Lower Hybrid Solitary Structures Research Articles

Formation of lower-hybrid solitary structures by modulational interaction between lower-hybrid and dispersive Alfvén waves

Abstract. We investigate the possibility that lower-hybrid solitary structures (LHSS), which are frequently observed in the Earth's ionosphere and magnetosphere, are formed as a result of a modulational interaction between lower-hybrid and dispersive Alfvén waves of initially small amplitude. A large amplitude lower-hybrid pump wave can excite density structures with length scales transverse to the geomagnetic field of the order of the ion gyroradius via a modulational instability. The structure formation in the nonlinear stage of the instability is investigated by numerical solutions of the governing equations, using plasma parameters relevant for LHSS observations in the upper ionosphere and in the magnetosphere. The numerical solutions reveal that the lower-hybrid waves become self-localized inside cylindrically symmetric (with respect to the ambient magnetic field) density cavities, in qualitative agreement with observations. Our model includes thermal electron effects but shows no stabilization at the ion sound gyroradius, suggesting that any preference of observed LHSS for that perpendicular scale likely is due to processes arresting the cavity collapse.

Lightning-induced plasma turbulence and ion heating in equatorial ionospheric depletions

The occurrence of lower-hybrid solitary structures in the ionoshere are triggered by lightning-induced whistlers, revealing a new coupling process between the troposphere and the ionosphere. A wide range of plasma instabilities exist in various regions of the terrestrial ionosphere, leading to the development of plasma turbulence, in particular close to the lower-hybrid frequency—the frequency of a longitudinal oscillation of ions and electrons in a magnetized plasma that must be near perpendicular to the magnetic field. Most observations have been carried out in the auroral regions, where intense lower-hybrid emissions are frequently observed, possibly producing solitary structures1 and ion heating2,3,4. Lower-hybrid turbulence with a smaller intensity has also been observed at mid- and low latitudes above thunderstorms5,6 and was shown to be triggered by the electromagnetic whistler wave generated by the lightning current. Here we present observations of equatorial plasma waves that demonstrate the existence of lower-hybrid solitary structures and the simultaneous occurrence of ion heating in deep, large-scale equatorial plasma depletions that form at night during disturbed geomagnetic conditions. These phenomena follow the development of lower-hybrid turbulence triggered by lightning-induced whistlers, revealing a new coupling process between the troposphere and the ionosphere. Since the energy source of the equatorial solitary structures is different from that involved in the auroral processes, our findings support the idea that the formation of lower-hybrid solitary structures may be a universal mechanism operating in inhomogeneous, magnetized plasma and possibly leading to ion heating and acceleration.

Nonlinear kinetic model for lower-hybrid solitary structures

Nonlinear drift-kinetic theory is proposed for lower-hybrid solitary structures in near-Earth plasmas, based on a two time scale kinetic description of nonlinear interactions between the lower-hybrid and dispersive Alfvén waves. The detailed derivation of the nonlinear coupling terms in an arbitrary geometry is presented, that include the ponderomotive potential, non-curl-free component of the perpendicular electron velocity, and the electron diffusion in velocity space. It is shown that the resonant particles are trapped by the combined effects of the slow and ponderomotive potentials, and that their density is further modified by their diffusion in velocity space, yielding a new type of coherent structure, which is identified as an electron hole, coupled with a nonlinear Schrödinger-type soliton. A numerical solution is found in the form of train of soliton-like lower-hybrid spikes, trapped inside a weakly two-dimensional slab electron hole.

Modulational interaction between the short-wavelength lower-hybrid waves and slow, large-scale density fluctuations

Conditions are formulated for modulational instability of two modes with disparate time and space scales, and the modulational interaction of fast and short-wavelength lower-hybrid waves with slow, large-scale inertial Alfvén and ion-acoustic waves is analyzed. Instability is driven by Reynolds’ stresses exerted on plasma by the lower-hybrid waves. Reynolds’ stresses lead to the formation of background density modulations in which the lower-hybrid wave can be localized. It is concluded that the lower-hybrid solitary structures observed in the auroral ionosphere can be created by Reynolds’ stresses of the lower-hybrid waves. In many respects, the observed structures exhibit properties of wave localizations that result from modulational instability.

