Electrostatic Lower Hybrid Waves Research Articles

Excitation of electrostatic lower hybrid wave by nonlinear interaction of hermite cosh-gaussian and cosh-gaussian laser beams in collisional plasma embedded with static magnetic field

Excitation of electrostatic lower hybrid wave by nonlinear interaction of hermite cosh-gaussian and cosh-gaussian laser beams in collisional plasma embedded with static magnetic field

Development of the ambipolar electric field in a compressed current sheet and the impact on magnetic reconnection

Satellite data analysis of a compressed gyro-scale current sheet prior to magnetic reconnection in the magnetotail shows that electrostatic lower hybrid waves localized to the region of a transverse ambipolar electric field at the centre of the current sheet are driven by $\boldsymbol{E} \times \boldsymbol{B}$ velocity shear and result from compression. The presence and location of shear-driven waves around the centre of the current sheet, where the magnetic field reverses and the density gradient is minimal, is consistent with our model. This is notable because the free energy source is the curvature of the electron $\boldsymbol{E} \times \boldsymbol{B}$ flow and not the density gradient. Laboratory experiments and particle-in-cell (PIC) simulations have shown that shear-driven lower hybrid fluctuations are capable of producing anomalous cross-field transport (viscosity) and resistivity, which can trigger magnetic reconnection. We estimate the terms in the generalized Ohm's Law directly from MMS data as the spacecraft cross a gyro-scale current sheet. Our analysis shows that the wave effects (resistivity, diffusion and viscosity) and pressure anisotropy effects are comparable. We also find that the quasi-static electric field gradient is correlated with a non-gyrotropic electron distribution function, which is consistent with our model. Furthermore, theoretical arguments suggest agyrotropy is an indicator of the possibility for magnetic reconnection to occur.

Observations of plasma waves generated by charged space objects

A sampling of the environment around inert space objects has determined, which linear and nonlinear waves are created by moving space debris of all sizes. Plasma waves excited by satellites and space debris moving through the Earth's plasma in low earth orbit have been measured with in situ electric field sensors on other satellites. These orbit driven plasma waves are of interest for proximity detection of space debris and sources of electrostatic and electromagnetic noise on spacecraft. Satellites and other space objects moving through the near-earth ionosphere between 200 and 1000 km altitude become electrically charged by both electron collection and photo emission in sunlight. These hypersonic, charged objects can excite a wide range of plasma waves. Measurements with the Radio Receiver Instrument (RRI) on the Swarm-E satellite have shown that electromagnetic plasma waves from known objects can be observed out to ranges of tens of kilometers. The amplitude, spectral, and polarization changes of the RRI data are consistent with electromagnetic, compressional Alfvén waves launched by charged space objects traveling across magnetic field lines. In addition, electrostatic lower hybrid waves or nonlinear ion acoustic pinned oscillations may have been self-generated and measured on the Swarm-E satellite. It is proposed that measurements of these waves with local electric field measurements or remote electromagnetic wave scatter may be useful to design systems for the location of orbiting objects. Spatial and temporal details of spacecraft charging are key to understanding the extent of waves associated with the object motion in space plasmas.

Electrostatic lower hybrid turbulence due to magnetic islands and particle heating in magnetopause reconnection regions

This investigation presents a model to understand the magnetopause turbulence in the lower hybrid frequency range at reconnection regions as observed by the magnetospheric multiscale mission. We have modeled 3D electrostatic lower hybrid wave (LHW) in cold magnetized plasma in the presence of magnetic islands. In this model, we have developed the modified nonlinear Schrödinger equation, contemplating that nonlinear effects are due to ponderomotive force. The dynamical equation of the system thus obtained is solved using numerical simulation techniques. The simulation results illustrate the formation and evolution of localized structures and the current sheets. Due to the nonlinear effects and magnetic reconnection, the current sheets become turbulent with time. A semi-analytical model is also given to illustrate the scale size of current sheets. The turbulent power spectra have also been studied. The spectral index of the power spectrum is found to be −2.7 (approximately) in the perpendicular direction and −2.2 (approximately) in the parallel direction, indicating anisotropy. Using the Folker–Plank diffusion equation with the new velocity space diffusion coefficient, we find the distribution function of energetic electrons due to these turbulent structures. We propose that LHW may be responsible for plasma heating in magnetopause.

