Intense Electrostatic Waves Research Articles

Wave breaking field of relativistically intense electrostatic waves in electronegative plasma with super-thermal electrons

The wave breaking limit of relativistically intense electrostatic waves in an unmagnetised electronegative plasma, where electrons are alleged to attach onto neutral atoms or molecules and thus forming a significant amount of negative ions, has been studied analytically. A nonlinear theory has been developed, using one-dimensional (1D) relativistic multi-fluid model in order to study the roles of super-thermal electrons, negative ion species and the Lorentz factor, on the dynamics of the wave. A generalised kappa-type distribution function has been chosen for the velocities of the electrons, to couple the densities of the fluids. By assuming the travelling wave solution, the equation of motion for the evolution of the wave in a stationary wave frame has been derived and numerical solutions have been presented. Studies have been further extended, using standard Sagdeev pseudopotential method, to discover the maximum electric field amplitude sustained by these waves. The dependence of wave breaking limit on the different input parameters such as the Lorentz factor, electron temperature, spectral index of the electron velocity distribution and on the fraction and the mass ratio of the negative to positive ion species has been shown explicitly. The wavelength of these waves has been calculated for a wide range of input parameters and its dependence on aforementioned plasma parameters have been studied in detail. These results are relevant to understand particle acceleration and relativistic wave breaking phenomena in high intensity laser plasma experiments and space environments where the secondary ion species and super-thermal electrons exist.

On application of stochastic differential equations for simulation of nonlinear wave–particle resonant interactions

Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: a microphysics of electron resonant scattering by electromagnetic waves and a macrophysics of electron adiabatic heating/transport by mesoscale plasma flows. Examples of such systems are Earth's radiation belts and Earth's bow shock, where ion-scale plasma injections and cross-shock electric fields determine a general electron energization, whereas electron scattering by waves relaxes anisotropy of electron distributions and produces small populations of high-energy electrons. The application of stochastic differential equations is a promising approach for including effects of resonant wave–particle interaction into codes tracing electrons in models of large-scale electromagnetic fields. This study proposes and verifies such equations for the system with non-diffusive wave–particle interactions, i.e., the system with nonlinear effects of phase trapping and bunching. We consider electron resonances with intense electrostatic whistler-mode waves often observed in the Earth's radiation belts. We demonstrate that nonlinear resonant effects can be described by stochastic differential equations with the non-Gaussian probability distribution of random variations of electron energies.

Solitary Waves Across Supercritical Quasi‐Perpendicular Shocks

AbstractWe consider intense electrostatic solitary waves (ESW) observed in a supercritical quasi‐perpendicular Earth's bow shock crossing by the Magnetospheric Multiscale Mission. The ESW have spatial scales of a few tens of meters (a few Debye lengths) and propagate oblique to a local quasi‐static magnetic field with velocities from a few tens to a few hundred kilometers per second in the spacecraft frame. Because the ESW spatial scales are comparable to the separation between voltage‐sensitive probes, correction factors are used to compute the ESW electric fields. The ESW have electric fields with amplitudes exceeding 600 mV/m (oriented oblique to the local magnetic field) and negative electrostatic potentials with amplitudes of a few tenths of the electron temperature. The negative electrostatic potentials indicate that the ESW are not electron phase space holes, while interpretation in terms of ions phase space holes is also questionable. Whatever is their nature, we show that due to the oblique electric field orientation the ESW are capable of efficient pitch‐angle scattering and isotropization of thermal electrons. Due to the negative electrostatic potentials the ESW Fermi reflects a significant fraction of the thermal electrons streaming from upstream (downstream) back to upstream (downstream) region, thereby affecting the shock dynamics. The role of the ESW in electron heating is discussed.