Conversion of localized lower hybrid oscillations and fast magnetosonic waves at a plasma density cavity

Analytic expressions are presented for conversion of localized lower hybrid oscillations and magnetosonic waves by scattering off a small scale density cavity. The governing equations are solved in slab geometry with wave vectors perpendicular to both the ambient magnetic field and the density gradient associated with density cavity using a scale length separation method. The theory predicts strong excitation of localized lower hybrid oscillations for a set of frequencies between the lower hybrid frequency of the ambient plasma and the minimum lower hybrid frequency inside the cavity. The theory is relevant for the lower hybrid solitary structures observed in space plasmas.

Excitation of localized rotating waves in plasma density cavities by scattering of fast magnetosonic waves.

An analytic description of electromagnetic waves in an inhomogeneous plasma is applied to investigate excitation of localized rotating waves below the lower hybrid frequency through scattering of fast magnetosonic waves on a density cavity. The magnetosonic wave is focused to left-handed rotating oscillations. We find the amplitude of the localized oscillations, resonance frequencies, and the width of the resonances. The theory is relevant for the lower hybrid solitary structures observed in space plasmas and is shown to be consistent with observations by the Freja satellite.

Correction to “Properties of lower hybrid solitary structures: A comparison between space observations, a laboratory experiment, and the cold homogeneous plasma dispersion relation”

[1] In the paper “Properties of lower hybrid solitary structures: A comparison between space observations, a laboratory experiment, and the cold homogeneous plasma dispersion relation” by P. W. Schuck, J. W. Bonnell, and J. L. Pinçon, (Journal of Geophysical Research, 109, A01310, doi:10.1029/2002JA009673, 2004), there are several typographical errors. In four places, the symbol ψ should be replaced with ϕ. The paragraphs with the corrected sentences are reproduced below. [2] [41] The term “electrostatic” seems to be a point of general confusion and contention in space physics. The electrostatic approximation “lies simply in the replacement of the vector electric field by the potential gradient E = −∇ϕ” [Stix 1992, p. 54]. The electrostatic field associated with a wave is longitudinal or along the direction of k, e.g., EL = −∇ϕ. The electromagnetic field associated with a wave is transverse or perpendicular to the direction of k, e.g., ET = −∂tA where A is the vector potential in the Coulomb gauge (∇ · A = 0). Throughout this discussion the terms longitudinal and transverse will be used to describe the orientation of E respect to k, and the terms perpendicular and parallel will be used to describe the orientation of E with respect to the background applied magnetic field B0 = B0. [3] [43] The electrostatic approximation is analogous to the familiar quasineutral approximation in plasma physics. The quasineutral approximation assumes that the densities of the ions and electrons are equal everywhere to lowest order (ni = ne). This does not mean that the electric field is zero. However, this assumption does mean that the Poisson equation cannot be used to determine the electric field. Once the electric field is determined by · J = 0, the charge separation can be estimated from Poisson's equation. Similarly, the electrostatic approximation assumes that E = −∇ϕ + (ET/EL). This approximation presumes that the electric field is predominantly longitudinal and curl free to lowest order. This does not imply that the magnetic fluctuation associated with the electrostatic wave is zero. However, this does imply that Faraday's law ∂tB = −∇ × E cannot be used to determine the magnetic fluctuation B. Once the current of the electrostatic wave is determined, the associated magnetic fluctuation may be estimated from Ampere's law ∇ × B ≈ μ0(J + ε0 ∂tEL) where J = JL + JT is an implicit function of EL with ∇ · JT = 0 and ∇ × JL = 0. (Note that the constraint ∇ · (J + ε0 ∂tEL) = 0 does not imply that J + ε0 ∂tEL = 0 i.e., JT ≠ 0 with the JL + ε0 ∂tEL = 0 (longitudinal components canceling).) Subsequently, ∇ × E may then be estimated from Faraday's law ∇ × E = −∂tB. The magnetic field associated with an “electrostatic” wave may be generally estimated from Ampere's law [Stix, 1992, p. 78]. However, experimentally the noise levels and sensitivity of the detector determine whether the magnetic fields associated with “electrostatic” waves are observable.

