Linear Fluid Theory Research Articles

Interplay between the non-resonant streaming instability and self-generated pressure anisotropies

ABSTRACT The non-thermal particles escaping from collision-less shocks into the surrounding medium can trigger a non-resonant streaming instability that converts parts of their drift kinetic energy into large amplitude magnetic field perturbations, and promote the confinement and acceleration of high energy cosmic rays. We present simulations of the instability using an hybrid-Particle-in-Cell approach including Monte Carlo collisions, and demonstrate that the development of the non-resonant mode is associated with important ion pressure anisotropies in the background plasma. Depending on the initial conditions, the anisotropies may act on the instability by lowering its growth and trigger secondary micro-instabilities. Introducing collisions with neutrals yield a strong reduction of the magnetic field amplification as predicted by linear fluid theory. In contrast, Coulomb collisions in fully ionized plasmas are found to mitigate the self-generated pressure anisotropies and promote the growth of the magnetic field.

Rotating spokes, potential hump and modulated ionization in radio frequency magnetron discharges

In this work, the transition from the gradient drift instability (GDI) into an m = 1 rotating spoke in the radio frequency magnetron discharge was studied by means of the two-dimensional axial-azimuthal (z − y) particle-in-cell/Monte Carlo collision method. The kinetic model combined with the linear analysis of the perturbation revealed that the cathode sheath (axial) electric field E z triggers the GDI, deforming the local potential until the instability condition is not fulfilled and the fluctuation growth stops in which moment the instability becomes saturated. The potential deformation consequently leads to the formation of the potential hump, surrounding which the azimuthal electric field E y is present. The saturation level of E y was found to be synchronized with and proportional to the time-changing voltage applied at the cathode, resulting in the RF-modulation of the electron heating in the E y due to drift. In the saturated stage of the instability, it was shown that the rotation velocity and direction of the spoke present in the simulations agree well with the experimental observation (Panjan 2019 J. Appl. Phys. 125 203303). In the instability linear stage, the instability mode wavelength and the growth rate were also found to be in good agreement with the prediction of the GDI linear fluid theory.

Twisted plasma waves driven by twisted ponderomotive force

We present the results of twisted plasma waves driven by twisted ponderomotive force. With the beating of two, co-propagating, Laguerre-Gaussian (LG) orbital angular momentum (OAM) laser pulses with different frequencies and also different twist indices, we can obtain the twisted ponderomotive force. Three-dimensional particle-in-cell simulations are used to demonstrate the twisted plasma waves driven by lasers. The twisted plasma waves have an electron density perturbation with a helical rotating structure. Different from the predictions of the linear fluid theory, the simulation results show a nonlinear rotating current and a static axial magnetic field. Along with the rotating current is the axial OAM carried by particles in the twisted plasma waves. A detailed theoretical analysis of twisted plasma waves is also given.

Numerical study on bottom-hinged plate wave energy converter geometry design

This study focuses on the fluence on the power harvest performance exerted by plate geometry, damping setting and number of plates. Linear potential fluid theory is applied to calculate the hydrodynamic coefficients of the plate in frequency domain, and motion of bottom-hinged plate with different damping coefficients in time domain. The power capture performance is carried out based on the character of the plate motion. The performance of the device in different wave periods is studied and the adaption of the device is evaluated. The parameterized study is conducted to research the width, thickness, and the cross section of the plate. It is found that a two-dimensional plate model cannot fully reveal the hydrodynamic characteristic of the bottom-hinged plate, the width of the plate is an important factor and should take into consideration. The thickness of the plate is not a sensitive factor. The cross section of the plate has a distinct influence on plate performance. The number of the plate segment with a fixed whole width is studied. It is found that dividing plate cannot improve the performance of the plate, and dividing the plate cannot improve the performance of the plate while facing non-front-inducing waves either.

Enhancement of the Nonresonant Streaming Instability by Particle Collisions.