Magnetospheric Multiscale Observations of an Ion Diffusion Region With Large Guide Field at the Magnetopause: Current System, Electron Heating, and Plasma Waves

AbstractWe report Magnetospheric Multiscale (MMS) observations of a reconnecting current sheet in the presence of a weak density asymmetry with large guide field at the dayside magnetopause. An ion diffusion region (IDR) was detected associated with this current sheet. Parallel current dominated over the perpendicular current in the IDR, as found in previous studies of component reconnection. Electrons were preferentially heated parallel to the magnetic field within the IDR. The heating was manifested as a flattop distribution below 400 eV. Two types of electromagnetic electron whistler waves were observed within the regions where electrons were heated. One type of whistler wave was associated with nonlinear structures in E|| with amplitudes up to 20 mV/m. The other type was not associated with any structures in E||. Poynting fluxes of these two types of whistler waves were directed away from the X‐line. We suggest that the nonlinear evolution of the oblique whistler waves gave rise to the solitary structures in E||. There was a perpendicular super‐Alfvénic outflow jet that was carried by magnetized electrons. Intense electrostatic lower hybrid drift waves were localized in the current sheet center and were probably driven by the super‐Alfvénic electron jet, the velocity of which was approximately equal to the diamagnetic drift of demagnetized ions. Our observations suggest that the guide field significantly modified the structures (Hall electromagnetic fields and current system) and wave properties in the IDR.

Intense Harmonic Emissions Observed in Saturn's Ionosphere

AbstractThe Cassini spacecraft's first Grand Finale orbit was carried out in April 2017. This set of 22 orbits had an inclination of 63° with a periapsis grazing Saturn's ionosphere, thus providing unprecedented coverage and proximity to the planet. Cassini's Radio and Plasma Wave Science instrument repeatedly detected intense electrostatic waves and their harmonics near closest approach in the dayside equatorial topside ionosphere. The fundamental modes were found to both scale and trend best with the H+ plasma or lower hybrid frequencies, depending on the plasma composition considered. The fine‐structured harmonics are unlike previous observations, which scale with cyclotron frequencies. We explore their generation mechanism and show strong evidence of their association with whistler mode waves, consistent with theory. The possibility of Cassini's presence in the ionosphere influencing the resonance and harmonics is discussed. Given their link to the lower hybrid frequency, these emissions may offer clues to constraining Saturn's ionospheric properties.

The Lunar Radar Sounder (LRS) Onboard the KAGUYA (SELENE) Spacecraft

The Lunar Radar Sounder (LRS) onboard the KAGUYA (SELENE) spacecraft has successfully performed radar sounder observations of the lunar subsurface structures and passive observations of natural radio and plasma waves from the lunar orbit. After the transfer of the spacecraft into the final lunar orbit and antenna deployment, the operation of LRS started on October 29, 2007. Through the operation until June 10, 2009, 2363 hours worth of radar sounder data and 8961 hours worth of natural radio and plasma wave data have been obtained. It was revealed through radar sounder observations that there are distinct reflectors at a depth of several hundred meters in the nearside maria, which are inferred to be buried regolith layers covered by a basalt layer with a thickness of several hundred meters. Radar sounder data were obtained not only in the nearside maria but also in other regions such as the farside highland region and polar region. LRS also performed passive observations of natural plasma waves associated with interaction processes between the solar wind plasma and the moon, and the natural waves from the Earth, the sun, and Jupiter. Natural radio waves such as auroral kilometric radiation (AKR) with interference patterns caused by the lunar surface reflections, and Jovian hectometric (HOM) emissions were detected. Intense electrostatic plasma waves around 20 kHz were almost always observed at local electron plasma frequency in the solar wind, and the electron density profile, including the lunar wake boundary, was derived along the spacecraft trajectory. Broadband noises below several kHz were frequently observed in the dayside and wake boundary of the moon and it was found that a portion of them consist of bipolar pulses. The datasets obtained by LRS will make contributions for studies on the lunar geology and physical processes of natural radio and plasma wave generation and propagation.

