Modified Two-stream Instability Research Articles

Effects of the applied fields' strength on the plasma behavior and processes in E × B plasma discharges of various propellants. II. Magnetic field

The effects of magnetic field intensity on the properties of the plasma discharge and on the underlying phenomena are studied for different propellants' ion mass. The plasma setup represents a 2D radial–azimuthal configuration with perpendicular electric and magnetic fields. The electric field is along the axial direction, and the magnetic field is along the radial direction. The magnetic field intensity is changed from 5 to 30 mT, with 5 mT increments. The studied propellant gases are xenon, krypton, and argon. The simulations are carried out using a reduced-order particle-in-cell code. It is shown that, for all the propellants, the change in the magnetic field intensity yields two distinct plasma regimes, where either the modified two-stream instability (MTSI) or the electron cyclotron drift instability (ECDI) are dominant. A third plasma regime is also observed for cases with moderate values of the magnetic field (15 and 20 mT), where the ECDI and the MTSI co-exist with comparable amplitudes. This described variation of plasma regime becomes clearly reflected in the radial distribution of the axial electron current density and the electron temperature anisotropy. At the relatively low-magnetic-field intensities (5 and 10 mT), the MTSI is mitigated. At relatively high magnitudes of the magnetic field (25 and 30 mT), the MTSI becomes strongly present, a long-wavelength wave mode develops, and the ECDI becomes suppressed. An exception to this latter observation was noticed for xenon, for which the ECDI was observed to be detectable with a notable strength up to the magnetic field value of 25 mT.

Kinetic simulation study of magnetized collisionless shock formation on a terawatt laser system

Perpendicular, magnetized, collisionless shocks in hydrogen and neon plasmas are studied with 2D particle-in-cell simulations for parameters accessible to experiments on OMEGA EP [Maywar et al., J. Phys.: Conf. Ser. 112, 032007 (2008)]. The simulations are performed with realistic ion-electron mass ratios by which the relative importance of different micro-instabilities can be accurately captured. The dispersion relation of the modified two-stream instability (MTSI), the main dissipation mechanism for these shocks, is used to find suitable parameters for upcoming experiments. Simulations show that magnetized collisionless shocks can be readily formed within a few tenths of an ion gyro-period in both hydrogen and neon gases, with a background magnetic field of 50 T, achievable using the magneto-inertial fusion electrical discharge system [Barnak et al., Rev. Sci. Instrum. 89, 033501 (2018)]. A portion of the ions are reflected to the upstream region and accelerated in both shock normal and tangential directions, indicating the formation of a supercritical shock. Shock front reformation is seen in longer time 1D simulations. The results show that the formation time and width of these shocks are determined by MTSI.

Conditions of appearance and dynamics of the modified two-stream instability in E × B discharges

The large differential drift motion between electrons and ions that is created by the E × B current can produce different instabilities, such as the electron cyclotron drift instability, perpendicular to the magnetic field, and the Modified Two-Stream Instability (MTSI), with a component along the magnetic field. In this paper, we derive and validate a stability condition for the apparition of the MTSI modes in 2D particle-in-cell simulations of E × B discharges in the radial-azimuthal plane of a Hall thruster. We verify that, by choosing properly the domain dimensions, it is possible to capture correctly the MTSI growth and its corresponding number of azimuthal periods. In particular, we show that an azimuthal length that is smaller than a certain threshold prevents the MTSI from growing. Moreover, we show that the MTSI growth does not depend on the plasma density, but is affected by the axial electric field (perpendicular to the simulation domain). Additionally, we show that during its linear growth in the early times of the simulations, the MTSI produces an enhanced heating of the electrons in the magnetic field direction as well as an increased cross field mobility. For longer times, in the nonlinear regime, the system evolves toward a more chaotic state with the presence of structures that mostly exhibit large azimuthal wavelengths.