Streaming cosmic rays can power the exponential growth of a seed magnetic field by exciting a nonresonant instability that feeds on their bulk kinetic energy. By generating the necessary turbulent magnetic field, it is thought to play a key role in the confinement and acceleration of cosmic rays at shocks. In this Letter we present hybrid-particle-in-cell simulations of the nonresonant mode including MonteCarlo collisions, and investigate the interplay between the pressure anisotropies produced by the instability and particle collisions in the background plasma. Simulations of poorly ionized plasmas confirm the rapid damping of the instability by proton-neutral collisions predicted by linear fluid theory calculations. In contrast we find that Coulomb collisions in fully ionized plasmas do not oppose the growth of the magnetic field, but under certain conditions suppress the pressure anisotropies and actually enhance the magnetic field amplification.

Electrostatic and electromagnetic waves driven by current free electron beam instability: Effects of positron, background composition, and ion-to-electron mass ratio

Counterstreaming electron beams drifting along the magnetic field in electron–proton plasmas may lead to the generation of electrostatic (ES) waves and structures widely observed in planetary magnetospheres. In electron–positron plasmas, streaming electron/positron beams along the background magnetic field may first result in ES waves followed by the electromagnetic (EM) waves with substantial magnetic field perturbations, as shown by Jao and Hau [Phys. Rev. E 98, 013203 (2018)]. In this study, we examine the formation of ES and EM waves driven by current free counterstreaming electron beams in electron–ion background plasmas and current free electron–positron beams in electron–proton–positron background plasmas based on one-dimensional EM particle-in-cell simulations with the drift velocity being along the background magnetic field. For the former cases, the effects of ion-to-electron mass ratios are examined, which have implications for two- and three-dimensional particle in cell simulations with reduced mass ratios. For the latter cases, the effects of positrons are examined, which have applications to astrophysical plasma environments and laboratory experiments. It is shown that the presence of positrons or light ions may shorten the occurrence times between the ES and EM waves driven by current free electron beam instability. The EM waves have relatively longer wavelengths as compared to the ES waves and the magnetic field evolution resembles parallel proton firehose instability. The effects of positrons, background compositions, and ion-to-electron mass ratios on the occurrence of ES and EM waves are consistent with the linear fluid theory.

Parallel firehose instability in electron-positron plasmas.

In a magnetized uniform plasma, firehose instability may arise as a result of pressure anisotropy of P_{||}>P_{⊥}, where P_{||} and P_{⊥} are the thermal pressure parallel and perpendicular to the magnetic field, respectively. In this paper, we examine the parallel firehose instability in electron-positron plasmas based on the particle simulations along with the linear fluid theory, which may give rise to the dispersion relation, instability criteria, and growth rate, etc., for comparisons with those calculated from the kinetic simulations. As for the firehose instability in electron-proton plasmas, the magnetic field grows rapidly and then decreases with oscillations. The nonlinear saturated state complies with the linear stability criterion, α=μ_{0}(P_{||}-P_{⊥})/B^{2}=1, derived from the fluid theory only for relatively smaller values of initial α or ω_{p}/ω_{c}, where ω_{p} and ω_{c} are the plasma and cyclotron frequencies, respectively. For relatively larger values of initial α and ω_{p}/ω_{c}, the saturated α values are smaller than 1 as a result of kinetic resonant effects. The dominant wave numbers are kc/ω_{p}<0.5 and the growth rates are in the range of 0.1-0.3ω_{c}, which are approximately consistent with the linear fluid theory for the same wavelengths. Both electrostatic and electromagnetic modes predicted by the linear fluid theory are identified in the kinetic simulations.