Medium‐latitude sources of plasmaspheric nonthermal continuum radiations observed close to harmonics of the electron gyrofrequency

Nonthermal continuum (NTC) radiation is, with auroral kilometric radiation (AKR), one of the two electromagnetic emissions generated within the Earth's magnetosphere and radiated into space. It is generally believed that NTC is emitted in the plasmapause density gradient after conversion of intense electrostatic waves, present near the magnetic equator, into electromagnetic waves. In this paper, we present a specific type of NTC event, of infrequent occurrence, displaying a finger‐like pattern not yet reported: banded emissions peaking at exact multiples of a common frequency, df, which decrease inbound toward the plasmapause boundary layer (PPBL). Analysis is presented that indicates that the corresponding sources are nearby sites of the PPBL where the local electron gyrofrequency fce equals df. The sources are radiating beams of limited cone angle size. The NTC sources for this event are shown to be located at about 20° magnetic latitude. This illustrates that the PPBL is active in radiating NTC waves not only near the magnetic equator but also up to the medium‐latitude range.

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.

Electron acceleration to energies beyond GeV by a relativistic ion beam instability

Synchrotron emission suggests the presence of TeV electrons at various astrophysical objects. We propose a mechanism for the acceleration of electrons to ultrahigh energies (UHE) by intense electrostatic waves (ESWs). The latter are driven by dense proton beams that move at relativistic speeds relative to a background plasma and the electrons are accelerated by their nonlinear interaction with the ESWs. We follow the evolution of the wave instability by means of particle-in-cell (PIC) simulations. After the instability has saturated, we obtain spatially confined electron voids in which secondary instabilities develop due to resonant interactions between the beams and the background protons, generating intense ESWs which accelerate electrons to ultrarelativistic speeds within times of a few hundred inverse plasma frequencies.

Double layers in the downward current region of the aurora

Abstract. Direct observations of magnetic-field-aligned (parallel) electric fields in the downward current region of the aurora provide decisive evidence of naturally occurring double layers. We report measurements of parallel electric fields, electron fluxes and ion fluxes related to double layers that are responsible for particle acceleration. The observations suggest that parallel electric fields organize into a structure of three distinct, narrowly-confined regions along the magnetic field (B). In the "ramp" region, the measured parallel electric field forms a nearly-monotonic potential ramp that is localized to ~ 10 Debye lengths along B. The ramp is moving parallel to B at the ion acoustic speed (vs) and in the same direction as the accelerated electrons. On the high-potential side of the ramp, in the "beam" region, an unstable electron beam is seen for roughly another 10 Debye lengths along B. The electron beam is rapidly stabilized by intense electrostatic waves and nonlinear structures interpreted as electron phase-space holes. The "wave" region is physically separated from the ramp by the beam region. Numerical simulations reproduce a similar ramp structure, beam region, electrostatic turbulence region and plasma characteristics as seen in the observations. These results suggest that large double layers can account for the parallel electric field in the downward current region and that intense electrostatic turbulence rapidly stabilizes the accelerated electron distributions. These results also demonstrate that parallel electric fields are directly associated with the generation of large-amplitude electron phase-space holes and plasma waves.

Ion outflow and associated perpendicular heating in the cusp observed by Interball Auroral Probe and Fast Auroral Snapshot