Electrostatic Waves and Electron Heating Observed Over Lunar Crustal Magnetic Anomalies

AbstractAbove lunar crustal magnetic anomalies, large fractions of solar wind electrons and ions can be scattered and stream back toward the solar wind flow, leading to a number of interesting effects such as electrostatic instabilities and waves. These electrostatic structures can also interact with the background plasma, resulting in electron heating and scattering. We study the electrostatic waves and electron heating observed over the lunar magnetic anomalies by analyzing data from the Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) spacecraft. Based on the analysis of two lunar flybys in 2011 and 2013, we find that the electron two‐stream instability (ETSI) and electron cyclotron drift instability (ECDI) may play an important role in driving the electrostatic waves. We also find that ECDI, along with the modified two‐stream instability (MTSI), may provide the mechanisms responsible for substantial isotropic electron heating over the lunar magnetic anomalies.

Evolution of the electron cyclotron drift instability in two-dimensions

The Electron Cyclotron Drift Instability driven by the electron E × B drift in partially magnetized plasmas is investigated with highly resolved particle-in-cell simulations. The emphasis is on two-dimensional effects involving the parallel dynamics along the magnetic field in a finite length plasma with dielectric walls. It is found that the instability develops as a sequence of growing cyclotron harmonics demonstrating wave breaking and complex nonlinear interactions, being particularly pronounced in ion density fluctuations at short wavelengths. At the same time, nonlinear evolution of fluctuations of the ion and electron density, as well as the anomalous electron current, shows cascade toward long wavelengths. Tendency to generate long wavelength components is most clearly observed in the spectra of the electron density and the anomalous current fluctuations. An intense but slowly growing mode with a distinct eigen-mode structure along the magnetic field develops at a later nonlinear stage enhancing the tendency toward long wavelength condensation. The latter mode having a finite wavelength along the magnetic field is identified as the Modified Two-Stream Instability (MTSI). It is shown that the MTSI mode results in strong parallel heating of electrons.

Nonlinear damping of a finite amplitude whistler wave due to modified two stream instability

A two-dimensional, fully kinetic, particle-in-cell simulation is used to investigate the nonlinear development of a parallel propagating finite amplitude whistler wave (parent wave) with a wavelength longer than an ion inertial length. The cross field current of the parent wave generates short-scale whistler waves propagating highly oblique directions to the ambient magnetic field through the modified two-stream instability (MTSI) which scatters electrons and ions parallel and perpendicular to the magnetic field, respectively. The parent wave is largely damped during a time comparable to the wave period. The MTSI-driven damping process is proposed as a cause of nonlinear dissipation of kinetic turbulence in the solar wind.

Kinetic Alfven wave instability in a Lorentzian dusty plasma: Non-resonant particle approach

Analysis of the electromagnetic streaming instability is carried out which is related to the cross field drift of kappa distributed ions. The linear dispersion relation for electromagnetic wave using Vlasov-fluid equations in a dusty plasma is derived. Modified two stream instability (MTSI) in a dusty plasma has been discussed in the limit ωpd2/c2k⊥2≪1. Numerical calculations of the growth rate of instability have been carried out. Growth rates of kinetic Alfvén instability are found to be small as compared to MTSI. Maximum growth rates for both instabilities occur in oblique directions for V0≥VA. It is shown that the presence of both the charged dust particles and perpendicular ion beam sensibly modify the dispersion relation of low-frequency electromagnetic wave. The dispersion characteristics are found to be insensible to the superthermal character of the ion distribution function. Applications to different intersteller regions are discussed.

Non-stationarity of the quasi-perpendicular bow shock: comparison between Cluster observations and simulations

