We present an investigation for the generation of intense magnetic fields in dense plasmas with an anisotropic electron Fermi-Dirac distribution. For this purpose, we use a new linear dispersion relation for transverse waves in the Wigner-Maxwell dense quantum plasma system. Numerical analysis of the dispersion relation reveals the scaling of the growth rate as a function of the Fermi energy and the temperature anisotropy. The nonlinear saturation level of the magnetic fields is found through fully kinetic simulations, which indicates that the final amplitudes of the magnetic fields are proportional to the linear growth rate of the instability. The present results are important for understanding the origin of intense magnetic fields in dense Fermionic plasmas, such as those in the next generation intense laser-solid density plasma experiments.
The temporal evolution of the magnetic field associated with electron thermal Weibel instability in optical-field ionized plasmas is measured using ultrashort (1.8 ps), relativistic (45 MeV) electron bunches from a linear accelerator. The self-generated magnetic fields are found to self-organize into a quasi-static structure consistent with a helicoid topology within a few ps and such a structure lasts for tens of ps in underdense plasmas. The measured growth rate agrees well with that predicted by the kinetic theory of plasmas taking into account collisions. Magnetic trapping is identified as…
The growth and saturation of magnetic fields due to the Weibel instability (WI) have important implications for laboratory and astrophysical plasmas, and this has drawn significant interest recently. Since the WI can generate a large magnetic field from no initial field, the maximum magnitudes achieved can have significant consequences for a number of applications. Hence, an understanding of the detailed dynamics driving the nonlinear saturation of the WI is important. This work considers the nonlinear saturation of the WI when counter-streaming populations of initially unmagnetized electrons …
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 Weibel instability is analyzed for quantum plasmas described by the Wigner-Maxwell model. For a suitable class of electromagnetic potentials, the Wigner-Maxwell system is linearized yielding a general dispersion relation for transverse electromagnetic waves. For a double Gaussian equilibrium with temperature anisotropy, the derived dispersion relation generalizes the classical Weibel instability equation. More detailed analytical results are obtained for the cases of extreme temperature anisotropy and for a three-dimensional water bag distribution. In all cases, quantum effects tends to we…
The shape of the anisotropic velocity distribution function, beyond the realm of strict Maxwellians can play a significant role in determining the evolution of the Weibel instability dictating the dynamics of self-generated magnetic fields. For non-Maxwellian distribution functions, we show that the direction of the maximum growth rate wavevector changes with shape. We investigate different laser-plasma interaction model distributions which show that their Weibel generated magnetic fields may require closer scrutiny beyond the second moment (temperature) anisotropy ratio characterization.
We discuss a fluid model with inclusion of the complete pressure tensor dynamics for the description of Weibel type instabilities in a counterstreaming beams configuration. Differently from the case recently studied in Sarrat et al. 2016, where perturbations perpendicular to the beams were considered, here we focus only on modes propagating along the beams. Such a configuration is responsible for the growth of two kind of instabilities, the Two-Stream Instability and the Weibel instability, which in this geometry becomes "time-resonant", i.e. propagative. This fluid description agrees with the…
The nonlinear evolution of the Weibel instability driven by the anisotropy of the electron distribution function in a collisionless plasma is investigated in a spatially one-dimensional configuration with a Vlasov code in a two-dimensional velocity space. It is found that the electromagnetic fields generated by this instability cause a strong deformation of the electron distribution function in phase space, corresponding to highly filamented magnetic vortices. Eventually, these deformations lead to the generation of short wavelength Langmuir modes that form highly localized electrostatic struc…
A new quasi-neutral model describing the Weibel instability of a high-current relativistic beam propagating through a resistive plasma is developed. It treats beam electrons as kinetic particles, and ambient plasma as a non-relativistic fluid. For a finite-temperature beam, a new class of negative energy magneto-sound waves is identified, which can possess negative energy. Their growth due to collisional dissipation in the cold return current destabilizes the beam-plasma system even for high beam temperatures. We perform detailed two- and three-dimensional particle-in-cell (PIC) simulations of…
The production of weakly relativistic plasma by microwave electric field with circular polarization has been studied. Electron distribution function obtained for this produced plasma and shown that it is non-equilibrium and anisotropic. It is shown that produced plasma accelerated on direction of propagation microwave electric field. The electron velocity on this direction strongly depends on electron origination phase during ionization and microwave electric field phase and it s amplitude. The dielectric tensor obtained for this plasma and the weibel instability studied for it.