The spatial properties of ionospheric ion outflows associated with perpendicular heating processes in the cusp are studied using a conjunction study from two satellites and ground radar systems. Low‐energy outflowing ions are measured in a wide longitudinal range, between 13,000 and 19,000 km in altitude, over the dayside polar cap by the Hyperboloid experiment aboard the Interball Auroral Probe (AP). These observations are related to conjugate convection field measurements by the Saskatoon‐Kapuskasing pair of the Super Dual Auroral Radar Network (SuperDARN). Data analysis suggests that outflowing ions originate from a wide magnetic local time range associated with both the dayside cusp region and the dayside cleft region. A direct cusp crossing by the Fast Auroral Snapshot (FAST) satellite at 2000‐km altitude shows a correlation between transverse ion heating in a thin latitudinal region (∼1.3°) and the presence of broadband extremely low frequency (BBELF) turbulence, in addition to more intense electrostatic waves near and just above the lower hybrid (LH) frequency. This event is unusual because on the basis of the statistical survey of Freja and FAST data, most of the ion‐heating events in the midaltitude auroral zone are correlated with enhanced emissions in the BBELF range. Furthermore, the electron population has energies that are too small to drive LH waves unstable. This event offers the opportunity to analyze the contribution of cusp magnetospheric ion injections to the heating of the ambient H+ and O+ ions. Kinetic instability calculations demonstrate that LH waves are destabilized by the ring distributions, which result from injections of high‐energy magnetosheath ions. Calculations show that a preheating mechanism by BBELF turbulence near the ion gyrofrequencies is also required so that LH heating is able to occur. The altitude dependence of the LH perpendicular heating is then analyzed by modeling the transport of the injected magnetospheric ions along magnetic field lines. It is shown that LH heating acts as an additional process from ∼2000 up to 10,000 km in altitude. In addition, trajectory calculations show that the low‐energy outflowing H+ and O+ ions observed along Interball AP orbit in the polar cap are heated inside the cusp at altitudes extending up to 15,000 km. These results are then assembled to construct a possible heating scenario inside the cusp for this data set. The contribution of the different energization mechanisms to the ion heating as a function of altitude is then discussed.

Acceleration of ionospheric O+ ions on open field lines in the low‐latitude boundary layer and the cusp region.

A common observation made by the toroidal imaging mass‐angle spectrograph on the polar orbiting Polar Spacecraft is the acceleration of ionospheric O+ and H+ to similar velocities on open field lines in the low‐latitude boundary layer (LLBL) and cusp regions. A detailed study of nine events made in the midaltitude cusp region is presented here and the acceleration can be split into two regions. On open field lines in the LLBL both H+ and O+ undergo rapid upward acceleration within approximately 0.75° invariant latitude. The acceleration aH+/ao+ ≈ 2 is inconsistent with the proposed electrostatic acceleration. Intense electrostatic waves often associated with the acceleration is consistent with energy transfer from the faster H+ to the slower O+ population via two‐stream instabilities. In the cusp region injected magnetosheath plasma is a possible free energy source for the acceleration of ionospheric ion populations: The component temperature ratio T‖/T⊥. of the upgoing, mirrored injected magnetosheath ions is generally lower than the downgoing ions consistent with a two‐stream instability driven energy transfer from the magnetosheath to the ionospheric ion populations.

Direct observation of localized parallel electric fields in a space plasma.

We report direct measurements of parallel electric fields related to particle acceleration in a collisionless space plasma. The electric field is that of a monotonic potential ramp localized to approximately 10 debye lengths along the magnetic field. Electrons accelerated by the parallel electric field are accompanied by intense electrostatic waves and nonlinear structures interpreted as electron phase-space holes.

Simulation and non-linear stage of the electrostatic waves observed during the AMPTE lithium release in the solar wind

During the AMPTE lithium releases in the solar wind intense electrostatic waves with frequencies between a few tens of Hz to several kHz were observed outside the diamagnetic cavity. The results of linear Vlasov theory have suggested that these waves may be generated through two types of instabilities. One is the ion-ion instability associated with the relative drift between the lithium ions and the solar wind protons, and the other is the ion-acoustic instability due to the relative drift between the electrons and the ions. In order to look at the non-linear behavior of the wave-particle interactions, and discern the effect of waves on the particles, full particle electrostatic simulations have been performed, and the results are presented here. It is shown that the ion-ion instability whose phase velocity is oblique to the solar wind velocity can cause considerable anisotropic “heating” of both the lithium ions and the solar wind protons.