Abstract. We have performed full particle electromagnetic simulations of a quasi-perpendicular shock. The shock parameters have been chosen to be appropriate for the quasi-perpendicular Earth's bow shock observed by Cluster on 24 January 2001 (Lobzin et al., 2007). We have performed two simulations with different ion to electron mass ratio: run 1 with mi/me=1840 and run 2 with mi/me=100. In run 1 the growth rate of the modified two-stream instability (MTSI) is large enough to get excited during the reflection and upstream gyration of part of the incident solar wind ions. The waves due to the MTSI are on the whistler mode branch and have downstream directed phase velocities in the shock frame. The Poynting flux (and wave group velocity) far upstream in the foot is also directed in the downstream direction. However, in the density and magnetic field compression region of the overshoot the waves are refracted and the Poynting flux in the shock frame is directed upstream. The MTSI is suppressed in the low mass ratio run 2. The low mass ratio run shows more clearly the non-stationarity of the shock with a larger time scale of the order of an inverse ion gyrofrequency (Ωci): the magnetic field profile flattens and steepens with a period of ~1.5Ωci−1. This non-stationarity is different from reformation seen in previous simulations of perpendicular or quasi-perpendicular shocks. Beginning with a sharp shock ramp the large electric field in the normal direction leads to high reflection rate of solar wind protons. As they propagate upstream, the ion bulk velocity decreases and the magnetic field increases in the foot, which results in a flattening of the magnetic field profile and in a decrease of the normal electric field. Subsequently the reflection rate decreases and the whole shock profile steepens again. Superimposed on this 'breathing' behavior are in the realistic mass ratio case the waves due to the MTSI. The simulations lead us to a re-interpretation of the 24 January 2001 bow shock observations reported by Lobzin et al. (2007). It is suggested that the high frequency waves observed in the magnetic field data are due to the MTSI and are not related to a nonlinear phase standing whistler. Different profiles at the different spacecraft are due to the non-stationary behavior on the larger time scale.

Mach number dependence of electron heating in high Mach number quasiperpendicular shocks

The efficiency of electron heating through microinstabilities generated in the transition region of a quasiperpendicular shock for a wide range of Mach numbers is investigated by utilizing particle-in-cell (PIC) simulation and model analyses. In the model analyses saturation levels of effective electron temperature as a result of microinstabilities are estimated from an extended quasilinear (trapping) analysis for relatively low (high) Mach number shocks. Here, modified two-stream instability (MTSI) is assumed to become dominant in low Mach number regime, while Buneman instability (BI) is assumed to become dominant in high Mach number regime. It is revealed that Mach number dependence of the effective electron temperature in the MTSI dominant case is essentially different from that in the BI dominant case. The effective electron temperature through the MTSI does not depend much on the Mach number, although that through the BI increases with the Mach number as in the past studies. The results are confirmed to be consistent with the PIC simulations both in qualitative and quantitative levels. The model analyses predict that a critical Mach number, above which a steep rise in electron heating rate occurs, may arise at the Mach number of a few tens.

Cluster observations showing the indication of the formation of a modified-two-stream instability in the geomagnetic tail

This study presents several observations of the Cluster spacecraft on September 24, 2003 around 15:10 UT, which show necessary prerequisites and consequences for the formation of the so-called modified-two-stream instability (MTSI). Theoretical studies suggest that the plasma is MTSI unstable if (1) a relative drift of electrons and ions is present, which exceeds the Alfvèn speed, and (2) this relative drift or current is in the cross-field direction. As consequences of the formation of a MTSI one expects to observe (1) a field-aligned electron beam, (2) heating of the plasma, and (3) an enhancement in the B-wave spectrum at frequencies in the range of the lower-hybrid-frequency (LHF). In this study we use prime parameter data of the CIS and PEACE instruments onboard the Cluster spacecraft to verify the drift velocities of ions and electrons, FGM data to calculate the expected LHF and Alfvèn velocity, and the direction of the current. The B-wave spectrum is recorded by the STAFF instrument of Cluster. Finally, a field aligned beam of electrons is observed by 3D measurements of the IES instrument of the RAPID unit. Observations are verified using a theoretical model showing the build-up of a MTSI under the given circumstances.