Dust density effects on electron density gradient driven lower hybrid waves in magnetized plasma

AbstractElectrostatic lower hybrid waves propagating transverse to the external magnetic field in magnetized dusty plasma are investigated, using the fluid equations and also including the effect of density gradient in plasma. Lower hybrid modes are considered important in laboratory, astrophysical as well as space plasmas in interpreting low frequency noises. Unlike other electrostatic waves, lower hybrid waves can resonantly interact with electrons as well as ions in plasma. The dust and gradient terms lead to novel growth of these waves in dusty plasma. A theoretical model is developed to investigate density gradient effects on lower hybrid waves in plasma comprised of electrons, ions and dust particles. The dependence of plasma components' density, strength of magnetic field, temperature and charge of electrons, ions and dust grains on the frequency and growth rate of electrostatic lower hybrid waves has been investigated and presented graphically. It has been observed that the number density of each plasma components directly affects the growth rate. The electrostatic waves are found to grow along the positive electron gradient and the dust effect depends on the gradient length chosen. Above a certain threshold value of gradient length, the waves are found to stabilize. A correlation of the obtained theoretical results with the experimental observations is also discussed.

Early Time Evolution of Turbulence in the Space Environment by Neutral Beam Injection

AbstractThe Space Measurement of A Rocket‐released Turbulence mission will demonstrate the production and evolution of turbulence in the space environment via a cascade of plasma physics processes. A sounding rocket will inject neutral barium atoms into the upper ionosphere at high speed across the magnetic field. The barium atoms photoionize, and the magnetic field confines them, leading to an ion ring distribution in velocity space that is unstable to electrostatic lower hybrid waves. Nonlinear induced scattering of lower hybrid waves produces electromagnetic magnetosonic and whistler waves that rapidly escape the source region and propagate into the radiation belts. In this paper, we present models and simulations of early time parts of this cascade until the lower hybrid waves are generated. We study the neutral atom injection, expansion, and ionization analytically and computationally. In a realistic scenario, the velocity distribution function is found to be nongyrotropic instead of a perfect ring in the plane perpendicular to the magnetic field. Using these results, we examine a representative region of the barium cloud and perform particle‐in‐cell simulations of the excitation of the lower hybrid waves. Of particular interest is the energy extracted from the kinetic energy of the barium ions, as this will ultimately affect the amplitude of the electromagnetic waves in the radiation belts. We find that for velocity distribution functions that deviate from an ideal ring distribution, the energy extracted from the fast barium ions increases.

Electrostatic and electromagnetic fluctuations detected inside magnetic flux ropes during magnetic reconnection

AbstractA series of magnetic flux ropes embedded in the ion diffusion region of a magnetotail magnetic reconnection event were investigated in this paper. Waves near the lower hybrid frequency were measured within each of the flux ropes and can be associated with the enhancements of energetic electrons in some of the flux ropes. The waves in the largest flux ropes were further explored in more detail. The electrostatic lower hybrid frequency range waves are detected at the edge, while electromagnetic lower hybrid frequency range waves are observed at the center of the flux rope. The electromagnetic waves are right‐hand polarized and propagated nearly perpendicular to magnetic field lines, with a wavelength of ion‐electron hybrid scale. The observations are analogous to simulations in which the electrostatic lower hybrid waves are confined to the edge of current sheet but can directly penetrate into the current sheet center in the form of the electromagnetic mode. The observations indicate that the electromagnetic lower hybrid frequency range waves can be excited inside magnetic flux ropes.

Evolution of lower hybrid turbulence in the ionosphere

Three-dimensional evolution of the lower hybrid turbulence driven by a spatially localized ion ring beam perpendicular to the ambient magnetic field in space plasmas is analyzed. It is shown that the quasi-linear saturation model breaks down when the nonlinear rate of scattering by thermal electron is larger than linear damping rates, which can occur even for low wave amplitudes. The evolution is found to be essentially a three-dimensional phenomenon, which cannot be accurately explained by two-dimensional simulations. An important feature missed in previous studies of this phenomenon is the nonlinear conversion of electrostatic lower hybrid waves into electromagnetic whistler and magnetosonic waves and the consequent energy loss due to radiation from the source region. This can result in unique low-amplitude saturation with extended saturation time. It is shown that when the nonlinear effects are considered the net energy that can be permanently extracted from the ring beam is larger. The results are applied to anticipate the outcome of a planned experiment that will seed lower hybrid turbulence in the ionosphere and monitor its evolution.

Density gradient effects on transverse shear driven lower hybrid waves

Shear driven instabilities are commonly observed in the near-Earth space, particularly in boundary layer plasmas. When the shear scale length (LE) is much less than the ion gyro-radius (ρi) but greater than the electron gyro-radius (ρe), the electrons are magnetized in the shear layer, but the ions are effectively un-magnetized. The resulting shear driven instability, the electron-ion hybrid (EIH) instability, is investigated in a new interpenetrating plasma configuration in the Auburn Linear EXperiment for Instability Studies. In order to understand the dynamics of magnetospheric boundary layers, the EIH instability is studied in the presence of a density gradient located at the boundary layer between two plasmas. This paper reports on a recent experiment in which electrostatic lower hybrid waves are identified as the EIH instability, and the effect of a density gradient on the instability properties are investigated.