The Weibel instability from counterstreaming plasma flows is a basic process highly relevant for collisionless shock formation in astrophysics. In this Letter we investigate, via two- and three- dimensional simulations, suitable configurations for laboratory investigations of the ion Weibel instability (IWI) driven by a fast quasi-neutral plasma flow launched into the target via the radiation pressure of an ultra-high-intensity (UHI) laser pulse ('Hole-Boring' process). The use of S-polarized light at oblique incidence is found to be an optimal configuration for driving IWI, as it prevents the…
The saturation mechanism of the Weibel instability is investigated theoretically by considering the evolution of currents in numerous cylindrical beams that are generated in the initial stage of the instability. Based on a physical model of the beams, it is shown that the magnetic field strength attains a maximum value when the currents in the beams evolve into the Alfven current and that there exist two saturation regimes. The theoretical prediction of the magnetic field strength at saturation is in good agreement with the results of two-dimensional particle-in-cell simulations for a wide ran…
A novel setup allows the Weibel instability and its interplay with the Biermann battery to be probed in laser-driven collisionless plasmas. Ab initio particle-in-cell (PIC) simulations of the interaction of short ($ \le ps$) intense $(a_0 \ge 1)$ laser-pulses with overdense plasma targets show observable Weibel generated magnetic fields. This field strength surpasses that of the Biermann battery, usually dominant in experiments, as long as the gradient scale length is much larger than the local electron inertial length; this is achievable by carefully setting the appropriate gradients in the f…
The kinetic instabilities of the Weibel-type are presently invoked in a large variety of astrophysical scenarios because anisotropic plasma structures are ubiquitous in space. The Weibel instability is driven by a temperature anisotropy which is commonly modeled by a bi-axis distribution function, such as a bi-Maxwellian or a generalized bi-Kappa. Previous studies have been limited to a bi-Kappa distribution and found a suppression of this instability in the presence of suprathermal tails. In the present paper it is shown that the Weibel growth rate is rather more sensitive to the shape of the…
Weibel-type instability can self-generate and amplify magnetic fields in both space and laboratory plasmas with temperature anisotropy. The electron Weibel instability has generally proven more challenging to measure than its ion counterpart owing to the much smaller inertia of electrons, resulting in a faster growth rate and smaller characteristic wavelength. Here, we have probed the evolution of the two-dimensional distribution of the magnetic field components and the current density due to electron Weibel instability, in $\rm CO_2$-ionized hydrogen gas (plasma) with picosecond resolution us…
The Weibel instability driven by two symmetric counter-streaming relativistic electron plasmas, also referred to as current-filamentation instability, is studied in a constant and uniform external magnetic field aligned with the plasma flows. Both the linear and non linear stages of the instability are investigated using analytical modeling and Particle-In-Cell (PIC) simulations. While previous studies have already described the stabilizing effect of the magnetic field, we show here that the saturation stage is only weakly affected. The different mechanisms responsible for the saturation are d…
The expansion of plasma with non-parallel temperature and density gradients, and the generation of magnetic field via the Biermann battery is modeled using particle-in-cell simulations that include collisional effects via Monte Carlo methods. A scaling of the degree of collisionality shows that an anisotropy can be produced, and drive the Weibel instability, for gradient scales shorter than the mean free path. For larger collision rates, the Biermann battery dominates as the cause of magnetic field generation. When the most energetic particles remain collisionless, the Nernst effect causes the…
The electron beam Weibel instability in the electrostatic collisionless shock is studied via particle in cell simulation. When the non-relativistic incoming plasmas collide with cold dilute plasmas, an electrostatic shock forms near the interface. Following that, a filamentary out-of-plane magnetic field is formed as a result of the Weibel instability. It is demonstrated that the anisotropy of incoming hot electrons is insufficient to trigger the Weibel instability. And the Weibel instability is excited by cold electrons in dilute plasmas. After being accelerated to relativistic velocities by …
