This study investigates the streaming instability triggered by ion motion in a plasma system that is finite in length, collisionless, and inhomogeneous. Employing numerical simulations using Particle-In-Cell (PIC) techniques and kinetic equations, the study examines how inhomogeneity emerges from integrating a cold ion beam with a background plasma within a confined system. The findings suggest that steady ion flow can modify ion sound waves through acoustic reflections from system boundaries, leading to instability. Such phenomena are known to be a hydrodynamic effect. However, there are also signatures of the beam-driven ion sound instability where kinetic resonances play a pivotal role. The main objective is to understand the impact of a finite-length system on beam-plasma instability and to identify the wave modes supported in such configurations.
We show that an electronic beam passing through the collisionless plasma of the "cold" ions and the "hot" Boltzmann electrons can give rise to the propagation of the supersonic ion-acoustic rarefaction shock waves. These waves are analogous to those predicted by Zeldovich [5] in gasodynamics and complementary to the ion-acoustic compression shock waves in collisionless plasma described by Sagdeev [3].
The research is aimed at the study of the properties of solutions for parallel MHD shock waves in collisionless plasma with heat fluxes, using 8-moment MHD approximation. Restrictions have been established on the upstream shock parameters preserving physical meaning of the downstream plasma parameters.
Most plasmas have a very thin sheath compared with the plasma dimension. This necessitates separate calculations of the plasma and sheath. The Bohm criterion provides the boundary condition for calculation of plasma profiles. To calculate sheath properties a value of electric field at the plasma-sheath interface has to be specified in addition to the Bohm criterion. The value of the boundary electric field and robust procedure to approximately patch plasma and collisionless sheath with a very good accuracy are reported.
We present space- and time-resolved experimental data of head-on-merging, supersonic plasma jets (of an argon/impurity mixture) in an initially collisionless regime for counter-streaming ions. The merging begins with collisionless interpenetration followed by a transition to collisional stagnation. The transition occurs due to an experimentally inferred rising mean-ionization level, which rapidly reduces the counter-streaming ion-ion mean free path. The measurements demonstrate a specific mechanism by which a collisionless interaction transitions to a collisional one and constrain collisionali…
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
The first kinetic study of transient growth for a collisionless homogeneous Maxwellian plasma in a uniform magnetic field is presented. A system which is linearly stable may display transient growth if the linear operator describing its evolution is non-normal, so that its eigenvectors are non-orthogonal. In order to include plasma kinetic effects a Landau fluid model is employed. The linear operator of the model is shown to be non-normal and the results suggest that the nonnormality of a collisionless plasma is intrinsically related to its kinetic nature, with the transient growth being more …
Low-frequency mangnetosonic pulses in a two-ion-species plasma are studied theoretically and by simulation with a one-dimensional electromagnetic simulation code based on a three-fluid model, with particular attention to the dynamics of minority heavy ions. It is found that heavy ions can gain some energy from the pulses. Because of this energy transfer, the pulses are damped even if the plasma is collisionless and pulse propagation is perpendicular to the magnetic field.
Dynamics of the magnetospheric plasma configuration intrinsically features intermittent slow and fast phases. The fast transition is a nonlinear process, loss of equilibrium which ends up the slow quasi-static evolution. The process is analysed as a dynamical bifurcation. It appears when marginal stability state is reached in the course of that evolution, either for tearing mode or for ballooning mode disturbances. The resulting force imbalance leads to spontaneous formation of nonlinear kinetic thin current structures. Those are either a pair of slow collisionless shocks or a specific anisotr…
Collisionless shocks are common features in space and astrophysical systems where supersonic plasma flows interact, such as in the solar wind, the heliopause, and supernova remnants. Recent experimental capabilities and diagnostics allow detailed laboratory investigations of high-Mach-number shocks, which therefore can become a valuable way to understand shock dynamics in various astrophysical environments. Using 2D particle-in-cell simulations with a Coulomb binary collision operator, we demonstrate the mechanism for generation of energetic electrons and experimental requirements for detectin…
The head-on collision of ion-acoustic solitary waves in a collisionless plasma with cold ions and Boltzmann electrons is studied. It is shown that solitary waves of sufficiently large amplitudes do not retain their identity after a collision. Their amplitudes decrease and their forms change. Dependences of amplitudes of the potential and densities of ions and electrons after a head-on collision of identical solitary waves on their initial amplitude are presented.