Core ion interactions with BB ELF, lower hybrid, and Alfvén waves in the high‐latitude topside ionosphere

We present simultaneous observations of ion distribution functions and plasma waves in the high‐latitude topside ionosphere (500–1000 km) near local midnight during substorm activation. Using a new instrument, the Suprathermal Ion Imager (SII), we are able to explore two‐dimensional ion distribution functions with unprecedented resolution in time (93 s−1) and energy, focusing on the lowest‐energy core (<1 eV) population and suprathermal extensions thereof. The GEODESIC sounding rocket flew through regions containing broadband extremely low frequency (BB ELF) waves, large‐amplitude Alfvén waves, and lower‐hybrid solitary structures (LHSS), all of which have been shown previously to correlate with ion heating. However, GEODESIC detected heating only in association with LHSS. Ion distributions in and near LHSS showed acceleration in the direction transverse to (TAI) with temperatures as high as 5–10 eV, appearing in regions 65 ± 25 m across. TAI were centered on much smaller structures (∼20 m across) of depleted plasma density and enhanced perpendicular electric fields from 0.1 to 10 kHz, consistent with observations from previous rocket flights. Also in agreement with previous findings, we find two distinct ion populations inside LHSS. The dominant population is composed of unheated, isotropic “core” Maxwellian ions having temperatures comparable to the surrounding ambient plasma, while roughly 10% of the plasma density corresponds to the TAI at pitch angles of 90 ± 5°. We argue that the TAI associated with LHSS is consistent with bulk heating of the core ions, and we describe two scenarios that can lead to the observed two‐temperature distributions. The BB ELF wave emissions were correlated with LHSS heating at short scales and anticorrelated with auroral electron precipitation at large scales. The GEODESIC instruments observed no large‐scale ion heating in association with BB ELF waves. Similarly, no ion heating was detected in the presence of large‐amplitude, short perpendicular wavelength Alfvén waves.

Properties of lower hybrid solitary structures: A comparison between space observations, a laboratory experiment, and the cold homogeneous plasma dispersion relation

Lower hybrid solitary structures have been observed by sounding rockets in the auroral ionosphere for over a decade and a half. Surprisingly, few laboratory experiments have attempted to reproduce this interesting phenomena. Recently, Rosenberg and Gekelman [2001] investigated the interaction between fluctuations near the lower hybrid resonance and field‐aligned density striations using the Large Plasma Device at the University of California, Los Angeles. The laboratory measurements of electromagnetic fluctuations localized in a plasma density gradient are new and interesting. This experiment represents another in a series of laboratory investigations that use predictions of the cold homogeneous plasma dispersion to interpret observations of lower hybrid fluctuations interacting with a zero‐order plasma density gradient [Bamber et al., 1994, 1995; Rosenberg and Gekelman, 1998]. This experiment is also the first attempt to directly compare laboratory phase velocity estimates with interferometric electric field measurements of lower hybrid solitary structures by the AMICIST, TOPAZ III and PHAZE II sounding rockets [Pinçon et al., 1997; Schuck et al., 1998; Bonnell et al., 1998]. This paper compares the laboratory and space measurements and concludes that they represent completely different phenomena. Furthermore, significant discrepancies between the predictions of the cold homogeneous plasma dispersion relation and the laboratory observations are presented. We speculate that these discrepancies arise because plasma density gradients, essential to description of the laboratory experiment, are neglected in the cold homogeneous plasma dispersion relation.

Comment on “Properties of lower hybrid solitary structures: A comparison between space observations, a laboratory experiment, and the cold homogeneous plasma dispersion relation” by Schuck et al.

Laboratory experiments involving the interaction of lower hybrid waves and density cavities with full width at half maximums ranging from 1 ≅ κ⟂δ ≤ 4, where δ = is the collisionless skin depth, were performed several years ago at the University of California, Los Angeles. The results were published in the Journal of Geophysical Research in December 2001 [Rosenberg and Gekelman, 2001]. These experiments are relevant to scaled parameters in the auroral ionosphere. This is a comment to the paper of Schuck et al. [2003], regarding the laboratory experiment on lower hybrid (LH) waves in the presence of a density striation. The main point Schuck et al. [2003] wish to make is that density striations in the auroral ionosphere are narrower than δ and that κ⟂δ ≈ 10 there. They argue that if this condition is not strictly satisfied in laboratory experiment then they are inappropriate to model the physics occurring in the ionosphere. In our experiments an incoming short perpendicular wavelength lower hybrid wave impinges upon a density striation which is many parallel (to B0) LH wavelengths long. A striking transformation occurs in which a cavity mode confined to the density gradient of the striation is excited. The mode localization does not depend on the ratio of the cavity diameter with respect to δ. We discuss the properties of lower hybrid waves, the experimental results as well as differences in the rocket and laboratory experiments.