We present experimental observations of electron-scale structures in an expanding high-energy-density (HED) plasma generated with a modest intensity $\sim 2 \times 10^{14}$ W/cm$^2$, $\sim1$ ns laser. The observed structures have wavelengths ($\sim 150-220 μm$) and growth rates ($\sim 0.4-1.0$ ns$^{-1}$) consistent with an electron-driven Weibel instability where the anisotropy in the electron distribution is small, $A\sim 0.002$. This instability is found to be a better match to the observed phenomena than other typical field-generation mechanisms found in HED plasmas, including counter-strea…
A relativistic electron beam propagating through plasma induces a return current in the system. Such a system of counterstreaming forward and return current is susceptible to host of instabilities out of which Weibel remains a dominant mode for destabilizing the system. Weibel instability has been widely investigated in simulations, experiments, as well as, analytically using fluid and kinetic treatments. A purely growing mode like Weibel instability can also be understood by using conservation theorems and energy principle analysis. An electrostatic analog to the Weibel instability, two strea…
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 …
Generation and amplification of magnetic fields in plasmas is a long-standing topic that is of great interest to both plasma and space physics. The electron Weibel instability is a well-known mechanism responsible for self-generating magnetic fields in plasmas with temperature anisotropy and has been extensively investigated in both theory and simulations, yet experimental verification of this instability has been challenging. Recently, we demonstrated a new experimental platform that enables the controlled initialization of highly nonthermal and/or anisotropic plasma electron velocity distrib…
We present the first 2X2V continuum Vlasov-Maxwell simulations of interpenetrating, unmagnetized plasmas to study the competition between two-stream, Oblique, and filamentation modes in the weakly relativistic regime. We find that after nonlinear saturation of the fastest-growing two-stream and Oblique modes, the effective temperature anisotropy, which drives current filament formation via the secular Weibel instability, has a strong dependence on the internal temperature of the counter-streaming plasmas. The effective temperature anisotropy is significantly more reduced in colder than in hott…
The time evolution and saturation of the Weibel instability at the ion Alfvén current are presented by ab initio particle-in-cell simulations. We found that the ion Weibel current in 3D could evolve into the Alfvén current where the magnetic field energy is sustained at 1.5\% of the initial beam kinetic energy. The current filaments are no longer isolated at saturation, but rather connected to each other to form a network structure. Electrons are continuously heated during the coalescence of the filaments, which is crucial for obtaining sustained magnetic fields with much stronger levels than …
An investigation of magnetic fields generated in an expanding bubble of plasma with misaligned temperature and density gradients (driving the Biermann battery mechanism) is performed. With gradient scales $L$, large-scale magnetic fields are generated by the Biermann battery mechanism with plasma $β\sim 1$, as long as $L$ is comparable to the ion inertial length $d_i$. For larger system sizes, $L/d_e > 100$ (where $d_e$ is the electron inertial length), the Weibel instability generates magnetic fields of similar magnitude but with wavenumber $k d_e \sim 0.2$. In both cases, the growth and satu…
First-principles kinetic simulations are used to investigate magnetic field generation processes in expanding ablated plasmas relevant to laser-driven foils and hohlraums. In addition to Biermann-battery-generated magnetic fields, strong filamentary magnetic filaments are found to grow in the corona of single expanding plasma plumes; such filaments are observed to dominate Biermann fields at sufficiently large focal radius, reaching saturation values of $\sim$ 100 T at National Ignition Facility-like drive conditions. The filamentary fields result from the ion Weibel instability driven by rela…
The quantum effect on the Weibel instability in an unmagnetized plasma is presented. Our analysis shows that the quantum effect tends to stabilize the Weibel instability in the hydrodynamic regime, whereas it produces a new oscillatory instability in the kinetic regime. A novel effect the quantum damping, which is associated with the Landau damping, is disclosed. The new quantum Weibel instability may be responsible for the generation of non-stationary magnetic fields in compact astrophysical objects as well as in the forthcoming intense laser-solid density plasma experiments.