Hybrid simulations of coupled Farley‐Buneman/gradient drift instabilities in the equatorial E region ionosphere

AbstractPlasma irregularities in the equatorial E region ionosphere are classified as Type I or Type II, based on coherent radar spectra. Type I irregularities are attributed to the Farley‐Buneman instability and Type II to the gradient drift instability that cascades to meter‐scale irregularities detected by radars. This work presents the first kinetic simulations of coupled Farley‐Buneman and gradient drift turbulence in the equatorial E region ionosphere for a range of zeroth‐order vertical electric fields, using a new approach to solving the electrostatic potential equation. The simulation models a collisional quasi‐neutral plasma with a warm, inertialess electron fluid and a distribution of NO+ ions. A 512 m wave with a maximum/minimum of ±0.25 of the background density perturbs the plasma. The density wave creates an electrostatic field that adds to the zeroth‐order vertical and ambipolar fields, and drives Farley‐Buneman turbulence even when these fields are below the instability threshold. Wave power spectra show that Type II irregularities develop in all simulation runs and that Type I irregularities with wavelengths of a few meters develop in the trough of the background wave in addition to Type II irregularities as the zeroth‐order electric field magnitude increases. Linear fluid theory predicts the growth of Type II irregularities reasonably well, but it does not fully capture the simultaneous growth of Type I irregularities in the region of peak total electric field. The growth of localized Type I irregularities represents a parametric instability in which the electric field of the large‐scale background wave drives pure Farley‐Buneman turbulence. These results help explain observations of meter‐scale irregularities advected by kilometer‐scale waves.

Fluid theory and kinetic simulation of two-dimensional electrostatic streaming instabilities in electron-ion plasmas

Electrostatic streaming instabilities have been proposed as the generation mechanism for the electrostatic solitary waves observed in various space plasma environments. Past studies on the subject have been mostly based on the kinetic theory and particle simulations. In this paper, we extend our recent study based on one-dimensional fluid theory and particle simulations to two-dimensional regimes for both bi-streaming and bump-on-tail streaming instabilities in electron-ion plasmas. Both linear fluid theory and kinetic simulations show that for bi-streaming instability, the oblique unstable modes tend to be suppressed by the increasing background magnetic field, while for bump-on-tail instability, the growth rates of unstable oblique modes are increased with increasing background magnetic field. For both instabilities, the fluid theory gives rise to the linear growth rates and the wavelengths of unstable modes in good agreement with those obtained from the kinetic simulations. For unmagnetized and weakly magnetized systems, the formed electrostatic structures tend to diminish after the long evolution, while for relatively stronger magnetic field cases, the solitary waves may merge and evolve to steady one-dimensional structures. Comparisons between one and two-dimensional results are made and the effects of the ion-to-electron mass ratio are also examined based on the fluid theory and kinetic simulations. The study concludes that the fluid theory plays crucial seeding roles in the kinetic evolution of electrostatic streaming instabilities.

Vlasov simulations of electron-ion collision effects on damping of electron plasma waves

Collisional effects can play an essential role in the dynamics of plasma waves by setting a minimum damping rate and by interfering with wave-particle resonances. Kinetic simulations of the effects of electron-ion pitch angle scattering on Electron Plasma Waves (EPWs) are presented here. In particular, the effects of such collisions on the frequency and damping of small-amplitude EPWs for a range of collision rates and wave phase velocities are computed and compared with theory. Both the Vlasov simulations and linear kinetic theory find the direct contribution of electron-ion collisions to wave damping significantly reduced from that obtained through linearized fluid theory. To our knowledge, this simple result has not been published before. Simulations have been carried out using a grid-based (Vlasov) approach, based on a high-order conservative finite difference method for discretizing the Fokker-Planck equation describing the evolution of the electron distribution function. Details of the implementation of the collision operator within this framework are presented. Such a grid-based approach, which is not subject to numerical noise, is of particular interest for the accurate measurements of the wave damping rates.

Two-dimensional electrostatic solitary structures in electron–positron plasmas

Due to the inertia symmetry the issue of whether electrostatic solitons may possibly form in pair plasmas has been addressed in a number of papers. Recently we have shown that pair solitons with interlacing electron and positron holes in electron–positron plasmas may form by means of streaming instability based on one-dimensional particle-in-cell simulations Jao and Hau (2012 Phys. Rev. E 86 056401). In this paper we present the first simulation results of two-dimensional electrostatic solitons in pair plasmas imbedded in a stationary background magnetic field. It is shown that the features of electrostatic solitary structures may depend on the ratio of to where and denote the electron cyclotron and plasma frequency, respectively. In particular, for weakly magnetized or unmagnetized plasmas with both parallel and transverse electric field with the same order of magnitude may first develop and be dissipated in the nonlinear stage such that electrostatic solitons are unable to form by the streaming instability, while for pair solitons resembling those occurring in one-dimensional simulations may possibly form. Comparisons between linear fluid theory and particle-in-cell simulations are made.