A review of lower hybrid solitary structures

The subject of lower-hybrid solitary structures (LHSS), sometimes called lower-hybrid cavities, is reviewed. LHSS are spatially localized structures embedded in space plasmas. They are characterized by localized electric field fluctuations at frequencies both above and below the ambient lower-hybrid resonance in a density depletion of a few percent to several tens of percent. The localized fluctuations are more intense than the ambient turbulence by a factor of three to five. The LHSS are observed to have dimensions across the magnetic field of a few to many thermal ion gyroradii, usually 10-100 m in the topside auroral ionosphere. Along the magnetic field the dimensions are inferred to be several kilometers to several hundred kilometers although there exist no direct measurements. Analysis of the electric field fluctuations within LHSS using plasma wave interferometers reveals that the phase fronts rotate relative to the geomagnetic field at the center of the LHSS: right-handed at frequencies above and left-handed at frequencies below the ambient lower-hybrid resonance. Within a gyrodiameter of LHSS, ions are found to be preferentially heated perpendicular to the geomagnetic field and local transit time acceleration is the likely mechanism for energization. Two classes of theories have been applied to LHSS: linear theories that assume that the density depletions are preexisting and use the observed spatial properties of the density depletions to compute the propagation characteristics of lower-hybrid waves, and nonlinear, strongly turbulent, collapse theories which assume that the density depletion and the electric field fluctuations are directly coupled through a ponderomotive force. The linear scattering theories successfully explain the rotational and frequency spectrum of LHSS electric field fluctuations. The nonlinear theories predict relations between field strength and cavity size, cavity spatial distributions, and electric field amplitude statistical distributions. None of these nonlinear predictions are validated by observations. Most observations of LHSS have been made by sounding rockets or satellites in the auroral ionosphere. However, recent observations demonstrate that LHSS exist at much higher altitudes in the magnetosphere. Overall, this evidence suggests that LHSS are a universal feature of whistler mode turbulence.

Ray trajectories of lower hybrid solitary structures

The correlation between large‐amplitude lower hybrid waves and density depletions, termed “spikelets,” “lower hybrid cavities,” or “lower hybrid solitary structures” has been attributed to the change in the refractive index computed from the homogeneous plasma dispersion relation. However, the appropriate refractive index includes the electron Hall term involving the density gradient. We demonstrate that the Hall term produces ray trajectories which are profoundly different from the homogeneous plasma dispersion relation.

The role of lower-hybrid-wave collapse in the auroral ionosphere.

In regions where lower-hybrid solitary structures (LHSS) are observed, the character of auroral lower-hybrid turbulence (LHT) (0-20 kHz) is investigated using the amplitude probability distribution of the electric field. The observed probability distributions are accurately described by a Rayleigh distribution with two degrees of freedom. The statistics of the LHT exhibit no evidence of the global modulational instability or self-similar wave collapse. We conclude that nucleation and resonant scattering in preexisting density depletions are the processes responsible for LHSS in auroral LHT.

Auroral ion acceleration from lower hybrid solitary structures: A summary of sounding rocket observations

In this paper we present a review of sounding rocket observations of the ion acceleration seen in nightside auroral zone lower hybrid solitary structures. Observations from Topaz3, Amicist, and Phaze2 are presented on various spatial scales, including the two‐point measurements of the Amicist mission. From this collection of observations we will demonstrate the following characteristics of transverse acceleration of ions (TAI) in lower hybrid solitary structures (LHSS). The ion acceleration process is narrowly confined to 90° pitch angle, in spatially confined regions of up to a few hundred meters across B. The acceleration process does not affect the thermal core of the ambient distribution and does not directly create a measurable effect on the ambient ion population outside the LHSS themselves. This precludes observation with these data of any nonlinear feedback between the ion acceleration and the existence or evolution of the density irregularities on which these LHSS events grow. Within the LHSS region the acceleration process creates a high‐energy tail beginning at a few times the thermal ion speed. The ion acceleration events are closely associated with localized wave events. Accelerated ions bursts are also seen without a concurrent observation of a localized wave event, for two possible reasons. In some cases, the pitch angles of the accelerated tail ions are elevated above perpendicular; that is, the acceleration occurred below the observer and the mirror force has begun to act upon the distribution, moving it upward from the source. In other cases, the accelerated ion structure is spatially larger than the wave event structure, and the observation catches only the ion event. The occurrence rate of these ion acceleration events is related to the ambient environment in two ways: its altitude dependence can be modeled with the parameter B2/ne, and it is highest in regions of intense VLF activity. The cumulative ion outflow from these LHSS TAI is consistent with Freja statistics for VLF‐type premidnight auroral upflow.

