Conical Distribution Research Articles

Path-integral formulation of ion heating

A description of the generation and evolution of ionospheric oxygen ion conic distributions by electromagnetic ion cyclotron resonance heating is formulated in terms of a path integral. All of the relevant physics is contained in this path integral, which may be used to calculate measurable properties of the conic distribution. Although the presentation is applied to this specific ionospheric context, the treatment may be generalized to treat other diffusion problems of interest.

Generation of electron conical distributions by upper hybrid waves in the Earth's polar region

The heating of electron populations through resonant wave‐particle interaction with upper hybrid turbulence is examined. It is first demonstrated that upper hybrid waves are easily excited by a population of warm electrons with a loss cone type distribution in a background of cold electron plasma. Quasi‐linear theory is then used to show that the upper hybrid turbulence can preferentially heat the warm electrons in the perpendicular direction. In analogy to ion conic formation, this perpendicular heating process is a viable mechanism of generating electron conical distributions observed in the Earth's midaltitude polar regions.

Viking observations of wave-particle interactions and ion wave instabilities in the high-latitude magnetosphere

Various wave and particle observations on auroral field lines made by the Swedish magnetospheric research satellite Viking are discussed with an emphasis on ion wave instabilities and production of conical ion distributions. Examples of ion waves driven by free energy sources such as particle beams and ion loss cone distributions are presented. Observations of ions that are accelerated locally transverse to the magnetic field close to the polar cusp field lines at altitudes from 10000 to 13500 km are presented with simultaneous wave measurements. The observations are discussed in the light of earlier simulation studies and their impact on future simulations is considered.

Simultaneous density and electric field fluctuation spectra associated with velocity shears in the auroral oval

Simultaneous satellite in situ measurements of density (ΔN/N) and electric field fluctuation (ΔE) spectra in the high‐latitude ionosphere are presented using two orbits of Dynamics Explorer 2 (DE 2) data traversing, respectively, the F region at 350 km altitude and the topside ionosphere at 900 km altitude. The spectral study was primarily confined to large structured velocity regions in the auroral oval. By means of the very complete set of energetic particle, dc and ac electric field, field‐aligned current, thermal plasma density, and temperature measurements available from DE 2, we were able to identify two categories of spectra associated with velocity shears irrespective of the height of the satellite. The first category was observed in very intense velocity shear regions of shear frequencies ∼10 Hz in conjunction with large field‐aligned current densities. Under these conditions the spatial spectra of ΔN/N and ΔE had identical power law indices of −1.8±0.2 between scale lengths of approximately 10 km and 300 m. At scale lengths shorter than 300 m the ΔE spectra steepened to an index of −3±0.5 while the spectral index of ΔN/N remained close to its original value of approximately −1.8±0.2, with large power spectral densities observed down to 10 m scale lengths. The second category was observed in more moderate velocity shear regions of shear frequencies ∼ 1 Hz in conjunction with weak field‐aligned currents. In this case the slopes of the density spectra were essentially unchanged, while the ΔE spectra had a much steeper slope of −3±0.5 between 10 km and a few hundred meters. Other factors identifying the two categories are as follows. The first category of spectra was characterized by the existence of upward flowing ions with conic distributions energized to 30 eV and possibly O+ ion cyclotron waves and large electron temperature enhancements. The second category of spectra was associated with wave activity in the 4‐ to 16‐kHz range, most probably O+ lower hybrid waves, and occasionally large ion temperature enhancements. The observations of ΔN/N and ΔE spectral behavior are compared to recent work on two‐dimensional plasma turbulence theory and nonlinear simulations of the collisional Kelvin‐Helmholtz (KH) instability. In particular, the spectral behavior associated with the moderate velocity shear category agrees well with some recent computations of the spatial power spectra of the KH instability (Keskinen et al., 1988).

