Current Filamentation Instability Research Articles

Nonlinear scaling of photon radiation power in relativistic plasma current filamentation instability with beam parameters

Nonlinear scaling of photon radiation power in relativistic plasma current filamentation instability with beam parameters

Ion effects on the scaling of magnetic field amplification in plasmas with the system size

Magnetic field amplification during the nonlinear stage of the current filamentation instability excited by ultra-relativistic electron beams is investigated with a two-dimensional electromagnetic particle-in-cell (PIC) simulation code, with special attention paid to the effects of plasma ions and the system size. The effect of plasma ions is shown to be significant and enhanced magnetic field amplification and beam energy deposition are found due to plasma cavity expansion and merger. When the system size in the transverse direction (perpendicular to the beam propagation direction) is enlarged by a factor of m, the transverse magnetic field energy is found to increase by a factor of m 2 in the case of the plasma with movable ions, in contrast to m with immovable ions. The results are also confirmed by three-dimensional PIC simulations.

Electron Polarization in Ultrarelativistic Plasma Current Filamentation Instabilities

Plasma current filamentation of an ultrarelativistic electron beam impinging on an overdense plasma is investigated, with emphasis on radiation-induced electron polarization. Particle-in-cell simulations provide the classification and in-depth analysis of three different regimes of the current filaments, namely, the normal filament, abnormal filament, and quenching regimes. We show that electron radiative polarization emerges during the instability along the azimuthal direction in the momentum space, which significantly varies across the regimes. We put forward an intuitive Hamiltonian model to trace the origin of the electron polarization dynamics. In particular, we discern the role of nonlinear transverse motion of plasma filaments, which induces asymmetry in radiative spin flips, yielding an accumulation of electron polarization. Our results break the conventional perception that quasisymmetric fields are inefficient for generating radiative spin-polarized beams, suggesting the potential of electron polarization as a source of new information on laboratory and astrophysical plasma instabilities.

Simulation study of coupled two-stream and current filamentation instability excited by accelerator electron beams in plasmas

A gas-discharge plasma device is simulated with COMSOL software, and the obtained plasma density profile is input into a two-dimensional particle-in-cell code, in which the transport of relativistic electron beams in the plasma with an actual density profile is investigated. The results show that the device can produce a wide range of high-density plasmas with the maximum density approaching 5.25×1022 m−3. With the relativistic electron beams produced from a linear electron accelerator, the gas-discharge plasma is shown to be an ideal medium for the investigation of coupled two-stream and current filamentation instability.

Saturation of the asymmetric current filamentation instability under conditions relevant to relativistic shock precursors

The current filamentation instability, which generically arises in the counterstreaming of 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 collisionless shock waves involves a hot, dilute beam of accelerated particles reflected at the shock front and a cold, dense inflowing background plasma. To determine the appropriate criterion for saturation in this case, we have performed large-scale two-dimensional particle-in-cell simulations of counterstreaming electron-positron pair and electron-ion plasmas. We show that, in interpenetrating pair plasmas, the relevant criterion is that of magnetic trapping as applied to the component (beam or plasma) that carries the larger inertia of the two; namely, the instability growth suddenly slows down once the quiver frequency of those particles equals or exceeds the instability growth rate. We present theoretical approximations for the saturation level. These findings remain valid for electron-ion plasmas provided that electrons and ions are close to equipartition in the plasma flow of larger inertia. Our results can be directly applied to the physics of relativistic, weakly magnetized shock waves, but they can also be generalized to other cases of study.

The role of plasma instabilities in relativistic radiation-mediated shocks: stability analysis and particle-in-cell simulations