A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a non-differential form from a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift $Δω$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $Δω\sim a^{1/2}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a loga…
The emergence of a density bump at the front of a collisionless electrostatic shock wave have been observed experimentally during the ablation of an aluminium foil by a femtosecond laser pulse. We have performed numerical simulations of the dynamics of this phenomena developing alongside the generation of a package of ion-acoustic waves, exposed to a continual flow of energetic electrons, in a collisionless plasma. We present the physical interpretation of the observed effects and show that the bump consists of transit particles, namely, the accelerated ions from the dense plasma layer, and th…
We present an approximation scheme for the dielectric response of thermal collisionless plasmas at arbitrary degeneracy. A T-fraction representation is obtained from the known expansions of the real part of the dielectric function for small and large arguments. The partial numerators and denominators of the continued fraction are generated by a modified Q-D algorithm. For several typical values of the degeneracy parameter $θ$, extensive tables for the expansion coefficients and the partial numerators and denominations are given allowing for an easy implementation of the fitting function. Also,…
A dust grain in a plasma has a fluctuating electric charge, and past work concludes that spherical grains in a stationary, collisionless plasma have an essentially Gaussian charge probability distribution. This paper extends that work to flowing plasmas and arbitrarily large spheres, deriving analytic charge probability distributions up to normalizing constants. We find that these distributions also have good Gaussian approximations, with analytic expressions for their mean and variance.
Two decades after the invention of chirped pulse amplification the physical mechanism of collisionless absorption of intense laser radiation in overdense matter is still not sufficiently well understood. We show that anharmonic resonance in the self-generated plasma potential of the single plasma layers (cold plasma model) or of the individual electrons (warm plasma), respectively, constitutes the leading physical mechanism of collisionless absorption in an overdense plasma. Analogously to collisions, resonance provides for the finite phase shift of the free electron current relative to the dr…
In this paper we have criticized the so-called Landau damping theory. We have analyzed solutions of the standard dispersion equations for longitudinal (electric) and transversal (electromagnetic and electron) waves in half-infinite slab of the uniform collisionless plasmas with non-Maxwellian and Maxwellian-like electron energy distribution functions. One considered the most typical cases of both the delta-function type distribution function (the plasma stream with monochromatic electrons) and distribution functions, different from Maxwellian ones as with a surplus as well as with a shortage i…
A theoretical analysis for astrophysics-oriented laser-matter interaction experiments in the presence of a strong ambient magnetic field is presented. It is shown that the plasma collision in the ambient magnetic field implies significant perturbations in the electron density and magnetic field distribution. This transient stage is difficult to observe in astrophysical phenomena, but it could be investigated in laboratory experiments. Analytic models are presented, which are supported by particle-in-cell simulations.
The expansion of a dense plasma into a dilute plasma across an initially uniform perpendicular magnetic field is followed with a one-dimensional particle-in-cell (PIC) simulation over MHD time scales. The dense plasma expands in the form of a fast rarefaction wave. The accelerated dilute plasma becomes separated from the dense plasma by a tangential discontinuity at its back. A fast magnetosonic shock with the Mach number 1.5 forms at its front. Our simulation demonstrates how wave dispersion widens the shock transition layer into a train of nonlinear fast magnetosonic waves.