Linear Fluid Theory for Weakly Inhomogeneous Plasmas with Strong Correlations

AbstractLinearized fluid equations for the collective modes of weakly inhomogeneous plasmas including strong coupling effects are derived from a recent kinetic theory based on an extended Singwi‐Tosi‐Land‐Sjölander (STLS) ansatz [H. Kählert, G. J. Kalman, and M. Bonitz, Phys. Rev. E 90, 011101(R) (2014)]. The equations are analogous to the equations of linearized elasticity theory with space dependent elastic moduli that correspond to those of a bulk system with the local fluid density. The identification of the latter as infinite‐frequency elastic moduli shows that the present version of the extended STLS theory accounts for the elastic properties of the fluid but does not capture the viscous behavior. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Dispersion relation and growth rate in thermal plasma-loaded traveling wave tube with corrugated waveguide hollow electron beam

A theory of relativistic traveling wave tube with magnetized thermal plasma-filled corrugated waveguide with annular electron beam is given. The dispersion relation is obtained by linear fluid theory. The characteristic of the dispersion relation is obtained by numerical solutions. The effect of plasma density, corrugated period, waveguide radius and plasma thermal effect on the dispersion relation and growth rate are analyzed. Some useful results are given.

Theoretical analysis of a thermal plasma-loaded relativistic traveling wave tube having corrugated slow wave structure with solid electron beam

A relativistic traveling wave tube with thermal plasma-filled corrugated waveguide is driven by a finite solid electron beam with the entire system immersed in a strong longitudinal magnetic field that magnetized plasma and electron beam. The dispersion relation for the relativistic traveling wave tube is obtained by linear fluid theory. The numerical results show that the growth rate decreases by increasing plasma temperature, waveguide radius, plasma density and electron beam energy. As show in this paper the effect of electron beam density and corrugation period is to increase growth rate.

Dispersion relation and growth rate in two-stream thermal plasma-loaded free-electron laser with helical wiggler

Linear theory of the two-stream free-electron laser consisting of a relativistic electron beam transported along the axis of thermal plasma-loaded helical wiggler is proposed and investigated. The dispersion relation is derived employing linear fluid theory. The characteristics of the dispersion relation are analyzed by numerical solutions. The results show in that in the special values of the plasma temperature the growth rate is considerably enhanced. It is also shown that the growth rate after critical plasma density gradually decreases. Moreover, in the presence of the two-electron beam the growth rate of electrostatic mode is two times greater than that for electromagnetic mode.

Electron-scale shear instabilities: magnetic field generation and particle acceleration in astrophysical jets

Strong shear flow regions found in astrophysical jets are shown to be important dissipation regions, where the shear flow kinetic energy flow is converted into electric and magnetic field energy via shear instabilities. The emergence of these self-consistent fields makes shear flows significant sites for radiation emission and particle acceleration. We focus on electron-scale instabilities, namely the collisionless, unmagnetized electron-scale Kelvin–Helmholtz instability (ESKHI) and a large-scale DC magnetic field generation mechanism on the electron scales. We show that these processes are important candidates to generate magnetic fields in the presence of strong velocity shears, which may naturally originate in energetic matter outbursts of active galactic nuclei and gamma-ray bursters. We show that the ESKHI is robust to density jumps between shearing flows, thus operating in various scenarios with different density contrasts. Multidimensional particle-in-cell (PIC) simulations of the ESKHI, performed with OSIRIS, reveal the emergence of a strong and large-scale DC magnetic field component, which is not captured by the standard linear fluid theory. This DC component arises from kinetic effects associated with the thermal expansion of electrons of one flow into the other across the shear layer, whilst ions remain unperturbed due to their inertia. The electron expansion forms DC current sheets, which induce a DC magnetic field. Our results indicate that most of the electromagnetic energy developed in the ESKHI is stored in the DC component, reaching values of equipartition on the order of in the electron time-scale, and persists longer than the proton time-scale. Particle scattering/acceleration in the self-generated fields of these shear flow instabilities is also analyzed.