Whistler waves, core ion heating, and nonstationarity in oblique collisionless shocks

One-dimensional full particle simulations of supercritical collisionless shocks with an ion and electron beta of 0.1 (particle to magnetic field pressure) over a wide Alfvén Mach number range and range of shock normal-magnetic field angles between ΘBn=60° and ΘBn=80° are presented. The whistler critical Mach number Mw, below which a linear phase-standing whistler can exist, is proportional to the square root of the ion-to-electron mass ratio and to cosΘBn. In small mass ratio simulations of oblique shocks, Mw can be artificially small and close to the first critical Mach number Mc, above which the process of ion reflection is needed in order to achieve shock dissipation. We use in the simulations the physical ion-to-electron mass ratio so that Mc and Mw are well separated. This also allows excitation of the modified two-stream instability (MTSI) between incoming ions and electrons. We find that in oblique but close to perpendicular (ΘBn⩾80°) shocks, upstream whistler waves do occur, but reformation is due to accumulation of reflected-gyrating ions at the upstream edge of the foot. In less oblique shocks above the whistler critical Mach number, the whistler amplitude in the foot upstream of the ramp grows, leading to vortices of the incoming ions and the reflected ions in velocity phase space, and eventually to phase mixing. The shock re-forms at the upstream edge of the whistler wave train, which is particularly evident in very high Mach number shocks where the scale of the foot is large compared with the whistler wave train. After reformation, the region with phase-mixed incoming and reflected ions constitutes a hot core downstream of the shock ramp. In this whistler induced reformation process, the MTSI results mainly in heating of the incoming ions in the foot.

Nonlinear evolution of modified two‐stream instability above ionosphere of Titan: Comparison with the data of the Cassini Plasma Spectrometer

The ionosphere of Titan, moon of Saturn, is directly exposed to the streaming plasma either of magnetospheric or solar wind origin. A turbulent interaction region is formed, called here flowside plasma mantle, where both cold ionospheric and hot streaming plasma are present at comparable densities. Within the framework of a one‐dimensional electromagnetic hybrid simulation using realistic electron mass we have shown that significant wave activity may be generated because of a modified two‐stream instability (MTSI). Having its free energy in the relative drift between the streaming ion flow and the ionospheric ions MTSI is very effective in generating “anomalous viscosity” type interaction leading to significant bulk velocity loss of the proton component of the external plasma flow and turbulent heating of the ionospheric ions. The stochastic energy transfer from the streaming plasma to the ionospheric ions may also increase the tailward planetary ion escape by collective pickup mechanism enhancing the rate of erosion of the atmosphere of Titan. We predict significant wave activity within the characteristic frequency range of about 1–10 Hz and at saturated wave electric field levels of about 5–25 mV/m. Similarly, according to our model calculations superthermal charged particles of ionospheric origin with kinetic energies of about few tens of eV are expected to be detectable by the charged particle analyzers onboard of Cassini spacecraft close to the upper edge of Titan's ionosphere.

Pickup protons at quasi-perpendicular shocks: full particle electrodynamic simulations

Abstract. We have performed 3 one-dimensional full particle electromagnetic simulations of a quasi-perpendicular shock with the same Alfvén Mach number MA~5, shock normal-magnetic field angle ΘBn=87° and ion and electron beta (particle to magnetic field pressure) of 0.1. In the first run we used an ion to electron mass ratio close to the physical one (mi/me=1024). As expected from previous high mass ratio simulations the Modified Two-Stream instability develops in the foot of the shock, and the shock periodically reforms itself. We have then self-consistently included in the simulation 10% pickup protons distributed on a shell in velocity space as a third component. In a run with an unrealistically low mass ratios of 200 the shock still reforms itself; reformation is due to accumulation of specularly reflected particles at the upstream edge of the foot. In a third run including pickup protons we used a mass ratio of 1024. The shock reforms periodically as in the low mass ratio run with a somewhat smaller time constant. The specular reflection of pickup protons results in an increase of the shock potential some distance ahead of the shock foot and ramp. The minimum scale of the cross shock potential during reformation is about 7 electron inertial length λe. We do not find any pickup proton acceleration in the ramp or downstream of the shock beyond the energy which specularly reflected ions gain by the motional electric field of the solar wind during their upstream gyration.