Collisionless dissipation of macroscopic energy into heat is an unsolved problem of space and astrophysical plasmas, e.g., solar wind and Earth's magnetosheath. The most viable process under consideration is the turbulent-cascade of macroscopic energy to kinetic-scales where collisionless-plasma-processes dissipate the energy. Space observations and numerical simulations show the formation of kinetic scale current sheets in turbulent plasmas. Instabilities in these CS can provide collisionless dissipation and influence the turbulence. Spatial gradients of physical quantities and non-Maxwellian…
The energy budget of a collisionless plasma subject to electrostatic fluctuations is considered, and the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion is calculated. This excess measures how much thermal energy is "available" for conversion into plasma instabilities, and therefore constitutes a nonlinear measure of plasma stability. A distribution function with zero available energy defines a "ground state" in the sense that its energy cannot decrease by any linear or nonlinear plasma motion. In a Vlasov plas…
We investigate the formation of collisionless magnetized shocks triggered by the interaction between magnetized plasma flows and miniature-sized (order of plasma kinetic-scales) magnetic obstacles resorting to massively parallel, full particle-in-cell simulations, including the electron kinetics. The critical obstacle size to generate a compressed plasma region ahead of these objects is determined by independently varying the magnitude of the dipolar magnetic moment and the plasma magnetization. We find that the effective size of the obstacle depends on the relative orientation between the dip…
After approximate replacing of Maxwellian distribution exponent with the rational polynomial fraction we have obtained precise analytical expression for and calculated the principal value of logarithmically divergent integral in the electron wave dispersion equation. At the same time our calculations have shown the presence of strong collisionless damping of the electromagnetic low-velocity (electron) wave in plasmas with Maxwellian-like electron velocity distribution function at some small, of the order of several per cents, differences from Maxwellian distribution in the main region of large…
The comparative analysis of the results of experimental investigations of the processes of formation, interaction and dynamics of vortex structures in pure electron and gas-discharge electron nonneutral plasmas taking place for the period of time much less than the electron-neutral collision time has been given. The general processes of formation and behavior of vortex structures in these two plasmas were considered. The phenomena, taking place only in one of these plasmas were also considered. It is shown that the existing difference in behavior of vortex structures is caused by different ini…
The electrostatic shielding of a charged absorbing object (dust grain) in a flowing collisionless plasma is investigated by using the linearized kinetic equation for plasma ions with a point-sink term accounting for ion absorption on the object. The effect of absorption on the attractive part of the grain potential is investigated. For subthermal ion flows, the attractive part of the grain potential in the direction perpendicular to the ion flow can be significantly reduced or completely destroyed, depending on the absorption rate. For superthermal ion flows, however, the effect of absorption …
Classical plasma with any degree degeneration of electronic gas is considered. In plasma two external electromagnetic field are propagation. It is required to find the plasma response on these fields. From kinetic Vlasov equation for collisionless plasmas distribution function in square-law approximation on sizes of intensivities of two electric fields is received. The formula for calculation electric current at any temperature (any degree of degeneration electronic gas) is deduced. This formula contains an one-dimensional quadrature. It is shown, that the nonlinearity account leads to occurre…
We present the first laboratory observations of time-resolved electron and ion velocity distributions in forming, magnetized collisionless shocks. Thomson scattering of a probe laser beam was used to observe the interaction of a laser-driven, supersonic piston plasma expanding through a magnetized ambient plasma. From the Thomson-scattered spectra we measure time-resolved profiles of electron density, temperature, and ion flow speed, as well as spatially-resolved magnetic fields from proton radiography. We observe direct evidence of the sweeping up and acceleration of ambient ions, magnetic fi…
A fluid description for collisionless magnetized plasmas that takes into account the effect of cyclotron resonance has been developed. Following the same approach as the Landau fluid closure, the heat flux components associated with transverse electromagnetic fluctuations are approximated by a linear combination of lower-order moments in wavenumber space. The closure successfully reproduces the linear cyclotron resonance for electromagnetic waves propagating parallel to the ambient magnetic field. In the presence of finite temperature anisotropy, the model gives approximately correct predictio…
Unmagnetized collisionless plasma system consisting of positive- and negative ions, and electrons are considered to study the head-on collision of ion-acoustic shock waves (IASWs) and its effects on the formation of shock (monotonic and oscillatory) waves and phase shift. The soliton solution is derived from the two-sided Korteweg-de Vries Burger (KdVB) equations. The KdVB equations are obtained using extend Poincare-Lighthill-Kuo (ePLK) method. It is assumed that the negative ions are immobile and the electrons follow the Boltzmann energy distribution in the plasma. The effects of plasma para…
Magnetized high-energy-density plasmas can often have strong electromagnetic fluctuations whose correlation scale is smaller than the electron Larmor radius. Radiation from the electrons in such plasmas, which markedly differs from both synchrotron and cyclotron radiation, and their energy and pitch-angle diffusion are tightly related. In this paper, we present a comprehensive theoretical and numerical study of the particles' transport in both cold, "small-scale" Langmuir and Whistler-mode turbulence and its relation to the spectra of radiation simultaneously produced by these particles. We em…
Two-dimensional Particle-In-Cell simulations are used to explore collisionless shock acceleration in the corona plasma surrounding the compressed core of an inertial confinement fusion pellet. We show that an intense laser pulse interacting with the long scale-length plasma corona is able to launch a collisionless shock around the critical density. The nonlinear wave travels up-ramp through the plasma reflecting and accelerating the background ions. Our results suggest that protons with characteristics suitable for ion fast ignition may be achieved in this way.
