Ion Two-stream Instability Research Articles

Ion Kinetics and Neutron Generation Associated with Electromagnetic Turbulence in Laboratory-Scale Counterstreaming Plasmas.

Electromagnetic turbulence and ion kinetics in counterstreaming plasmas hold great significance in laboratory astrophysics, such as turbulence field amplification and particle energization. Here, we quantitatively demonstrate for the first time how electromagnetic turbulence affects ion kinetics under achievable laboratory conditions (millimeter-scale interpenetrating plasmas with initial velocity of 2000 km/s, density of 4×10^{19} cm^{-3}, and temperature of 100eV) utilizing a recently developed high-order implicit particle-in-cell code without scaling transformation. It is found that the electromagnetic turbulence is driven by ion two-stream and filamentation instabilities. For the magnetized scenarios where an applied magnetic field of tens of Tesla is perpendicular to plasma flows, the growth rates of instabilities increase with the strengthening of applied magnetic field, which therefore leads to a significant enhancement of turbulence fields. Under the competition between the stochastic acceleration due to electromagnetic turbulence and collisional thermalization, ion distribution function shows a distinct super-Gaussian shape, and the ion kinetics are manifested in neutron yields and spectra. Our results have well explained the recent unmagnetized experimental observations, and the findings of magnetized scenario can be verified by current astrophysical experiments.

Effects of the Wavelength of the Plasma Waves on Cross-Field Electron Transport in Partially Magnetized Plasmas

In this article, the effects of increasing plasma density on the cross-field electron transport driven by kinetic instabilities are investigated. A 2-D collisionless particle-in-cell (PIC) simulation is performed on cases with only singly charged ions and with a mixture of singly and doubly charged ions, at different levels of plasma density. It is observed using the PIC simulations that the level of plasma density affects the plasma waves that are driven by the microinstabilities, including the electron cyclotron drift instability (ECDI) and ion–ion two-stream instability (IITSI). The simulation results suggest that the enhancement of cross-field electron transport is correlated with the excitation of smaller wavelength modes and the increased amplitude of the plasma waves.

Effects of multiply charged ions on microturbulence-driven electron transport in partially magnetized plasmas

Nonlinear interaction between kinetic instabilities in partially magnetized plasmas in the presence of multiply charged ion streams is investigated using kinetic simulations. It was observed by Hara and Tsikata [Phys. Rev. E 102, 023202 (2020)] that the axial ion–ion two-stream instability due to singly and doubly charged ion streams, coupled with the azimuthal electron cyclotron drift instability (ECDI), enhances cross-field electron transport. In the present study, it is observed that the addition of triply charged ions (as a third ion species) contributes to damping of the excited modes, leading to a reduction in the cross-field electron transport. The net instability-driven electron transport is shown to be a function not only of the azimuthal modes, such as the ECDI, but of the multiple ion species that dictate the development of additional plasma waves. It is found that trapping of the higher ion charge states within the plasma waves results in broadening of the ion velocity distribution functions.

Ion acceleration at two collisionless shocks in a multicomponent plasma.

Intense laser-plasma interactions are an essential tool for the laboratory study of ion acceleration at a collisionless shock. With two-dimensional particle-in-cell calculations of a multicomponent plasma we observe two electrostatic collisionless shocks at two distinct longitudinal positions when driven with a linearly polarized laser at normalized laser vector potential a_{0} that exceeds 10. Moreover, these shocks, associated with protons and carbon ions, show a power-law dependence on a_{0} and accelerate ions to different velocities in an expanding upstream with higher flux than in a single-component hydrogen or carbon plasma. This results from an electrostatic ion two-stream instability caused by differences in the charge-to-mass ratio of different ions. Particle acceleration in collisionless shocks in multicomponent plasma are ubiquitous in space and astrophysics, and these calculations identify the possibility for studying these complex processes in the laboratory.

Electrostatic Turbulence and Debye-scale Structures in Collisionless Shocks

Abstract We present analysis of more than 100 large-amplitude bipolar electrostatic structures in a quasi-perpendicular supercritical Earth’s bow shock crossing, measured by the Magnetospheric Multiscale spacecraft. The occurrence of the bipolar structures is shown to be tightly correlated with magnetic field gradients in the shock transition region. The bipolar structures have negative electrostatic potentials and spatial scales of a few Debye lengths. The bipolar structures propagate highly oblique to the shock normal with velocities (in the plasma rest frame) of the order of the ion-acoustic velocity. We argue that the bipolar structures are ion phase space holes produced by the two-stream instability between incoming and reflected ions. This is the first identification of the ion two-stream instability in collisionless shocks.