An experimental investigation and new correlation of viscosity of ZnO–EG nanofluid at various temperatures and different solid volume fractions

This paper presents an experimental investigation on effects of temperature and particle volume concentration on the dynamic viscosity of ZnO–EG nanofluid. The viscosity of Zinc oxide nanoparticles with mean diameter of 18nm dispersed in ethylene glycol was determined by using a ‘Spindle-type’ Brookfield commercial viscometer. The experiments were conducted for the temperatures ranging from room condition up to 50°C, while the nano-fluids and the particle volume fraction ranging from 0.25% to 5%.It has been found that, in general, the nanofluid dynamic viscosity increases considerably with particle volume fraction but does not significantly change (decrease) with increasing temperature. Two experimental correlations were developed based on the data, which relate the viscosity with particle volume fraction and the nanofluid temperature. The proposed models showed reasonably excellent agreement with the experimental results. The Data has also shown that the Einstein’s formula and some other ones originated from the classical linear fluid theory seem to be limited to nanofluids of only low particle fractions.

Fluid aspects of electron streaming instability in electron-ion plasmas

Electrons streaming in a background electron and ion plasma may lead to the formation of electrostatic solitary wave (ESW) and hole structure which have been observed in various space plasma environments. Past studies on the formation of ESW are mostly based on the particle simulations due to the necessity of incorporating particle's trapping effects. In this study, the fluid aspects and thermodynamics of streaming instabilities in electron-ion plasmas including bi-streaming and bump-on-tail instabilities are addressed based on the comparison between fluid theory and the results from particle-in-cell simulations. The energy closure adopted in the fluid model is the polytropic law of d(pρ−γ)/dt=0 with γ being a free parameter. Two unstable modes are identified for the bump-on-tail instability and the growth rates as well as the dispersion relation of the streaming instabilities derived from the linear theory are found to be in good agreement with the particle simulations for both bi-streaming and bump-on-tail instabilities. At the nonlinear saturation, 70% of the electrons are trapped inside the potential well for the drift velocity being 20 times of the thermal velocity and the pρ−γ value is significantly increased. Effects of ion to electron mass ratio on the linear fluid theory and nonlinear simulations are also examined.

Enhancements of Cherenkov Radiation by Two Electron Beams

An approach to the enhancement of Cherenkov radiation source driven by two electron beams (TEBs) is presented in this paper. The Cherenkov radiation source is composed of a cylindrical grating, and TEBs with a velocity separation are concentric and separated. By a field matched method, the dispersion equation is derived with a linearized fluid theory and solved by numerical calculation. The numerical results show that a considerable enhancement of growth rate is realized at an optimized voltage ratio due to two stream instability. Moreover, with a help of 2-D particle-in-cell simulations, the improvement of output power induced by the two stream instability is demonstrated, and the decreased of output power is observed as the increased distance of two electron beams.

Linear theory of magnetized ion-channel free-electron laser

A theory of wiggler pumped ion-channel free-electron laser (WPIC-FEL) and an axial magnetic field is presented. The motion of a relativistic electron is analyzed in the field configuration consisting of a helical wiggler magnetic field, a uniform axial magnetic field, and an electrostatic electric field produced by an ion-channel. An equation for the function Φ, which determines the rate of change of axial velocity with energy, is derived. Numerical calculations are made to illustrate the effects of two electron beam guiding devices on the trajectories. By means of linear fluid theory, the sixth-degree polynomial dispersion equation for electromagnetic and space-charge waves is derived. The dependence of growth rate-frequency curves on the ion-channel frequency and axial magnetic field is studied numerically.