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 dominant saturation mechanism.
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 …
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 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 propor…
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…
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…
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 …
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 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…
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…
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…
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…
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…
For a Weibel shock to form, two plasma shells have to collide and trigger the Weibel instability. At saturation, this instability generates in the overlapping region magnetic filaments with peak field $B_f$. In the absence of an external guiding magnetic field, these filaments can block the incoming flow, initiating the shock formation, if their size is larger than the Larmor radius of the incoming particles in the peak field. Here we show that this results still holds in the presence of an external magnetic field $B_0$, provided it is not too high. Yet, for $B_0 \gtrsim B_f/2$, the filaments …
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…
A careful study of plasma-material interactions is essential to understand and improve the operation of devices where plasma contacts a wall. Key contributions of this work include (i) novel continuum kinetic algorithms with novel boundary conditions that directly discretize the Vlasov/Boltzmann equation using the discontinuous Galerkin method, (ii) fundamental studies of a plasma sheath physics with collisions, ionization, and physics-based wall emission, and (iii) theoretical and numerical studies of the linear growth and nonlinear saturation of the kinetic Weibel instability, including its …
When two collisionless plasma shells collide, they interpenetrate and the overlapping region may turn Weibel unstable for some values of the collision parameters. This instability grows magnetic filaments which, at saturation, have to block the incoming flow if a Weibel shock is to form. In a recent paper [J. Plasma Phys. (2016), vol. 82, 905820403], it was found implementing a toy model for the incoming particles trajectories in the filaments, that a strong enough external magnetic field $\mathbf{B}_0$ can prevent the filaments to block the flow if it is aligned with. Denoting $B_f$ the peak …
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…
We study in a fully kinetic framework the generation of seed magnetic fields through the Weibel instability driven in an initially unmagnetized plasma by a large-scale shear force. We develop an analytical model that describes the development of thermal pressure anisotropy via phase mixing, the ensuing exponential growth of magnetic fields in the linear Weibel stage, and its saturation when the seed magnetic fields become strong enough to instigate gyromotion of particles and thereby inhibit their free-streaming. The predicted scaling dependencies of the saturated seed fields on key parameters…
Sustained interpenetrating plasma flows for the investigation of late time kinetic instability evolution
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Massachusetts Institute of Technology（麻省理工学院）；Dartmouth College（达特茅斯学院）；Instituto de Investigaciones Energéticas y Aplicaciones Industriales（能源研究与工业应用研究所）
Magnetic field amplification by relativistic streaming plasma instabilities is central to a wide variety of high-energy astrophysical environments as well as to laboratory scenarios associated with intense lasers and electron beams. We report on a new secondary nonlinear instability which arises for relativistic dilute electron beams after the saturation of the linear Weibel instability. This instability grows due to the transverse magnetic pressure associated with the beam current filaments, which cannot be quickly neutralized due to the inertia of background ions. We show that it can amplify…
Turbulent Magnetogenesis and Large-scale Magnetic Dynamo Amplification in Ion--electron Plasmas
KU Leuven（荷语鲁汶大学）；Royal Belgian Institute for Space Aeronomy（比利时皇家空间空气动力学研究所）；National Research Council (CNR-ISTP)（国家研究委员会）；Università della Calabria（卡拉布里亚大学）；University of Delaware（特拉华大学）
We study the stability of current filaments produced by the Weibel, or current filamentation, instability in weakly magnetized counter-streaming plasmas. It is shown that a resonance exists between the current-carrying ions and a longitudinal drift-kink mode that strongly deforms and eventually breaks the current filaments. Analytical estimates of the wavelength, growth rate and saturation level of the resonant mode are derived and validated by three-dimensional particle-in-cell simulations. Furthermore, self-consistent simulations of counter-streaming plasmas indicate that this drift-kink mod…
By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of turbulent dynamo, and study the dynamo process for a full range of magnetic Prandtl number Pm and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on Pm in a conducting fluid and R (a function of ionization fraction) in partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regi…
Plasma streaming instabilities play an important role in magnetic field amplification and particle acceleration in relativistic shocks and their environments. However, in the far shock precursor region where accelerated particles constitute a highly relativistic and dilute beam, streaming instabilities typically become inefficient and operate at very small scales when compared to the gyroradii of the beam particles. We report on a plasma cavitation instability that is driven by dilute relativistic beams and can increase both the magnetic field strength and coherence scale by orders of magnitud…
We derive scaling relations based on free-fall and isotropy assumptions for the kinematic small-scale dynamo growth rate and amplification factor over the course of the mixing, saturation, and decay phases of the Rayleigh-Taylor instability (RTI) in a fully-ionized plasma. The scaling relations are tested using sets of three dimensional, visco-resistive MHD simulations of the RTI and found to hold in the saturation phase, but exhibit discrepancies during the mixing and decays phases, suggesting a need to relax either the free-fall or isotropy assumptions. Application of the scaling relations a…
Nonlinear Saturation of the Acoustic Resonant Drag Instability
Weizmann Institute of Science（魏茨曼科学研究所）；Princeton University（普林斯顿大学）；University of Otago（奥塔哥大学）；Kavli Institute for Particle Astrophysics & Cosmology (KIPAC), Stanford University（斯坦福大学卡弗里粒子天体物理与宇宙学研究所）
We explore the physics of the gyro-resonant cosmic ray streaming instability (CRSI) including the effects of ion-neutral (IN) damping. This is the main damping mechanism in (partially-ionized) atomic and molecular gas, which are the primary components of the interstellar medium (ISM) by mass. Limitation of CRSI by IN damping is important in setting the amplitude of Alfvén waves that scatter cosmic rays and control galactic-scale transport. Our study employs the MHD-PIC hybrid fluid-kinetic numerical technique to follow linear growth as well as post-linear and saturation phases. During the line…