Electric field and plasma density measurements in the strongly driven daytime equatorial electrojet: 1. The unstable layer and gradient drift waves

Electric field and plasma density instrumentation on board a sounding rocket launched from Punta Lobos, Peru, detected intense electrostatic waves indicative of plasma instabilities in the daytime equatorial electrojet. Simultaneous measurements taken by the Jicamarca radar showed strong 3‐m type 1 electrojet echoes as well as evidence of kilometer scale horizontally propagating waves. The in situ electric field wave spectra displayed three markedly different height regions within the unstable layer: (1) a two‐stream region on the topside between 103 and 111 km where the electron current was considered to be strongest, (2) a gradient drift region between 90 and 106.5 km where the upward directed, zero‐order electron density gradient was unstable, and (3) an “interaction” region between 103 and 106.5 km where both of these instabilities were linearly unstable. The unstable altitudes and differentiation showed good agreement with the simultaneous 3‐m Jicamarca backscatter radar observations. In the region where the density gradient was unstable, large‐amplitude waves with large scale sizes (wavelengths of roughly 1–2 km) were observed. These kilometer scale waves dominated the observed in situ spectrum despite the fact that the peak in the linear gradient drift growth rate occurred at wavelengths of only a few hundred meters. Comparisons of the measured δE and δn/n components of the large‐scale waves verify the basic process inherent to the gradient drift instability: density enhancements were observed coincident with westward electric fields, and density depletions were associated with eastward fields. The amplitudes (10–15 mV/m) of these horizontal waves were strong enough to drive vertical two‐stream secondary waves. In the region where these waves existed and the electrojet current was strongest, evidence of wave steepening was seen, and the resulting waveforms of the large structures displayed a “flat‐topped” nature. In the lower region of the electrojet the irregularity power occurred over a broad range of wavelengths, estimated to be in the range of tens of meters to kilometers, and fell off rapidly for the shorter wavelengths. Throughout the gradient drift region, shorter‐scale waves often occurred in bursts which appeared controlled by the larger electric field structures.

A magnetospheric critical velocity experiment: Particle results

In March of 1983, a barium injection sounding rocket experiment (the Star of Lima) was conducted to investigate Alfvén's critical ionization velocity (CIV) hypothesis in space. Included in the instrumented payload was a University of California, San Diego (UCSD), particle detection experiment consisting of five retarding potential analyzers. Despite conditions that appeared to be optimal for the critical velocity effect, the particle data, in agreement with optical observations, indicate that a fractional ionization of only ˜5×10−4 was observed, indicating that the conditions required for the effect to occur are still not well understood. However many of the required phenomena associated with the CIV effect were observed; in particular a superthermal electron population was formed at the expense of ion drift kinetic energy in the presence of intense electrostatic waves near the lower hybrid frequency. The amount of ionization produced is plausibly consistent with the observed electron flux, but could also be accounted for by residual solar UV at the injection point. It is shown based on the UCSD data set that one obvious explanation for the low ionization efficiency, namely that the ionizing superthermal electrons may rapidly escape along field lines, can be ruled out.

The generation of electrostatic noise in the plasma sheet boundary layer

The one and two ion beam instability is considered as a possible explanation for the observations of broadband electrostatic noise in the plasma sheet region of the geomagnetic tail. When only hot streaming plasma sheet boundary layer ions are present, no broadband waves are excited. Cold, streaming ionospheric ions can generate electrostatic broadband waves propagating in the slow beam acoustic mode, but the growth rates of the waves are significantly enhanced when hot boundary layer ions are present. (Both the slow and fast beam acoustic modes can be excited, depending on the relative ion drift.) This model predicts that the wave intensity of the broad band noise should peak in the plasma sheet boundary layer. Observations of less intense electrostatic waves in the lobes and plasma sheet are likely a result of the absence of hot ion beams or large ion temperatures, respectively, which result in smaller growth rates. The ion beam instability may play an important role in the formation of the central plasma sheet.

