Ion-ion Two-stream Instability Research Articles

Three-dimensional coupling of electron cyclotron drift instability and ion–ion two stream instability

Electron cyclotron drift instability (ECDI) and ion–ion two stream instability (IITSI) are both kinetic instabilities that can be present in low-temperature, partially magnetized plasmas. The coupling of instabilities in a three-dimensional configuration leads to the existence of more than one unstable roots to the kinetic dispersion relation. In this paper, a generalized method has been developed for numerically evaluating solutions to the three-dimensional dispersion relation for coupled ECDI and IITSI, assuming cold singly and doubly charged ions and a Maxwellian velocity distribution function for the electrons. The present study demonstrates the coupling between ECDI and IITSI that affects the most unstable mode as a function of the wavenumbers in three dimensions and various plasma properties, including the applied electric field, magnetic field, electron temperature, ion velocities, and plasma density. One of the most notable results is that, while the most unstable mode with the largest growth rate is in the direction of the E×B drift in the two-dimensional cases, the most unstable mode for the three-dimensional configuration occurs in the oblique direction between the applied electric field and the E×B drift. This agrees with experimental observations in cross field plasma sources using coherent Thomson scattering.

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.

Magnetic Field Amplification by the Weibel Instability at Planetary and Astrophysical Shocks with High Mach Number.

Collisionless shocks are ubiquitous in the Universe and often associated with a strong magnetic field. Here, we use large-scale particle-in-cell simulations of nonrelativistic perpendicular shocks in the high-Mach-number regime to study the amplification of the 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 particle-in-cell simulations are fully consistent with those taken insitu at Saturn's bow shock by the Cassini spacecraft.

Cross-field electron diffusion due to the coupling of drift-driven microinstabilities.

In this paper, the nonlinear interaction between kinetic instabilities driven by multiple ion beams and magnetized electrons is investigated. Electron diffusion across magnetic field lines is enhanced by the coupling of plasma instabilities. A two-dimensional collisionless particle-in-cell simulation is performed accounting for singly and doubly charged ions in a cross-field configuration. Consistent with prior linear kinetic theory analysis and observations from coherent Thomson scattering experiments, the present simulations identify an ion-ion two-stream instability due to multiply charged ions (flowing in the direction parallel to the applied electric field) which coexists with the electron cyclotron drift instability (propagating perpendicular to the applied electric field and parallel to the E×B drift). Small-scale fluctuations due to the coupling of these naturally driven kinetic modes are found to be a mechanism that can enhance cross-field electron transport and contribute to the broadening of the ion velocity distribution functions.

Influence of neutral pressure on instability enhanced friction and ion velocities at the sheath edge of two-ion-species plasmas

The Instability Enhanced Friction theory [Baalrud et al., Phys. Rev. Lett. 103, 205002 (2009)] is extended to account for the influence of neutral pressure in predicting the flow speed of each ion species at the sheath edge of plasmas containing two ion species. Particle-in-cell simulations show that the theory accurately predicts both the neutral pressure cutoff of ion-ion two-stream instabilities and the ion flow speeds at the sheath edge as pressure is varied over several orders of magnitude. The simulations are used to directly calculate the instability-enhanced ion-ion friction force. At sufficiently high neutral pressure, the simulations also provide evidence for collisional modifications to the Bohm criterion.

Effect of ion-to-electron mass ratio on the evolution of ion beam driven instability in particle-in-cell simulations