Electron acceleration at comet 67P/Churyumov-Gerasimenko

We report the observation by the Ion and Electron Sensor (IES) of energetic (>1 keV) electrons in the plasma environment of comet 67P Churyumov-Gerasimenko (67P). Most of the electrons in the cometary coma are expected to be of solar wind, photoionization, or electron impact origin and are therefore not expected to exceed some hundreds of eV in energy. During the Vega flybys of comet Halley, 1 keV electrons were also observed, and these are explained as having been accelerated by lower hybrid (LH) waves resulting from the two-stream instability involving the solar wind and pickup-ion flows. These waves resonate with the cyclotron motion of the ions and the longitudinal motion of electrons and are on the order of several Hz, at least in the case of 67P. We postulate that the energetic electrons we have observed intermittently during December 2015 through January 2016 are also the result of such a process and that Landau damping causes the acceleration and subsequent abrupt decrease in this energy (also seen at Halley). We show from this study an event on 19 January 2016 when IES simultaneously observed accelerated electrons, solar wind protons, water ions, and LH waves. A dispersion analysis shows that the ion–ion two-stream instability has positive growth rates for such waves during the observation period.

Enhancement of collisionless shock ion acceleration by electrostatic ion two-stream instability in the upstream plasma

Ion acceleration in electrostatic collisionless shocks is driven by the interaction of the high-power laser with specially tailored near-relativistic critical density plasma. 2D EPOCH particle-in-cell simulations show that the ion acceleration is dependent on the target material used. In materials with low charge-to-mass ratio.

Influence of ion streaming instabilities on transport near plasma boundaries

Plasma boundary layers are susceptible to electrostatic instabilities driven by ion flows in presheaths and, when present, these instabilities can influence transport. In plasmas with a single species of positive ion, ion-acoustic instabilities are expected under conditions of low pressure and large electron-to-ion temperature ratio (). In plasmas with two species of positive ions, ion–ion two-stream instabilities can also be excited. The stability phase-space is characterized using the Penrose criterion and approximate linear dispersion relations. Predictions for how these instabilities affect ion and electron transport in presheaths, including rapid thermalization due to instability-enhanced collisions and an instability-enhanced ion–ion friction force, are briefly reviewed. Recent experimental tests of these predictions are discussed along with research needs required for further validation. The calculated stability boundaries provide a guide to determine the experimental conditions at which these effects can be expected.

Instability-enhanced friction in the presheath of two-ion-species plasmas

The speed at which ions enter a sheath is a fundamental property of a plasma that also provides a useful boundary condition in modeling. A recent theory proposed that this can be significantly influenced by an instability-enhanced friction force arising from two-stream instabilities in the presheath when multiple ion species are present. Although experiments appeared to confirm this theory, recent particle simulations have brought it into question. We reconcile this controversy using direct numerical solutions of the dispersion relation, which show that there is a dependence on the electron–ion temperature ratio that was not considered previously. In addition, particle-in-cell simulations are used to show that ion–ion two-stream instabilities can arise near the sheath edge and generate an enhanced ion–ion friction force. Only by accounting for the instability-enhanced friction force can theory predict the simulated ion speeds at the sheath edge.

A study of solitary wave trains generated by injection of a blob into plasmas

We have investigated the evolution of consecutive electrostatic solitary waves (ESWs) generated upon injection of a finite-sized blob into plasmas using one-dimensional electrostatic particle-in-cell simulations. Strong charge separation developed at the leading edge of the blob, producing a huge electrostatic potential in which electrons were trapped and heated. Ions were reflected from the boundaries of the blob, forming fast, cold ion beams in the forward and backward directions. The forward ion beams interacted with the hot electrons, which were escaping from the potential developed at the leading edge of the blob, to produce successive ESWs. On the other hand, the backward ion beams formed ion phase space holes as a result of the ion two-stream instability. The present study demonstrates that localized density perturbations in plasmas can be a viable source of consecutive ESWs observed in space.