Particle simulation of plasma heating by a large-amplitude shear Alfvén wave through its transverse modulation in collisionless plasmas

We investigate the nonlinear dynamics of a large-amplitude shear Alfvén wave (AW) with circular polarization in collisionless plasmas by using a 2D3V fully relativistic electromagnetic particle-in-cell (PIC) simulation code. We found that when the amplitude, A = δB/B0, of the shear AW is larger than , the shear AW spontaneously becomes unstable for the modified two-stream instability (MTSI), resulting in the excitation of small-scale quasi-electrostatic waves with electric fields parallel to a uniform magnetic field. We found that the electrons are heated mostly in the direction parallel to the magnetic field due to the quasi-electrostatic lower hybrid waves by the MTSI. Subsequently, the shear AW becomes unstable with strong transverse modulation, resulting in the excitation of ion acoustic waves that can heat ions. About 70% of the AW energy can be converted to plasma heating of both electrons and ions. The plasma heating time is within about 250ωci−1, which is shorter than the collision time between protons and neutral hydrogens in the upper chromosphere. The obtained results could be very important for plasma heating of coronal loops in the upper chromosphere.

Influence of κ-distributed ions on the two-stream instability

This paper is the first approach for analyzing the influence of κ-distributed particles on the modified two-stream instability (MTSI). It is assumed that the plasma consists of a magnetized Maxwellian electron contribution and unmagnetized κ-distributed ions drifting across the electrons. Within an electrostatic approximation, the influence of the κ parameter on the maximum growth rate of the MTSI is evaluated for the special case of parallel drift velocity and wave propagation.

Wave activity above the ionosphere of Titan: Predictions for the Cassini mission

In this paper we present a study of the beam‐driven wave generation mechanisms in linear approximation which are viable in the flowside plasma mantle of Saturn's moon, Titan. The flowside plasma mantle is defined, by analogy with the dayside plasma mantle of the planet Venus and Mars, as being the interaction region between the “cold” ionospheric plasma and “hot” streaming plasma of magnetospheric or solar wind origin, with both types of plasma being present in comparable densities. Since no in situ plasma and field measurements are currently available in Titan's flowside mantle, we performed our model calculations in a broad plasma parameter space encompassing the plasma characteristics determined by Voyager 1 in Titan's wake. Two types of beam instability modes were found to be dominant: a fluid‐like (nonresonant) modified two‐stream instability (MTSI) and the kinetic (beam resonant) ion‐ion acoustic instability (IIAI). The two instability modes are characterized by distinct frequency ranges (an order or below the lower hybrid frequency for the MTSI and a few times the lower hybrid frequency for the IIAI) and are found to be dominant in well‐separated spatial regions determined by the presence/absence of cold ionospheric electrons. Giving a global rather than a specific description of the instability types expected to be the most important growing modes within Titan's flowside mantle, we intend to make predictions concerning the wave characteristics of the dominant wave modes measurable by the plasma wave instrument on board the Cassini spacecraft.

Electron dynamics in the current disruption region

Turbulent magnetic field observed at substorm onsets in the near‐Earth magnetotail is often regarded as a manifestation of the disruption of the local tail current. The present study examines the associated dynamics of electrons using data from the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer. Two well‐known events were selected, which took place on 28 August 1986 and 1 June 1985. The results are summarized as follows: (1) during the early period of the 28 August 1986 event, the average perpendicular energy changed very little even though the total magnetic field strength (BT) fluctuated by an order of magnitude; (2) except the period of (1), tends to change in proportion to BT in both events; and (3) and the density N tend to be anticorrelated, whereas such a tendency cannot be found for the parallel average energy. The successive trigger of the Ion Weibel instability (IWI) and the modified two‐stream instability (MTSI) is a possible explanation for (1). As the plasma sheet thins, the IWI may be triggered first, followed by the MTSI, which becomes unstable at higher frequencies than the IWI and energizes electrons. The observed sequence of magnetic turbulence and electron energization in the 28 August event is consistent with this idea. On the other hand, (1) can also be explained as far as magnetic turbulence is localized near the neutral sheet irrespective of its trigger mechanism. In this case electrons stay mostly outside of the turbulent region, and accordingly the variations of the average electron energy do not have to be correlated with the variations of magnetic field in the turbulence region. In contrast, when the source current of the magnetic turbulence is not located closely (compared with its characteristic scale), the resultant magnetic disturbance is more coherent and is distributed widely along the flux tube. In this case the observed magnetic field can represent the magnetic variation that electrons actually undergo, which explains (2). Result (3) indicates that for the full understanding, the electron dynamics need to be addressed in a three‐dimensional configuration. As the present study is based on two events, it remains to be understood how common the observed features are among current disruption events. However, the results of the present study as well as their implications for the magnetic turbulence, such as its confinement near the neutral sheet, provide additional information for further understanding of the current disruption process.