In particle-in-cell (PIC) simulation studies of ion-ion two-stream instability, a reduced ion-to-electron mass ratio is often employed to save computation time. It is tacitly assumed that electrons do not play a significant role in the evolution of the instability as the ion-ion interactions are regarded to occur on time scales much slower than the response time of electrons. However, as the effect of such a reduced mass ratio has never been closely examined, we have studied the evolution of the ion beam driven instability using a one-dimensional electrostatic PIC code by rescaling the simulation parameters according to the ion-electron mass ratio. We made a reference simulation run with a mass ratio of 100 first and compared the results to the simulation results using the real mass ratio with parameters rescaled from those of the reduced mass ratio. External electric fields were applied in these simulations, which accelerated the electrons and excited an ion acoustic type instability, forming electron phase space holes. Merging of the electron holes affected the ion dynamics significantly when the reduced mass ratio was used, while the interplay between the electron and ion dynamics became different depending on the rescaling methods in the case of the real mass ratio. Another simulation test with much enhanced external electric field results in similar mass ratio dependence. The present simulation results clearly show that the reduced mass ratio should be used cautiously in PIC simulations as the electron dynamics can modify the ion instabilities significantly by affecting the ion motions.

Determining the Bohm criterion in plasmas with two ion species

A model that uniquely determines the flow speed of each ion species at the sheath edge of two ion species plasmas is developed. In this analysis, ion-ion two-stream instabilities can play an important role because they significantly enhance the friction between ion species. Two-stream instabilities arise when the difference in flow speeds between the ion species exceeds a critical value: V1−V2≡ΔV≥ΔVc. The resultant instability-enhanced friction rapidly becomes so strong that ΔV cannot significantly exceed ΔVc. Using the condition provided by ΔV=ΔVc and the generalized Bohm criterion, the speed of each ion species is uniquely determined as it leaves a quasineutral plasma and enters a sheath. Previous work [S. D. Baalrud et al., Phys. Rev. Lett. 103, 205002 (2009)] considered the cold ion limit (Ti→0), in which case ΔVc→0 and each ion species obtains a common “system” sound speed at the sheath edge. Finite ion temperatures are accounted for in this work. The result is that ΔVc depends on the density and thermal speed of each ion species; ΔVc has a minimum when the density ratio of the two ion species is near one, and becomes larger as the density ratio deviates from unity. As ΔVc increases, the speed of each ion species approaches its individual sound speed at the sheath edge.

Kinetic theory of instability-enhanced collisional effects

The Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy is used to derive a generalization of the Lenard–Balescu plasma kinetic equation that accounts for wave-particle scattering due to instabilities that originate from discrete particle motion. Application to convective instabilities is emphasized for which the growing waves either propagate out of the domain of interest or modify the particle distribution to reduce the instability amplitude before nonlinear amplitudes are reached. Two such applications are discussed: Langmuir’s paradox and determining the Bohm criterion for multiple ion species plasmas. In these applications, collisions are enhanced by ion-acoustic and ion-ion two-stream instabilities, respectively. The relationship between this kinetic theory and quasilinear theory is discussed.

Interpretation on the Origin of Enhanced Ion Acoustic Line Spectra in the High Ionosphere

大量的实验研究表明, 在顶部极光区电离层, 利用EISCAT非相干散射雷达和Millstone Hill雷达可以观测到不对称、增强的离子声波谱线. 考虑到低能H+离子束沉降到背景电离层, 以及电离层顶部O+离子的外流事件, 采用含有场向热流项的双麦克斯韦分布描述H+离子束的分布函数, 进而基于离子－离子双流不稳定性理论来解释增强的离子声波谱线. 场向热流的引入可以减小离子声波谱线的不对称现象, 这样得到的结果更符合实际.