ABSTRACT Relativistic radiation-mediated shocks are likely formed in prodigious cosmic explosions. The structure and emission of such shocks are regulated by copious production of electron–positron pairs inside the shock-transition layer. It has been pointed out recently that substantial abundance of positrons inside the shock leads to a velocity separation of the different plasma constituents, which is expected to induce a rapid growth of plasma instabilities. In this paper, we study the hierarchy of plasma microinstabilities growing in an electron-ion plasma loaded with pairs and subject to a radiation force. Linear stability analysis indicates that such a system is unstable to the growth of various plasma modes which ultimately become dominated by a current filamentation instability driven by the relative drift between the ions and the pairs. These results are validated by particle-in-cell simulations that further probe the non-linear regime of the instabilities, and the pair-ion coupling in the microturbulent electromagnetic field. Based on this analysis, we derive a reduced-transport equation for the particles via pitch-angle scattering in the microturbulence and demonstrate that it can couple the different species and lead to non-adiabatic compression via a Joule-like heating. The heating of the pairs and, conceivably, the formation of non-thermal distributions, arising from the microturbulence, can affect the observed shock-breakout signal in ways unaccounted for by current single-fluid models.

The effect of the plasma density gradient on current filamentation instability

AbstractThe filamentation instability is one of the basic beam‐plasma instabilities that play a significant role in the energy deposition mechanism of the relativistic electrons generated by the laser‐plasma interaction in the fast ignition scenario. In this paper, the effect of the density gradient into plasma on the filamentation instability was investigated in the Weibel unstable plasma, where the plasma temperature anisotropy can play an important role. Results indicated that the density gradient enhances the instability growth rate so that decreasing the density gradient from the critical surface to the core of fuel leads to instability for longer regions in k space. Also, investigations in the region close to the critical surface showed that for decreasing the beam number density nb ≤ 0.01n0, the instability occurs for while this can be different for higher values. Increasing the beam relativistic factor causes a decreasing peak of instability growth rate because of a reduction in beam current, whereas the initial thermal spread of plasma amplifies the filamentation instability.

Magnetized current filaments as a source of circularly polarized light

We show that the Weibel or current filamentation instability can lead to the emission of circularly polarized radiation. Using particle-in-cell simulations and a radiation post-processing numerical algorithm, we demonstrate that the level of circular polarization increases with the initial plasma magnetization, saturating at ${\sim }13\,\%$ 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 tested in currently available laboratory conditions, show that the recent observation of circular polarization in gamma-ray burst afterglows could be attributed to the presence of magnetized current filaments driven by the Weibel or current filamentation instability.

Growth of concomitant laser-driven collisionless and resistive electron filamentation instabilities over large spatiotemporal scales

Collective processes in plasmas often induce microinstabilities that play an important role in many space or laboratory plasma environments. Particularly notable is the Weibel-type current filamentation instability, which is believed to drive the creation of collisionless shocks in weakly magnetized astrophysical plasmas. Here, this instability class is studied through interactions of ultraintense and short laser pulses with solid foils, leading to localized generation of megaelectronvolt electrons. Proton radiographic measurements of both low- and high-resistivity targets show two distinct, superimposed electromagnetic field patterns arising from the interpenetration of the megaelectronvolt electrons and the background plasma. Particle-in-cell simulations and theoretical estimates suggest that the collisionless Weibel instability building up in the dilute expanding plasmas formed at the target surfaces causes the observed azimuthally symmetric electromagnetic filaments. For a sufficiently high resistivity of the target foil, an additional resistive instability is triggered in the bulk target, giving rise to radially elongated filaments. The data reveal the growth of both filamentation instabilities over large temporal (tens of picoseconds) and spatial (hundreds of micrometres) scales. In the interaction of ultraintense, short laser pulses with solid targets, the collisionless Weibel instability is observed. For a sufficiently high resistivity of the target, an additional resistive instability appears.

Probing ultrafast magnetic-field generation by current filamentation instability in femtosecond relativistic laser-matter interactions

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 $2.70 \pm 0.39\,\rm kT\,\mu m$ 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 around the irradiated target surface, and that they grow to amplitudes strong enough to broaden the angular distribution of the probe electron bunch a few tens of femtoseconds after the laser pulse maximum. Our results highlight the potential of wakefield-accelerated electron beams for ultrafast probing of relativistic laser-driven phenomena.