Survey of collective instabilities and beam–plasma interactions in intense heavy ion beams

This paper presents a survey of the present theoretical understanding based on advanced analytical and numerical studies of collective processes and beam–plasma interactions in intense heavy ion beams for applications to ion-beam-driven high energy density physics and heavy ion fusion. The topics include: discussion of the conditions for quiescent beam propagation over long distances; and the electrostatic Harris instability and the transverse electromagnetic Weibel instability in highly anisotropic, intense one-component ion beams. In the longitudinal drift compression and transverse compression regions, collective processes associated with the interaction of the intense ion beam with a charge-neutralizing background plasma are described, including the electrostatic electron–ion two-stream instability, the multispecies electromagnetic Weibel instability, and collective excitations in the presence of a solenoidal magnetic field. The effects of a velocity tilt on reducing two-stream instability growth rates are also discussed. Operating regimes are identified where the possible deleterious effects of collective processes on beam quality are minimized.

Oblique Ion Two‐Stream Instability in the Foot Region of a Collisionless Shock

The electrostatic behavior of a collisionless plasma in the foot region of high Mach number perpendicular shocks is investigated through a two-dimensional linear analysis and electrostatic particle-in-cell (PIC) simulations. The simulations are double periodic and taken as a proxy for the situation in the foot region. The linear analysis for relatively cold unmagnetized plasmas with a reflected proton beam shows that the obliquely propagating Buneman instability is strongly excited. We also found that when the electron temperature is much higher than the proton temperature, the most unstable mode is the highly obliquely propagating ion two-stream instability excited through the resonance between ion plasma oscillations of the background protons and of the beam protons, rather than the ion acoustic instability that is dominant for parallel propagation. To investigate nonlinear behavior of the ion two-stream instability, we have made PIC simulations for the shock foot region in which the initial state satisfies the Buneman instability condition. In the first phase, electrostatic waves grow two-dimensionally by the Buneman instability to heat electrons. In the second phase, highly oblique ion two-stream instability grows to heat mainly ions. This result is in contrast to previous studies based on one-dimensional simulations, for which the ion acoustic instability further heats electrons. The present result implies that the overheating problem of electrons for shocks in supernova remnants is resolved by considering the ion two-stream instability propagating highly obliquely to the shock normal and that multidimensional analysis is crucial to understand the particle heating and acceleration processes in shocks.

Propagating double layers in electronegative plasmas

Double layers have been observed to propagate from the source region to the diffusion chamber of a helicon-type reactor filled up with a low-pressure mixture of Ar∕SF6 [N. Plihon et al., J. Appl. Phys. 98, 023306 (2005)]. In the present paper the most significant and new experimental results are reported. A fully self-consistent hybrid model in which the electron energy distribution function, the electron temperature, and the various source terms are calculated is developed to investigate these propagating double layers. The spontaneous formation of propagating double layers is only observed in the simulation for system in which the localized inductive heating is combined with small diameter chambers. The conditions of formation and the properties of the propagating double layers observed in the simulation are in good agreement with that of the experiment. By correlating the results of the experiment and the simulation, a formation mechanism compatible with ion two-stream instability is proposed.

Instabilities of Ar/SF6 inductive plasma discharges

Relaxation oscillations are studied in three low-pressure inductive plasma discharges operated with argon and sulfur hexafluoride gas mixtures. Two distinct phenomena, downstream instabilities and source oscillations, occur in certain domains of gas pressure, radio frequency power, and electronegative gas chemistry. The downstream instabilities develop at some location well below the plasma source. They are consistent with ion two-stream instabilities, in inductively coupled plasmas (ICPs) with sufficiently long downstream regions. Source oscillations consist of large amplitude density variations within the ICP plasma. They are consistent with capacitive to inductive mode transitions, in ICPs with sufficiently large capacitive currents.

Downstream instabilities of electronegative plasma discharges

Relaxation oscillations are observed in low-pressure inductive plasma discharges operated with argon and SF6 gas mixtures. The data suggest that instabilities may develop periodically at some downstream location. Linear fluid and kinetic calculations predict ion two-stream instabilities when the positive and negative ions develop sufficiently large drift velocities of opposite sign in the downstream region. The thresholds and the growth rates of the instabilities are calculated and are found in fair agreement with the observations. The instability models can explain several key experimental features.

Effects of a solenoidal focusing field on the electron–ion two-stream instability in high-intensity ion beams

A rigid-beam model is used to investigate the influence of a solenoidal focusing field B 0 e ̂ z on the electron–ion two-stream instability that can occur in high-intensity ion beams when an (unwanted) component of background electrons is present. A relatively weak solenoidal magnetic field strongly constrains the transverse electron motion and can lead to a significant reduction in instability growth rate whenever ω 2 ce ⪢2( n b e b / n e e) ω 2 pe . Here, ω ce = eB 0/ m e c is the electron gyrofrequency, ω pe =(4 πn e e 2/ m e ) 1/2 is the electron plasma frequency, and n b and n e are the ion and electron number densities.