A multi-satellite study of accelerated ionospheric ion beams above the polar cap

Abstract. This paper presents a study of nearly field-aligned outflowing ion beams observed on the Cluster satellites over the polar cap. Data are taken at geocentric radial distances of the order of 5–9 RE. The distinction is made between ion beams originating from the polar cusp/cleft and beams accelerated almost along the magnetic field line passing by the spacecraft. Polar cusp beams are characterized by nearly field-aligned proton and oxygen ions with an energy ratio EO+ / EH+, of the order of 3 to 4, due to the ion energy repartition inside the source and to the latitudinal extension of the source. Rapid variations in the outflowing ion energy are linked with pulses/modifications of the convection electric field. Cluster data allow one to show that these perturbations of the convection velocity and the associated ion structures propagate at the convection velocity. In contrast, polar cap local ion beams are characterized by field-aligned proton and oxygen ions with similar energies. These beams show the typical inverted V structures usually observed in the auroral zone and are associated with a quasi-static converging electric field indicative of a field-aligned electric field. The field-aligned potential drop fits well the ion energy profile. The simultaneous observation of precipitating electrons and upflowing ions of similar energies at the Cluster orbit indicates that the spacecraft are crossing the mid-altitude part of the acceleration region. In the polar cap, the parallel electric field can thus extend to altitudes higher than 5 Earth radii. A detailed analysis of the distribution functions shows that the ions are heated during their parallel acceleration and that energy is exchanged between H+ and O+. Furthermore, intense electrostatic waves are observed simultaneously. These observations could be due to an ion-ion two-stream instability.

Phase space vortices in collisionless plasmas

Abstract. Results on the formation and propagation of electron phase space vortices from laboratory experiments are summarized. The electron phase space vortices were excited in a strongly magnetized Q-machine plasma by applying a pulse to a segment of a waveguide surrounding the plasma. Depending on the temporal variation of the applied pulse, one or more phase space vortices can be excited, and their interaction can be followed in space and time. We were able to demonstrate, for instance, an irreversible coalescence of two such vortices. These results are extended by numerical simulations, showing how electron phase space vortices can also be formed by beam instabilities. Furthermore, a study of ion phase space vortices is performed by numerical simulations. Both codes allow for an externally applied magnetic field in three spatial dimensions. Ion phase space vortices are formed by the nonlinear saturation of the ion-ion two-stream instability, excited by injecting an ion beam at the plasma boundary. By following the evolution of the ion distribution of the velocity perpendicular to the direction of propagation of the injected ion beam, we find a significant ion heating in the direction perpendicular to the magnetic field associated with the ion phase space vortices being formed. The results are relevant, for instance, for the interpretation of observations by instrumented spacecraft in the Earth's ionosphere and magnetosphere.

Electron energization in the topside auroral ionosphere: on the importance of ion-acoustic turbulence

EISCAT observations show enhancements of electron temperatures up to 8000 K in the topside ionosphere during active auroral conditions. These temperature enhancements correlate with electron density enhancements in the altitude region 170–230 km, which indicate that auroral electron precipitation in the 100–500 eV range is associated with the electron heating. Electron densities in other altitude intervals show no such correlation and thereby indicate that auroral particles outside the energy range 100–500 eV are not the major regular cause for this bulk electron heating. We also present observations of ion acoustic turbulence in connection with the bulk electron heating events. Such turbulence will give a greatly enhanced Joule heating in the presence of field-aligned currents because of the resulting anomalous resistivity by the turbulently fluctuating electric fields. This heating will occur in addition to the classical collisonal heating by precipitating particles, and is probably a major heat source for the topside ionospheric electrons. In fact, the precipitating electrons in the 100–500 eV range may themselves be runaway suprathermal electrons produced by the ion-acoustic turbulence. An ion-ion two-stream instability is suggested to be the cause of the observed enhanced ion-acoustic fluctuations.

Scattering of electromagnetic waves from a plasma: Enhanced ion acoustic fluctuations due to ion‐ion two‐stream instabilities

Observations by the ElSCAT and Millstone Hill radars of strongly enhanced, often asymetric, ion acoustic line spectra in the topside auroral ionosphere have been reported recently by a number of researchers. Such strongly enhanced ion acoustic line spectra are shown to arise naturally in a plasma unstable to the ion‐ion two‐stream instability. A linear theory of density fluctuations is used for the calculations, which should be applicable to weakly unstable non‐magnetized plasmas near the onset threshold of the instability.

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

In a plasma in which both the ions and electrons are magnetized we investigate low-frequency electrostatic instabilities driven by an anisotropic ion beam drifting parallel to the external magnetic field. The instability spectrum is found to be dominated by the ion-acoustic and ion-ion two-stream instabilities. Detailed comparisons are made with the isotropie case.