Particle acceleration mechanisms in space plasmas

There are many possible mechanisms for particle acceleration in space plasmas. Among these are two broadly defined types that may be characterised on the one hand by large scale electric field structures and on the other hand by stochastic mechanisms and enhanced wave activity. Double layers (DLs) are an example of the first type. They sustain a net potential difference, across which particles are accelerated. Crucial questions concern the generator maintaining the potential, the rate of energy transfer, equilibrium and matching conditions. Magnetic reconnection at an X-type neutral line is another example and shares many characteristics with DLs, such as the cutting of field lines and constraints set by external MHD motions. Particle acceleration by the growth of the modified two- stream instability (MTSI) is an example of the second type. The MTSI is driven by cross magnetic field ion motion and rapidly accelerates electrons. It has been seen as a link in the critical ionisation velocity (CIV) mechanism, which has been extensively studied both in experiments and theory. Crucial questions concern the evolution of the particle energy distribution, the wave source and the saturation of the driving instability.

Energetic electrons produced by lower hybrid waves in the cometary environment and soft X ray emission: Bremsstrahlung and K shell radiation

Electron acceleration by lower hybrid waves is a phenomenon well known in fusion studies (e.g., the so‐called lower hybrid current drive), and it is also responsible for electron energization in many space environments. In the latter case, lower hybrid wave turbulence is of a self‐generated type. It can be produced by the modified two‐stream instability (MTSI) of the counterstreaming ion populations resulting from the mass‐loading effect, for example, contamination of the solar wind flow or interstellar plasma with the newly born ions. In the cometary case analyzed in this paper these ions are produced by photoionization of the neutral gas outflow evaporated from the cometary nucleus. The interesting feature about lower hybrid oscillations is that they can be in simultaneous Cherenkov resonance with unmagnetized slow ions and fast but magnetized electrons, and owing to this, serve as a powerful tool for energy coupling leading to electron energization. In situ measurements at Comet Halley revealed the existence of intense lower hybrid turbulence inside the cometary bow shock. The quasi‐linear theory of the MTSI evolution constructed in this paper demonstrates a consistency of these wave measurements with the large flux of energetic electrons also measured during the encounter with Comet Halley. Energetic electrons penetrating inside the cometary atmosphere produce soft X ray emission by a combination of bremsstrahlung and line radiation of oxygen atoms. Theoretical results are found to be in good agreement with six independent observations of the X ray cometary emission by the Röntgen satellite and Beppo‐SAX telescopes.

Preliminary nonlocal analysis of cross‐field current instability for substorm expansion onset

The modified‐two‐stream instability (MTSI) is one of the modes of the cross‐field current instability which has recently been considered as one plausible mechanism for substorm expansion onset and intensification. This paper extends the previous analysis of this instability to nonlocal treatment under the simplifying assumptions of electrostatic perturbations and neglect of thermal and kinetic effects. The result enables us to gain new insights on the onset threshold of the instability. We find that a current sheet with a constant velocity associated with the current (exemplified by the Harris equilibrium current sheet) is stable with respect to MTSI, whereas one with a prominent velocity peak at its center is unstable when it is sufficiently thin. This result therefore indicates that the onset threshold of the instability is very sensitive to the global characteristics of the current sheet, and its value can be determined only through nonlocal analysis. The higher onset threshold than that predicted by the local theory allows one to better understand why a substantial cross‐tail current enhancement can develop and a thin current sheet can remain stable for an extended period before the onset of substorm expansion and current disruption.