We present results from experiments on the head-on merging of two supersonic plasma jets in an initially collisionless regime for the counter-streaming ions. The plasma jets are of either an argon/impurity or hydrogen/impurity mixture and are produced by pulsed-power-driven railguns. Based on time- and space-resolved fast-imaging, multi-chord interferometry, and survey-spectroscopy measurements of the overlapping region between the merging jets, we observe that the jets initially interpenetrate, consistent with calculated inter-jet ion collision lengths, which are long. As the jets interpenetr…
Recent laboratory experiments with laser-produced plasmas have observed and studied a number of fundamental physical processes relevant to magnetized astrophysical plasmas, including magnetic reconnection, collisionless shocks, and magnetic field generation by Weibel instability, opening up new experimental platforms for laboratory astrophysics. We develop a fully kinetic simulation model for first-principles simulation of these systems including the dynamics of magnetic fields---magnetic field generation by the Biermann battery effect or Weibel instability; advection by the ion flow, Hall eff…
Collisionless shock acceleration of carbon ions (C$^{6+}$) is investigated in the ultra-relativistic regime of laser-plasma interaction by accounting for the radiation reaction force and the pair production in particle-in-cell simulations. Both radiation reaction force and pair plasma formation tend to slow down the shock velocity, reducing the energy of the accelerated ions, albeit extending the time scales of the acceleration process. Slab plasma target achieves lower energy spread while target with a tailored density profile yields higher ion acceleration energies.
Microtearing modes have been widely reported as a tearing parity electron temperature gradient driven plasma instability, which leads to fine scale tearing of the magnetic flux surfaces thereby resulting in reconnection of magnetic field lines and formation of magnetic islands. In slab geometry it has previously been shown that the drive mechanism requires a finite collision frequency. However, we find in linear gyrokinetic simulations that a collisionless fine-scale tearing parity instability exists even at low and zero collision frequency. Detailed studies reveal that these slab modes are al…
The dissipation mechanism of the magnetic energy in turbulent collisionless space and astrophysical plasmas is still not well understood. Its investigation requires efficient kinetic simulations of the energy transfer in collisionless plasma turbulence. In this respect, hybrid-kinetic simulations, in which ions are treated as particles and electrons as an inertial fluid, have begun to attract a significant interest recently. Hybrid-kinetic models describe both ion- and electron scale processes by ignoring electron kinetic effects so that they are computationally much less demanding compared to…
In contrast to hydrodynamic vortices, vortices in plasma contain an electric current circulating around the center of the vortex, which generates a magnetic field localized inside. Using computer simulations, we demonstrate that the magnetic field associated with the vortex gives rise to a mechanism of dissipation of the vortex pair in a collisionless plasma, leading to fast annihilation of the magnetic field with its energy transforming into the energy of fast electrons, secondary vortices, and plasma waves. Two major contributors to the energy damping of double vortex system, namely, magneti…
We have used the Sagdeev pseudo-potential technique to investigate the arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of adiabatic warm ions, isothermal cold electrons and nonthermal hot electrons immersed in an external uniform static magnetic field. We have used the phase portraits of the dynamical system describing the nonlinear behaviour of ion acoustic waves to confirm the existence of different solitary structures. We have also investigated the transition of different solitary structures: soliton (before the form…