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…
While electron kinetic effects are well known to be of fundamental importance in several situations, the electron mean-flow inertia is often neglected when lengthscales below the electron skin depth become irrelevant. This has led to the formulation of different reduced models, where electron inertia terms are discarded while retaining some or all kinetic effects. Upon considering general full-orbit particle trajectories, this paper compares the dispersion relations emerging from such models in the case of the Weibel instability. As a result, the question of how lengthscales below the electron…
Recent full-particle simulations of electron-positron reconnection have revealed that the Weibel instability plays an active role in controlling the dynamics of the current layer and maintaining fast reconnection. A four-beam model is developed to explore the development of the instability within a narrow current layer characteristic of reconnection. The problem is reduced to two coupled second-order differential equations, whose growing eigenmodes are obtained via both asymptotic approximations and finite difference methods. Full particle simulations confirm the linear theory and help probe t…
We present a particle-in-cell simulation of the generation of a collisionless turbulent shock in a dense plasma driven by an ultra-high-intensity laser pulse. From the linear analysis, we highlight the crucial role of the laser-heated and return-current electrons in triggering a strong Weibel-like instability, giving rise to a magnetic turbulence able to isotropize the target ions.
The Weibel instability in the quantum plasma case is treated by means of a fluid-like (moments) approach. Quantum modifications to the macroscopic equations are then identified as effects of first or second kind. Quantum effects of the first kind correspond to a dispersive term, similar to the Bohm potential in the quantum hydrodynamic equations for plasmas. Effects of the second kind are due to the Fermi statistics of the charge carriers and can become the dominant influence for strong degeneracy. The macroscopic dispersion relations are of higher order than those for the classical Weibel ins…
The linear growth rate and saturation level of magnetic fields for Weibel instabilities driven by ion temperature anisotropy, defined as $α=(T_\perp/T_\parallel)-1$ where $T_\perp$ and $T_\parallel$ are ion temperatures perpendicular and parallel to the wave vector, are derived in the small $α$-limit. It is shown that the ratio of the saturated magnetic energy to the initial ion energy scales as the fourth power of the electron to ion mass ratio, $m/M$, for an initially unmagnetized plasma with $α\leq M/m$. Particle-in-cell simulations confirm the mass scaling and also show that the electron e…
A Particle-in-Cell (PIC) numerical simulation of the electron Weibel instability is applied in a frame of Darwin (radiationless) approximation of the self-consistent fields of sparse plasma. As a result, we were able to supplement the classical picture of the instability and, in particular, to obtain the dependency of the basic characteristics (the time of development and the maximum field energy) of the thermal anisotropy parameter, to trace the dynamic restructuring of current filaments accompanying the nonlinear stage of the instability and to trace in detail the evolution of the initial an…
In this paper, we report our recent findings on the relativistic Weibel instability and its nonlinear saturation by performing numerical simulations of collisionless plasmas. Analysis of the obtained numerical results revealed that the nonlinear phase of the Weibel instability can be described by characteristic phases based on the Weibel filaments' current density in terms of particle and Alfvén limit currents. We also analyzed the relativistic kink instability based on the energy principle in the magnetohydrodynamic (MHD) regime, and found that the Weibel filaments do not suffer from the kink…
The Weibel instability could be responsible for the generation of magnetic fields in various objects such as gamma-ray bursts, jets from active galactic nuclei, and clusters of galaxies. Using numerical simulations, the development of the Weibel instability at a temperature gradient is studied. It is found that current sheets are first generated at the gradient, and then they are rounded off and turn into current filaments. During this process, return currents are generated around the filaments and they prevent filaments from merger. The magnetic fields around the filaments persist at least un…
The formation of non-relativistic collisionless shocks in laboratory with ultrahigh intensity lasers is studied via \emph{ab initio} multi-dimensional particle-in-cell simulations. The microphysics behind shock formation and dissipation, and the detailed shock structure are analyzed, illustrating that the Weibel instability plays a crucial role in the generation of strong subequipartition magnetic fields that isotropize the incoming flow and lead to the formation of a collisionless shock, similarly to what occurs in astrophysical scenarios. The possibility of generating such collisionless shoc…
Astrophysical and high-energy-density laboratory plasmas often have large-amplitude, sub-Larmor-scale electromagnetic fluctuations excited by various kinetic-streaming or anisotropy-driven instabilities. The Weibel (or the filamentation) instability is particularly important because it can rapidly generate strong magnetic fields, even in the absence of seed fields. Particles propagating in collisionless plasmas with such small-scale magnetic fields undergo stochastic deflections similar to Coulomb collisions, with the magnetic pitch-angle diffusion coefficient representing the effective "colli…
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 study the Weibel instability in a degenerate Fermi plasma. We disclose new type of quantum Weibel instabilities. In particular, a novel oscillatory Weibel instability is found and its growth rate is obtained. We reveal a transverse zero-sound in a quantum degenerate electron gas, which has no counterpart in the classical consideration.