Effects of neutral interactions on velocity-shear-driven plasma waves

In a laboratory experiment, we demonstrate the substantial effects that collisions between charged and neutral particles have on low-frequency (Ωi ≪ ω ≪ Ωe) shear-driven electrostatic lower hybrid waves in a plasma. We establish a strong (up to 2.5 kV/m) highly localized electric field with a length scale shorter than the ion gyroradius, so that the ions in the plasma, unlike the electrons, do not develop the full E × B drift velocity. The resulting shear in the particle velocities initiates the electron-ion hybrid (EIH) instability, and we observe the formation of strong waves in the vicinity of the shear with variations in plasma densities of 10% or greater. Our experimental configuration allows us to vary the neutral background density by more than a factor of two while holding the charged particle density effectively constant. Not surprisingly, increasing the neutral density decreases the growth rate/saturation amplitude of the waves and increases the threshold electric field necessary for wave formation, but the presence of neutrals affects the dominant wave frequency as well. We show that a 50% increase in the neutral density decreases the wave frequency by 20% while also suppressing the electric field dependence of the frequency that is observed when fewer neutrals are present. The majority of these effects, as well as the values of the frequencies we observe, closely match the predictions of previously developed linear EIH instability theory, for which we present the results of a numerical solution.

Electron beam driven lower hybrid waves in a dusty plasma

An electron beam propagating through a magnetized dusty plasma drives electrostatic lower hybrid waves to instability via Cerenkov interaction. A dispersion relation and the growth rate of the instability for this process have been derived taking into account the dust charge fluctuations. The frequency and the growth rate of the unstable wave increase with the relative density of negatively charged dust grains. Moreover, the growth rate of the instability increases with beam density and scales as the one-third power of the beam density. In addition, the dependence of the growth rate on the beam velocity is also discussed.

Excitation of lower hybrid waves by a gyrating ion beam in a negative ion plasma

A gyrating ion beam propagating through a magnetized plasma cylinder containing K+ positive ions, electrons, and SF6− negative ions drives electrostatic lower hybrid waves to instability via Cyclotron interaction. Numerical calculations of the unstable mode frequencies and growth rates of both the unstable positive ion and negative ion modes have been carried out for the existing negative ion plasma parameters. It is found that the unstable mode frequencies of both the modes increase, with the relative density of negative ions. In addition, the growth rates of both the unstable modes also increases with relative density of negative ions. Moreover, the growth rates of both the unstable modes scale as the one-third power of the beam density. The frequencies of both the unstable modes also increase with the magnetic fields. The real part of the unstable wave frequency increases as almost the square root of the beam energy.

Excitation of lower hybrid waves by a spiraling ion beam in a magnetized dusty plasma cylinder

A spiraling ion beam propagating through a magnetized dusty plasma cylinder drives electrostatic lower hybrid waves to instability via cyclotron interaction. Numerical calculations of the growth rate and unstable mode frequencies have been carried out for the Princeton Q-1 device using the experimental dusty plasma parameters [e.g., Barkan et al., Planet. Space Sci. 43, 905 (1995)]. It is found that as the density ratio δ(=nio∕neo, where ni0 is the ion plasma density and ne0 is the electron density) of negatively charged dust grains to electrons increases, the unstable mode frequency of the lower hybrid waves increases. In addition, the growth rate of the instability also increases with the density ratio δ. In other words, the presence of negatively charged dust grains can further destabilize the lower hybrid wave instability. The growth rate has the largest value for the modes where Jl(pnro) is maximum [here pn=xn∕r0, where pn is the perpendicular wave number in cm−1, r0 is the plasma radius, and xn are the zeros of the Bessel function J1(x)] i.e., whose eigenfunctions peak at the location of the beam. The growth rate scales as one third power of the beam current.

Images of electrostatic lower-hybrid-wave beam propagation in tokamak plasmas using a paraxial WKB approach

A multidimensional paraxial Wentzel-Kramers-Brillouin approach is used to yield the distribution of wave potential for electrostatic lower-hybrid wave propagation in tokamak plasmas under current-drive conditions. This so-called beam tracing allows a more detailed description of wave properties than standard ray tracing. Namely, it accounts for diffraction effects, hence energy flow, in the direction perpendicular to the group velocity.