Stabilizing influence of axial momentum spread on the two-stream instability in intense heavy ion beams

This paper makes use of the Vlasov–Maxwell equations to describe the electron–ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating through a stationary population of (unwanted) background electrons in the acceleration region or beam transport lines. The ion beam is treated as continuous in the z-direction, and the electrons are electrostatically confined in the transverse direction by the space-charge potential produced by the excess ion charge. The analysis is carried out for arbitrary beam intensity, consistent with transverse confinement of the beam particles, and arbitrary fractional charge neutralization by the background electrons. For the case of overlapping step-function ion and electron density profiles, corresponding to Kapchinskij–Vladimirskij (KV) electron and ion distributions in the transverse direction, detailed stability properties are calculated including parallel kinetic effects over a wide range of system parameters for dipole perturbations with azimuthal mode number ℓ=1. The instability growth rate is found to increase with increasing beam intensity, increasing fractional charge neutralization, and decreasing proximity of the conducting wall. For space-charge-dominated beams, it is shown that Landau damping associated with a modest axial momentum spread of the beam ions and background electrons has a strong stabilizing influence on the two-stream instability.

Effects of axial momentum spread on the electron–ion two-stream instability in high-intensity ion beams

Use is made of the Vlasov–Maxwell equations to describe the electron–ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating through a stationary population of (unwanted) background electrons. The ion beam is treated as continuous in the z-direction, and the electrons are electrostatically confined in the transverse direction by the space-charge potential produced by the excess ion charge. The analysis is carried out for arbitrary beam intensity, consistent with transverse confinement of the beam particles, and arbitrary fractional charge neutralization by the background electrons. For the case of overlapping step-function ion and electron density profiles, corresponding to monoenergetic electrons and ions in the transverse direction, detailed stability properties are calculated, including the important effects of an axial momentum spread, over a wide range of system parameters for dipole perturbations with azimuthal mode number ℓ=1. The two-stream instability growth rate is found to increase with increasing beam intensity, increasing fractional charge neutralization, and decreasing proximity of the conducting wall. It is shown that Landau damping associated with a modest axial momentum spread of the beam ions and background electrons has a strong stabilizing influence on the instability.

Microinstability threshold of an axially focused neutralized ion beam

The response to electrostatic perturbations, φ=φ̂(r,z)ei(lθ−ωt), is investigated for the Migma Exyder, a proposed disk-shaped device where ions are trapped in the periphery and focused towards the axis [Nucl. Instrum. Methods A 271, 214 (1988)]. The ions are modeled as a relativistic monoenergetic distribution with a small spread in the impact parameter (the distance of closest approach to the axis) and with the axial extent ΔZ much shorter than the radial extent R0. It is found that odd l modes do not give rise to a low-frequency response. For l=0, an energy principle for low frequency ion–ion interactions is formulated, and it is shown that the extremizing perturbation is located in a narrow region surrounding the axis. The threshold is proportional to the total number of stored particles, N=4ε0(π−2)γ(γ2−1) ×mic2R0/q2i, where γ is the usual relativistic factor, and this stability condition therefore allows for a high density on axis in highly focused systems. Compared to a cylindrical shape, a disk-shaped plasma gives an improvement in the density by the factor R0/ΔZ. The threshold in particle number for the relativistic ion–ion two-stream instability scales as γ3 and thus with relativistic effects the instability is further suppressed. Inclusion of the electron response increases the threshold even further. Preliminary investigations indicate that finite frequency l=0 modes can give a lower threshold than the zero frequency case, at least for nonrelativistic beam energies. These finite frequency instabilities can arise from coupling between positive and negative energy modes. Finite l modes arise if electrons are magnetized at the axis of the device. A balance between the electron field energy and the cross field electron convection establishes discrete modes. When these modes resonate with the ion bounce motion or azimuthal drift motion, bands of instability arise with relatively low density thresholds compared to the l=0 case.

Anisotropic-ion-beam-plasma interaction: drift perpendicular to magnetic field

Using kinetic theory, low-frequency electrostatic instabilities driven by an anisotropic ion beam are investigated: In our model both the ions and electrons are magnetized, while the beam drift is across the external magnetic field. Both the ion-acoustic and ion–ion two-stream instabilities are excited. Regions of parameter space for the existence of either instability are distinguished. Detailed comparisons are made with the isotropie case.