Tethered two‐point measurements of solitary auroral density cavities

The OEDIPUS‐C sounding rocket observed localized plasma density depletions in the topside auroral ionosphere using two Langmuir probes situated on separate subpayloads several hundred meters apart. One probe was biased in electron saturation (+5 V) and the second in ion saturation (−5 V). Both of these measurements are consistent with density depletions of tens of percent. The depletions have cross‐field dimensions of tens of meters and occur in regions of VLF hiss, suggesting they are likely signatures of lower hybrid solitary structures. Time delays between event detections on the two subpayloads are consistent with spatially localized structures traversed in succession. The two‐point measurements show directly that the cavities extend at least 800 m along the geomagnetic field line, and the apparent electric potential within them is depressed by roughly 0.5 V.

PHAZE II observations of lower hybrid burst structures occurring on density gradients

PHAZE II sounding rocket observations of VLF waves and plasma density measurements made with a HF wave instrument rather than a fixed bias Langmuir probe show conclusively that the observed lower hybrid solitary structures (LHSS) are associated with density fluctuations. LHSS occur on the positive and negative gradients of plasma density fluctuations of 25–50%. These findings lend support to theories of ambient lower hybrid waves exciting resonances created by pre‐existing density gradients rather than wave collapse or refraction mechanisms; the issue of how the gradients are created is still unresolved.

Theory, simulation, and observation of discrete eigenmodes associated with lower hybrid solitary structures

A three‐dimensional fluid description of nonlinear lower hybrid waves is investigated in the context of plasma density depletions. The objective is a basic understanding of lower hybrid solitary structures associated with transverse ion acceleration in the topside auroral ionosphere. The equations are linearized about a parabolic density depletion and solved. The solution consists of potential structures (eigenfunctions) which rotate in angle about the center of the density depletion. The eigenfrequencies are discrete for |ω| < ωLH. These eigenfunctions rotate in a left‐handed sense about the geomagnetic field and the solutions fall off exponentially outside the density depletion. The eigenfrequencies are continuous for |ω| > ωLH and κz ≠ 0 but become discrete for kz = 0 in agreement with previous two‐dimensional results [Seyler, 1994]. Simulations of the full nonlinear system are performed, and rotating eigenmodes are extracted from the spectrum. The results agree with the analytic results obtained from the linearized equations. The spectral properties of a lower hybrid solitary structure from the TOPAZ III sounding rocket are reexamined and found to be consistent with theoretical predictions for lower hybrid waves trapped within a density depletion as presented herein. A local wavelet frequency‐wavenumber spectrum is constructed from data taken by moving an interferometer through a simulation at a typical rocket velocity. The results compare favorably with the local frequency‐wavenumber spectrum of a lower hybrid solitary structure observed by the TOPAZ III sounding rocket.

Observation and analysis of lower hybrid solitary structures as rotating eigenmodes

Lower hybrid solitary structures (LHSS) are observed to be composed of wave modes rotating in the right‐handed sense about the geomagnetic field. The data analyzed were measured at altitudes near 800 km in the auroral ionosphere by the plasma wave interferometer aboard the AMICIST rocket. Clear evidence of these modes is obtained by an estimation of the local frequency‐wavenumber spectrum derived from wavelet analysis of the electric field. This evidence demonstrates that the phase velocity direction reverses as the payload traverses the structure, implying that the structure is composed of rotating electric fields. These observations are consistent with the result of three‐dimensional numerical simulations investigating lower hybrid wave behavior in the presence of a density cavity. This suggests that the observed characteristics of LHSS may be explained by the excitation of localized lower hybrid eigenmodes and the scattering of background VLH hiss from plasma density depletions.