Erratum: “A theoretical analysis on electrostatic lower-hybrid wave propagation in plasmas with magnetic ripple: Nonlinear oscillations, resonances, ray tracing, and spectral gap” [Phys. Plasmas 6, 1131 (1999)

Erratum: “A theoretical analysis on electrostatic lower-hybrid wave propagation in plasmas with magnetic ripple: Nonlinear oscillations, resonances, ray tracing, and spectral gap” [Phys. Plasmas <b>6</b>, 1131 (1999)

Spiral electron beam interaction with whistler waves at cyclotron resonances

The interaction of a radially bounded electron beam spiraling in a magnetoplasma with a quasi-monochromatic whistler at the Cherenkov and Doppler-shifted resonance conditions is investigated. For the linear stage of the interaction, the instability growth rate as well as the radial flux of wave energy emitted by the thin spiral beam are calculated. Compared to previous works considering a cylindrical beam or electrostatic lower hybrid waves, the present study gives the possibility to extend the investigation of the whistler-beam interaction to wider ranges of physical parameters, and, in particular, to situations where the beam is injected obliquely with respect to the ambient magnetic field. The main physical process occurring during the dissipative beam-wave interaction—that is, which takes into account the energy leakage out of the bounded beam volume—is the nonlinear self-organization of part of the beam electrons which leads to the formation of dynamically stable bunches that are continuously decelerated or accelerated while keeping resonance with the emitted wave. In a long time evolution, bunches are the main cause which supports the wave emission whereas the nonresonant beam electrons practically do not exchange energy with the wave. It is shown that the efficiency of the electromagnetic wave emission by a thin spiral beam is less at the cyclotron resonances than at the Cherenkov resonance.

Resistive instabilities in Hall current plasma discharge

Plasma perturbations in the acceleration channel of a Hall thruster are found to be unstable in the presence of collisions. Both electrostatic lower-hybrid waves and electromagnetic Alfvén waves transverse to the applied electric and magnetic field are found to be unstable due to collisions in the E×B electron flow. These results are obtained assuming a two-fluid hydrodynamic model in slab geometry. The characterisitic frequencies of these modes are consistent with experimental observations in Hall current plasma thrusters.

Lower-Hybrid Instability with Ion Streaming and Dust-Charge Fluctuation in a Dusty Plasma

Using Vlasov-kinetic model, a dispersion relation of the low-frequency and electrostatic lower-hybrid wave is obtained accounting for the streaming of ions and dust charge fluctuations in a finite temperature and collisionless magnetized dusty plasma. It is found that the damping of this mode is the sum of the Landau damping and the charge fluctuation effect. This lower-hybrid mode can be excited when the ion streaming velocity in the direction of the magnetic field exceeds the parallel phase velocity of the mode and when the magnitude of the Landau damping exceeds the magnitude of the damping due to the dust charge fluctuation. Thus, the lower-hybrid-like mode in a dusty plasma will be damped rapidly by the unmagnetized ions compared to that due to the dust charge fluctuation process.

A theoretical analysis on electrostatic lower-hybrid wave propagation in plasmas with magnetic ripple: Nonlinear oscillations, resonances, ray tracing, and spectral gap

The analytical expression for the frequency of the unperturbed radial electrostatic lower-hybrid (LH) ray oscillations is derived, which constitutes the first analytically calculable result in nonlinear LH ray dynamics. For LH current drive (CD) conditions, and after comparing the frequency of the unperturbed LH ray motion with the frequency of the ripple perturbation, it is concluded that the electrostatic LH ray dynamics is generally regular in cylindrical plasmas with magnetic ripple. It is also found analytically that including the magnetic ripple in ray-tracing calculations does not lead to a final closure of the spectral-gap problem for LHCD in circular-poloidal-cross-section tokamaks having sufficiently low electron density, in addition to a high enough aspect ratio and safety factor, in which case electrostatic LH wave propagation turns out to be independent of the latter, and the unperturbed LH ray oscillations become basically linear. This is an important null result that helps to show that the conventional ray-tracing picture widely used in LHCD modeling (that is to say, a standardly coupled LH spectrum propagating according to geometrical optics in an established tokamak equilibrium) is not to be taken as final. The analysis presented, carried out within an explicitly Hamiltonian formalism and addressing the role of resonances between the frequency of the unperturbed LH ray motion and the frequencies of the perturbations due to magnetic ripple and toroidicity, is detailed and careful, with analytical results and conclusions being supported by numerical calculations.

Excitation of lower hybrid waves by a density-modulated electron beam in a plasma cylinder

A density-modulated electron beam propagating through a plasma cylinder drives electrostatic lower hybrid waves to instability via Cerenkov interaction. The lower hybrid wave instability has the largest growth rate γ when the frequency and wave number of the modulation are comparable to that of the unstable wave. The growth rate of the instability increases with the modulation index Δ and is maximized for Δ=1. For Δ=0, γ turns out to be ∼0.43×107 sec−1. The growth rate scales as the one-third power of the beam density. The real frequency of the unstable wave increases as almost the square root of the beam voltage. The results of the theory are applied to explain some of the experimental observations of Chang [Phys. Rev. Lett. 35, 285 (1975)].