Ion-ion two-stream instability in multispecies laser-produced plasma

Experimental observations of the high-energy ions (g 10 keV/Z), expanding from a laser-produced plasma, have shown strong evidence of coronal electrostatic fields. In this paper, it is shown by a linear analysis that a multispecies streaming plasma can be subject to a two-stream ion-ion instability leading to density modulations. The effect of the charge-to-mass ratio on growth rate for different species accelerated by the same background electric field has been investigated. The theoretical model is consistent with experimental observations.

Quasi-neutral particle simulation model with application to ion wave propagation

A new class of particle simulation models has been developed which eliminates the high-frequency space charge oscillations while keeping the low-frequency ion-density fluctuations unmodified. Physically, the quasi-neutrality is maintained as the adiabatic electrons follow the ion-density fluctuations so as to establish the Debye shielding. It is, therefore, possible to use an integration time step comparable to the characteristic time scale of the low-frequency oscillations so that realistic plasma parameters can be used in the present simulation model. Applications to ion sound wave propagation, ion-ion two-stream instability, and the low-frequency fluctuation spectrum in a magnetic field are given. The way in which to include the nonadiabatic electrons in the model is also discussed.

Plasma Turbulence Generated by Ion-Ion Two-Stream instability

An instability is generated by injecting a high density ion-beam with a large cross-section into an unmagnetized homogeneous plasma. The linear dispersion relation of the wave in the ion-ion two-stream system is experimentally confirmed. Three-dimensional investigations of the turbulence thus produced reveal some new features: The turbulent waves propagate at large angles to the beam with extremely short correlation lengths. At these angles a rapid relaxation of the velocity distribution of the ions is observed until the beam temperature reaches around 0.2 T e . the observed rapid heating of ions can be explained by a theory incorporating the effect of orbit modification.

Beam-Generated Collisionless Ion-Acoustic Shocks

A numerical study of a one-dimensional collisionless ion-acoustic shock generated by an injection of a plasma beam is presented. The electrons are assumed to be hot and isothermal, and obey the Boltzmann distribution; the ions are described by the Vlasov equation which is solved by a direct finite difference scheme. There is a threshold beam velocity ubm, above which shock is not generated. ubm is a function of the beam-background density ratio and the electron-ion temperature ratio, and is larger than the limit of the ion-ion two-stream instability uts. For beam velocities ranging from zero to uts a shock is observed followed by a region of fully developed two-stream instability. For beam velocities between uts and ubm, a shock and a phase-space vortex are formed and in between them a quiescent region grows. A stable two-stream remains behind the vortex.

Heating of Counterstreaming Ion Beams in an External Magnetic Field

Ion heating by a strong ion-ion two-stream instability perpendicular to a magnetic field in the presence of a relatively cold electron background (Te≪miVd2) is considered. The magnetic field strength is such that the ion trajectories are straight, whereas the electrons are bound to the field lines (krLe≪1≪krLi). Theory is presented for both quasilinear and nonlinear stages of the evolution of the system for the case that the instability is electrostatic [(B2/8π) (1+β) >nmiVd2/8] and is compared with a series of computer simulation experiments. It is found that the quasilinear theory gives a fairly accurate description of spatially averaged plasma properties until the ion beams have been sufficiently modulated for ions to be trapped by the waves. In the subsequent nonlinear stage, stabilization occurs when the ion trapping period is equal to the reciprocal growth rate associated with the instability. The directed ion beam energy is mainly converted into random ion energy. The possible role of this instability in high Mach number shocks is discussed.

Simulation of Counterstreaming Plasmas with Application to Collisionless Electrostatic Shocks

A one-dimensional sheet-charge model is used to simulate homogeneous conterstreaming plasmas with no magnetic field. We demonstrate that the only electrostatic instability capable of dissipating a substantial fraction of the relative ion-drift energy and thus generating a turbulent, collisionless shock is the ion-ion two-stream instability. Furthermore, it is shown that such a shock cannot occur at high Mach numbers.