We present results of a 2D3V kinetic Vlasov simulation of the Weibel instability. The kinetic Vlasov simulation allows us to investigate the velocity distribution of dilute plasmas, in which the effect of collisions between particles is negligible, and has the advantage that the accuracy of the calculated velocity distribution does not depend on the density of plasmas at each point in the physical space. We succeed in reproducing some features of the Weibel instability shown by other simulations, for example, the exponentially growing phase, the saturation of the magnetic field strength, the f…
Collisionless shocks can be produced as a result of strong magnetic fields in a plasma flow, and therefore are common in many astrophysical systems. The Weibel instability is one candidate mechanism for the generation of sufficiently strong fields to create a collisionless shock. Despite their crucial role in astrophysical systems, observation of the magnetic fields produced by Weibel instabilities in experiments has been challenging. Using a proton probe to directly image electromagnetic fields, we present evidence of Weibel-generated magnetic fields that grow in opposing, initially unmagneti…
We consider a situation in when the interaction of relativistically intense EM waves with an isotropic electron positron plasma takes place, i.e.,we consider short pulse lasers with intensity up to 1021 W/cm2, in which the photon density is of the order of 1030cm3 and the strength of electric field E = 10^9 statvolt/cm. Such a situation is possible in astrophysical and laboratory plasma which are subject to intense laser radiation, thus leading to non thermal equilibrium field radiations. Such interaction of the super-strong laser radiation with an isotropic pair plasma leads to the generation…
An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe in accordance with previous works the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not account…
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…
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 …
The transition between non resonant (Weibel-type) and resonant (whistler) instabilities is investigated numerically in plasma configurations with an ambient magnetic field of increasing amplitudes. The Vlasov-Maxwell system is solved in a configuration where the fields have three components but depend only on one coordinate and on time. The nonlinear evolution of these instabilities is shown to lead to the excitation of electromagnetic and electrostatic modes at the first few harmonics of the plasma frequency and, in the case of a large ambient magnetic field, to a long-wavelength, spatial mod…
We investigate ion-scale kinetic plasma instabilities at the collisionless shock using linear theory and nonlinear Particle-in-Cell (PIC) simulations. We focus on the Alfvén-ion-cyclotron (AIC), mirror, and Weibel instabilities, which are all driven unstable by the effective temperature anisotropy induced by the shock-reflected ions within the transition layer of a strictly perpendicular shock. We conduct linear dispersion analysis with a homogeneous plasma model to mimic the shock transition layer by adopting a ring distribution with finite thermal spread to represent the velocity distributio…
Collisionless shocks are ubiquitous in the Universe and often associated with strong magnetic field. Here we use large-scale particle-in-cell simulations of non-relativistic perpendicular shocks in the high-Mach-number regime to study the amplification of magnetic field within shocks. The magnetic field is amplified at the shock transition due to the ion-ion two-stream Weibel instability. The normalized magnetic-field strength strongly correlates with the Alfvénic Mach number. Mock spacecraft measurements derived from PIC simulations are fully consistent with those taken in-situ at Saturn's bo…
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 PIC simulations, and provides an important touchstone for the phenomenology of such plasma systems.