Sardar et al. [Phys. Plasmas 23, 073703 (2016)] have studied the stability of small amplitude dust ion acoustic solitary waves in a collisionless unmagnetized electron - positron - ion - dust plasma. They have derived a Kadomtsev Petviashvili (KP) equation to investigate the lowest - order stability of the solitary wave solution of the Korteweg-de Vries (KdV) equation for long-wavelength plane-wave transverse perturbation when the weak dependence of the spatial coordinates perpendicular to the direction of propagation of the wave is taken into account. In the present paper, we have extended th…
The coupling between a rapidly expanding cloud of ionized debris and an ambient magnetized plasma is revisited with a hybrid (kinetic ion/fluid electron) simulation code that allows a study over a wide range of plasma parameters. Over a specified range of hypothetical conditions, simple scaling laws in terms of the total debris mass and explosion speed are derived and verified for the maximal size of the debris cloud and the fraction of debris that free-streams from the burst along the magnetic field. The amount of debris that escapes from the burst with minimal coupling to the background magn…
It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of solution of the dispersion equation are simultaneously realizing. These are the branch of fast forward waves determined mainly by Maxwell equations of electromagnetic field, as well as the branch of forward and backward slow waves determined in the whole by kinetic properties of electrons in the collective electrical field. The physical nature of wave movem…
Collisionless Larmor Coupling and Blob Formation in a Laser-Plasma Expanding into a Magnetized Ambient Plasma
University of California–Los Angeles（加州大学洛杉矶分校）；Laboratoire d’Optique Appliquée (LOA), CNRS, École polytechnique, ENSTA, Institut Polytechnique de Paris（应用光学实验室，法国国家科学研究中心，巴黎综合理工学院，ENSTA，巴黎理工学院）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Vlasov-Maxwell equilibria are described by the self-consistent solutions of the time-independent Maxwell equations for the real-space dynamics of electromagnetic fields, and the Vlasov equation for the phase-space dynamics of particle distributions in a collisionless plasma. These two systems (macroscopic and microscopic) are coupled via the source terms in Maxwell's equations, which are sums of velocity-space 'moment' integrals of the particle distribution function. This paper considers 'the inverse problem for collisionless equilibria' (IPCE), viz. "given information regarding the real-space…
Strongly magnetizing a plasma adds a range of waves that do not exist in unmagnetized plasmas and enlarges the laser-plasma interaction (LPI) landscape. In this paper, we use particle-in-cell (PIC) simulations to investigate strongly magnetized LPI in one dimension under conditions relevant for magneto-inertial fusion experiments, focusing on a regime where the electron-cyclotron frequency is greater than the plasma frequency and the magnetic field is at an oblique angle with respect to the wave vectors. We show that when electron-cyclotron-like hybrid wave frequency is about half the laser fr…
In this paper, the central concern is to analyze the influence of the forces that controls the ion dynamics inside a magnetized plasma sheath under collisionless conditions. The ionization effects are considered within the sheath. The magnetic field is tilted in x-z plane and makes an angle with the x-axis. The motivation of the paper is to see the effect of both field strength variation and the variation of the inclination angle on the force fields inside the sheath. The pitch length and pitch angle for the particle velocity field is also calculated and has been found to vary widely with the …
So far, only one distribution function giving rise to a collisionless nonlinear force-free current sheet equilibrium allowing for a plasma beta less than one is known (Allanson et al., 2015; 2016). This distribution function can only be expressed as an infinite series of Hermite functions with very slow convergence and this makes its practical use cumbersome. It is the purpose of this paper to present a general method that allows us to find distribution functions consisting of a finite number of terms (therefore easier to use in practice), but which still allow for current sheet equilibria tha…