The plasma environment during particle beam injection into space plasmas: 1. Electron beams

A new isolated‐system, two‐dimensional electrostatic simulation model is used to investigate the plasma environment in the vicinity of a spacecraft during the injection of electron beams. The propagation of the electron beam and the plasma response to the beam injection are found to vary dramatically depending on the ratio of the ambient plasma density to the beam density. When the ambient plasma density is low, most of the beam electrons are drawn back into the spacecraft by the electric field associated with the charging of the spacecraft. Return currents are associated with field‐aligned flow of the ambient electrons and result in regions of charge imbalance away from the spacecraft. The resulting space‐charge fields produce strong perpendicular heating of the ions on a time scale of the ion plasma period, resulting in conical distributions. As the ambient plasma density is increased, the response time of the plasma to the electric fields associated with the beam injection is decreased. The beam is then increasingly neutralized, and the interaction of the beam with the spacecraft is correspondingly reduced. The fraction of the beam particles that propagate away from the vicinity of the spacecraft is increased. When the ambient plasma density is much larger than the beam density, the beam is able to propagate freely into the plasma. Coherent wave structures are produced in the beam near the spacecraft, while further downstream the beam becomes increasingly turbulent.

A numerical study of suprathermal ionospheric ion trajectories in three‐dimensional electric and magnetic field models

A numerical study of the magnetospheric trajectories of ions upflowing from the ionosphere has been performed using three‐dimensional magnetic and electric field models. Ion trajectories have been divided into three main types corresponding to (1) gravitational ions trapped between the magnetic and gravitational mirror points and drifting nearly along the local electric equipotential, (2) ions just escaping from the gravitational field and then convected to the magnetopause due to the loss of the main part of their kinetic energy, (3) trapped and pseudo‐trapped ions whose trajectories are mainly determined by the magnetic field topology (beams and conics) because of their large kinetic energy. Particles from conic distributions injected at inadequate local times and/or altitudes to gain enough energy to precipitate reach the dayside magnetopause after several bounce periods. An application of these numerical studies to ion beams is presented by Bosqued et al. (1986).

Effect of pulse shape and distribution on the plastic deformation of a circular plate

The dynamic plastic deformation of a simply-supported circular plate subjected to a pressure distribution, which is an arbitrary function of radius and time, is found to depend on the moment history applied by the pressure and the moment history applied by the pressure excess over a conical distribution. Each of these moment histories can be replaced by an equivalent rectangular pulse in determining the final deformation at the center of the plate.

AUREOL-3 Results on Ion Precipitation

This paper attempts to summarize recent experimental studies on suprathermal (<14 keV) ion precipitation in the morning side auroral zone from ion composition data provided by the low-altitude (400-2000 km) AUREOL-3 polar orbiting satellite. Plasma measurements show that on auroral and polar cap field-lines upflowing ionospheric ions, mostly O+ and H+, are commonly observed. Imbedded in the discrete auroral region different narrow bands of ion precipitation are observed with a clear energy-lattitude dispersion. These structures can be interpreted as H+ ion beams which have experienced velocity filter effects after ejection either from the conjugate ionosphere or from reconnection regions in the magnetotail. Finally the low energy (< 200 eV) ion precipitation (H+, O+, He+) found equatoward of the precipitation region of more energetic and adiabatically accelerated ions can be satisfactorily explained by the drift of ionospheric ions, ejected with conical distributions and then convected earthward and eastward in a few bounce times.

Ion heating by waves with frequencies below the ion gyrofrequency

Waves with frequencies satisfying ω1 + ω2 = Ω can heat ions. In this nonlinear interaction mechanism, coupling of a wave with frequency ω1 and an ion trajectory, distorted by a wave with frequency ω2, results in a force varying at the gyrofrequency Ω at the ion position. The heating rate, verified by test particle calculations, is found for both broadband and coherent waves in the small gyroradius limit and is applied to ion conics above the auroral zone. This heating mechanism may be significant in other geophysical and astrophysical environments.

Internal field distribution on Au in the Au-Fe system in the limit of very small concentration.