The effects of density gradients on the convective amplification of upper hybrid waves in the magnetosphere

Intense (⩾ 10 mV m −1) electrostatic plasma waves near the upper hybrid frequency have been observed between ± 50° magnetic latitude during spacecraft plasmapause crossings. We present wave growth rate and three-dimensional convective amplification calculations which suggest how intense upper hybrid (IUH) events can occur over such a wide range of latitudes. The effects of wave refraction are shown to be crucial to the proper calculation of convective amplification. We first calculate upper hybrid wave growth for an IUH event at 10° MLAT during which a complete electron distribution function with a loss cone feature was measured simultaneously with the waves. We show that a parallel density gradient may be necessary to account for the observed amplification. Without such a density gradient, the dipole magnetic field gradient would quickly refract the wave vector component parallel to the local field lines out of the unstable region in wave vector space. Upon mapping the distribution function observed at 10° MLAT to other latitudes by conserving the electrons' magnetic moments, we then find that the mapped distribution could produce large amplification at higher latitudes only if there is an appropriate parallel density gradient. At the equator, the long magnetic field gradient scale length enables large amplitudes to be attained without a density gradient. The results of our UH ray tracing analysis are related to theories and observations of magnetospheric continuum radiation.

Beam‐driven electron acoustic waves upstream of the Earth's bow shock

Intense electrostatic waves of short wavelength are frequently observed upstream of the earth's bow shock. These waves are very impulsive, and their peak amplitudes correlate strongly with the temporal flux profiles of simultaneously observed energetic ions and electrons which are reflected from the shock. Our paper suggests an explanation of this broadband electrostatic noise in terms of electron acoustic waves driven unstable by the ion and/or electron beams. These waves do not exist in thermodynamic equilibrium plasma and therefore require nonthermal distributions for their occurrence. A simple model is developed for finite temperature beam and background particles with Maxwellian or Lorentzian distributions. The beam‐associated instability can be classified as being due to Landau resonance or negative wave energy. Depending on the plasma parameters the mode discussed here naturally extends and links to the ion acoustic wave or electron plasma oscillation. A numerical parameter study is provided for various beam plasma situations. The frequency theoretically obtained ranges between the ion and the electron plasma frequency, and the wavelength amounts to several Debye lengths for maximum growth. Since the beam mode has a linear dispersion relation, the Doppler‐shifted frequency in the spacecraft frame should depend linearly on the beam velocity and on the wave vector as well. It is anticipated that these characteristics may allow parts of the observed broadband high‐frequency noise to be identified as beam‐driven electron acoustic waves.

Electric field and plasma density measurements in the auroral electrojet

Intense electrostatic waves in the auroral E region have been detected simultaneously on two payloads launched in a mother‐daughter configuration from Kiruna, Sweden. The data sets comprise electric field and density measurements from the ambient (dc) conditions to fluctuations as high as 50 kHz. The dc electric field measured by both payloads was 54 mV/m northwest, which corresponded to an electron drift velocity of 1080 m/s. This electric field drove two‐stream waves perpendicular to both B and E observed by both spacecraft throughout an altitude region which agrees quite well with the range predicted by linear two‐stream theory. The power in the waves depended on the electron density gradient, diminishing near 107 km where the gradient changed direction for a few kilometers. This observation is consistent with a gradient drift wave contribution to the instability process, since the auroral zone geometry does permit a component of the electric field perpendicular to B to be parallel to the vertical electron density gradient. Electric field spectra corroborate these results, as a strong component was detected at longer wavelengths (several hundred meters), the spectral regime associated with this instability. The spectra measured on both payloads also reveal an enhanced nearly coherent wave of a few meters wavelength at the topside of the layer (120 km), which also appears as electrostatic and parallel to the current. This spectral feature may be the consequence of a narrow range of wavelengths excited near the two‐stream instability threshold. Descending through the layer, the fluctuations fill out to a broadband, turbulent spectrum, extending to scale sizes down to the order of centimeters. Long wavelength waves form the strongest spectral component below 105 km. Power observed perpendicular to the direction of the current may indicate the presence of secondary plasma waves.