On the local measurement of electric currents and magnetic fields using Thomson scattering in Weibel-unstable plasmas

We demonstrate the capability of the Thomson Scattering (TS) diagnostic to measure locally the microscopic electron and ion currents in counter-streaming plasmas unstable to the Weibel or current-filamentation instability. Synthetic TS spectra are calculated with particle distribution functions obtained from particle-in-cell simulations and used to accurately reproduce the simulated currents. We show that this technique allows accurate local measurements of the magnetic field, thus opening the way for the complete experimental characterization of the growth rate, saturation, and nonlinear dynamics of electromagnetic instabilities in plasmas. We illustrate the application of this diagnostic to experimental TS data, which yields local measurements of the magnetic field in Weibel-unstable plasmas and indicates that the magnetic energy density reaches ∼1% of the kinetic energy density of the flows, in agreement with previous numerical studies.

Enhanced collective stopping and drift of electron beams in fusion plasmas with heavy-ion species

The transport and energy deposition of relativistic electron beams in transversely nonuniform plasmas are investigated with two-dimensional electromagnetic particle-in-cell simulations. For the beam with radius much larger than plasma skin depth, the current filamentation instability excited by the electron beam can be observed, which breaks the beam into filaments and leads to the formation of strong magnetic fields consequently. The effects of plasma ion species are significant and asymmetric transverse magnetic fields are formed in plasmas with heavy-ion species due to the asymmetric neutralization of beam space charge by plasma ions. The asymmetric transverse magnetic fields contribute to the directional drift of beam electrons to lower plasma density regions, which may accelerate the filaments merger process and lead to highly localized beam-energy deposition in plasmas.

Interaction of ultra relativistic fireball beam with plasma

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 ∼1017 cm−3. 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 generates large local plasma gradients, intense transverse magnetic fields, and enhanced emission of radiation. We suggest that these effects may be observed experimentally for the first time.

Physics of relativistic collisionless shocks. II. Dynamics of the background plasma.

In this second paper of a series, we discuss the dynamics of a plasma entering the precursor of an unmagnetized, relativistic collisionless pair shock. We discuss how this background plasma is decelerated and heated through its interaction with a microturbulence that results from the growth of a current filamentation instability in the shock precursor. We make use, in particular, of the reference frame R_{w} in which the turbulence is mostly magnetic. This frame moves at relativistic velocities towards the shock front at rest, decelerating gradually from the far to the near precursor. In a first part, we construct a fluid model to derive the deceleration law of the background plasma expected from the scattering of suprathermal particles off the microturbulence. This law leads to the relationship γ_{p}∼ξ_{b}^{-1/2} between the background plasma Lorentz factor γ_{p} and the normalized pressure of the beam ξ_{b}; it is found to match nicely the spatial profiles observed in large-scale 2D3V particle-in-cell simulations. In a second part, we model the dynamics of the background plasma at the kinetic level, incorporating the inertial effects associated with the deceleration of R_{w} into a Vlasov-Fokker-Planck equation for pitch-angle diffusion. We show how the effective gravity in R_{w} drives the background plasma particles through friction on the microturbulence, leading to efficient plasma heating. Finally, we compare a Monte Carlo simulation of our model with dedicated PIC simulations and conclude that it can satisfactorily reproduce both the heating and the deceleration of the background plasma in the shock precursor, thereby providing a successful one-dimensional description of the shock transition at the microscopic level.

Physics of Weibel-Mediated Relativistic Collisionless Shocks.

We develop a comprehensive theoretical model of relativistic collisionless pair shocks mediated by the current filamentation instability. We notably characterize the noninertial frame in which this instability is of a mostly magnetic nature, and describe at a microscopic level the deceleration and heating of the incoming background plasma through its collisionless interaction with the electromagnetic turbulence. Our model compares well to large-scale 2D3V particle-in-cell simulations, and provides an important touchstone for the phenomenology of such plasma systems.

Physics of relativistic collisionless shocks: The scattering-center frame.

