasma [Phys. Plasmas 21, 012108 (2014)]. This inhomogeneity forms as a result of the ionization of the carbon nanotubes. In the present work a full 1D3V Particle-in-Cell (PIC) simulations have been carried out for the propagation of relativistic electron beams (REB) through an inhomogeneous backgrou…
A new transverse mode in a two-stream magnetized quantum plasma is studied by means of a quantum hydrodynamic model, under non-relativistic and ideal Fermi gas assumptions. It is found that Fermi pressure effects induce a minimum cutoff wavelength for instability, unlike the classical case which is unstable for larger wavenumbers. The external magnetic field is also shown to produce a stabilizing effect. Conditions for the applicability of the model and specific parameters for experimental observations are thoroughly discussed.
Radiation from many astrophysical sources, e.g. gamma-ray bursts and active galactic nuclei, is believed to arise from relativistically shocked collisionless plasmas. Such sources often exhibit highly transient spectra evolving rapidly, compared with source lifetimes. Radiation emitted from these sources is typically associated with non-linear plasma physics, complex field topologies and non-thermal particle distributions. In such circumstances a standard synchrotron paradigm may fail to produce accurate conclusions regarding the underlying physics. Simulating spectral emission and spectral ev…
We analyse the full shock formation process in electron-ion plasmas in theory and simulations. It is accepted that electromagnetic shocks in initially unmagnetised relativistic plasmas are triggered by the filamentation instability. However, the transition from the first unstable phase to the quasi-steady shock is still missing. We derive a theoretical model for the shock formation time, taking into account the filament merging in the non-linear phase of the filamentation instability. This process is much slower than in electron-positron pair shocks, so that the shock formation is longer by a …
A regime where a uniformly magnetized plasma could be unstable to a spatial perturbation in the magnetic field is explored. In this regime, a uniformly magnetized state does not maximize the entropy. The physical implication is discussed in the context of the current generation, the magnetic reconnection, and the dynamo effect.