In this first paper of a series dedicated to the microphysics of unmagnetized, relativistic collisionless pair shocks, we discuss the physics of the Weibel-type transverse current filamentation instability that develops in the shock precursor, through the interaction of an ultrarelativistic suprathermal particle beam with the background plasma. We introduce in particular the notion of the "Weibel frame," or scattering center frame, in which the microturbulence is of mostly magnetic nature. We calculate the properties of this frame, using first a kinetic formulation of the linear phase of the instability, relying on Maxwell-Jüttner distribution functions, then using a quasistatic model of the nonlinear stage of the instability. Both methods show that (i) the Weibel frame moves at subrelativistic velocities relative to the background plasma, therefore at relativistic velocities relative to the shock front; (ii) the velocity of the Weibel frame relative to the background plasma scales with ξ_{b}, i.e., the pressure of the suprathermal particle beam in units of the momentum flux density incoming into the shock; and (iii) the Weibel frame moves slightly less fast than the background plasma relative to the shock front. Our theoretical results are found to be in satisfactory agreement with the measurements carried out in dedicated large-scale 2D3V particle-in-cell simulations.

Fluid description of collisional current filamentation instability of a weakly ionized plasma in the presence of magnetic field

In this paper, the collisional filamentation instability of an electron beam-weakly magnetized and ionized plasma has been investigated in the presence of background plasma, using the fluid description. By describing the equilibrium configuration in the presence of binary collision terms between charged and neutral particles and using the local approximation method, the dispersion relation (DR) of instable mode (filamentation instability) has been obtained and the effect of collision and magnetic field driven-destabilization and current-driven stabilization on the growth rate of instability has been studied. The results show the cut-off wave number and the magnetic threshold for the filamentation instability in the collisional magnetized plasma in which the instability will disappear for the larger wave number and larger magnetic fields. Studies show that the value of cut-off wave number and magnetic threshold are raised by increasing the electron beam current density.

Modulation of proton beams by relativistic electron beam-plasma instability

Two-dimensional electromagnetic particle-in-cell simulations are performed to investigate the transport of relativistic electron beams co-moved with a proton beam in background plasmas. For the beam with the radius much larger than the plasma skin depth, the current filamentation instability excited by the relativistic electron beam can be clearly observed and the transverse magnetic fields in the plasma increase significantly. The proton beam is modulated strongly by the electromagnetic fields in plasmas, and a netlike structure in the beam profile is formed with a high density contrast, which can be provided as an effective tool to diagnose the instability. The dynamic effects of plasma ions are shown to be important and play a significant role in the dynamic evolution of the proton beam.

Conditions for the onset of the current filamentation instability in the laboratory

The current filamentation instability (CFI) is capable of generating strong magnetic fields relevant to the explanation of radiation processes in astrophysical objects and leads 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 two-dimensional 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 growth rate and as long as the role of the competing electrostatic two-stream instability (TSI) is negligible. We also show that the longitudinal energy spread, typical of plasma-based accelerated electron–positron fireball beams, plays a minor role in the growth of CFI in these scenarios.

Perpendicular relativistic shocks in magnetized pair plasma

Perpendicular relativistic ($\gamma_0=10$) shocks in magnetized pair plasmas are investigated using two dimensional Particle-in-Cell simulations. A systematic survey, from unmagnetized to strongly magnetized shocks, is presented accurately capturing the transition from Weibel-mediated to magnetic-reflection-shaped shocks. This transition is found to occur for upstream flow magnetizations $10^{-3}<\sigma<10^{-2}$ at which a strong perpendicular net current is observed in the precursor, driving the so-called current-filamentation instability. The global structure of the shock and shock formation time are discussed. The MHD shock jump conditions are found in good agreement with the numerical results, except for $10^{-4} < \sigma < 10^{-2}$ where a deviation up to 10\% is observed. The particle precursor length converges toward the Larmor radius of particles injected in the upstream magnetic field at intermediate magnetizations. For $\sigma>10^{-2}$, it leaves place to a purely electromagnetic precursor following from the strong emission of electromagnetic waves at the shock front. Particle acceleration is found to be efficient in weakly magnetized perpendicular shocks in agreement with previous works, and is fully suppressed for $\sigma > 10^{-2}$. Diffusive Shock Acceleration is observed only in weakly magnetized shocks, while a dominant contribution of Shock Drift Acceleration is evidenced at intermediate magnetizations. The spatial diffusion coefficients are extracted from the simulations allowing for a deeper insight into the self-consistent particle kinematics and scale with the square of the particle energy in weakly magnetized shocks. These results have implications for particle acceleration in the internal shocks of AGN jets and in the termination shocks of Pulsar Wind Nebulae.