Nonsaturation of hyperfine fields on Au and Fe has been studied primarily with regard to the existence of the Aharoni angle. With the use of both nuclear orientation and magnetic resonance on $^{189m}\mathrm{Au}$ in Fe, the hypothesis of a conical field distribution is shown to be unfounded---even at very moderate external magnetic field values---for well-prepared samples with small Au concentration. [$^{181}\mathrm{Ta}(^{12}\mathrm{C},xn)^{189m}\mathrm{Au}$, mass separation, $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ dilution refrigeration, $\ensuremath{\gamma}$ anisotropies, Ge detection].

Observations of ionospheric magnetospheric coupling: DE and Chatanika coincidences

Observations from several experiments on board the Dynamics Explorer 1 and 2 (DE 1 and 2) spacecraft and ground‐based radar measurements from the Chatanika radar are combined in order to examine the details of ionospheric/magnetospheric coupling in the local evening sector. DE 1 and DE 2 were in coplanar polar orbits that provided measurements almost simultaneously in time and magnetically coincident with the Chatanika radar from L = 3 to L = 17. The coupling processes are inferred from the density, temperature, composition, and angular distributions of the low‐energy plasma observed from the E region of the ionosphere to magnetospheric altitudes of 2.5 earth radii (RE). Plasma characteristics of the plasmasphere, main trough, auroral zone, and polar cap can be studied in this data set. In the comparison of the data, it is clear that the only ionospheric trace of the plasmapause is seen as an increase of the electron temperature. The minimum plasma density in the high‐latitude trough of the ionosphere is magnetically coincident with a region of observed low‐energy bidirectional conical distributions of H+ and He+ at the DE 1 altitude of 1.5 to 1.8 RE. Polarward of this region, DE 1 observes unidirectional conies consisting of H+ and He+ ions that are magnetically coincident with low‐altitude (150‐km) auroral ionization as observed by the Chatanika radar. Over the polar cap, only field‐aligned outward flows of H+, He+, and O+ are seen. These observations imply that as L increases, the dominant coupling mechanism between the ionosphere and magnetosphere in the measured energy range changes from equilibrium diffusion to perpendicular acceleration and, finally, to parallel acceleration.

Ion acceleration by lower hybrid waves in the suprauroral region

In an effort to describe ion‐conic acceleration, particle plasma simulation is used to study the generation of VLF waves below field‐aligned potential drops and the effect of the resulting turbulence on the ion population in the suprauroral region. To model the situation, a weak, energetic electron beam traveling along the magnetic field is allowed to destabilize a cool electron‐ion plasma. To describe the ion acceleration observed in the simulation, a theoretical model is developed using mode‐mode coupling processes to generate the low phase velocity VLF waves with which the ions first interact. By scaling the simulation results to suprauroral conditions, we demonstrate that the VLF turbulence generated below field‐aligned potential drops can account for the acceleration of ions observed in energetic ion conic distributions.

Conical ion distributions at one earth radius — observations from the acceleration region?

Thermal ion measurements from the Retarding Ion Mass Spectrometer (RIMS) on Dynamics Explorer 1 (DE 1) in the night side auroral region were surveyed for evidence of ion acceleration. The RIMS measurements showed evidence for ion acceleration in the 2–10,000 km altitude range, with ion distributions peaked near 90°, and with temperatures of 1 to 10 eV. Two illustrations of the RIMS data for such observations are given here. The conical distributions are found at the low latitude edge of the auroral region, just outside the plasmapause. In the first example, the three major ion species (H+, He+, and O+) show evidence of acceleration. The angular distributions are peaked at different pitch angles, indicating that the different species have been accelerated at different altitudes. The H+ flux is higher than the O+ flux in this first example, in the RIMS energy range (0–50 eV). This is apparently typical of the RIMS observations on the night side. In the second example, only O+ is transversely accelerated.

Theory of the current‐driven ion cyclotron instability in the bottomside ionosphere

A theory of the current‐driven electrostatic ion cyclotron (EIC) instability in the collisional bottomside ionosphere is presented. It is found that electron collisions are destabilizing and are crucial for the excitation of the EIC instability in the collisional bottomside ionosphere. Furthermore, the growth rates of the ion cyclotron instability in the bottomside ionosphere maximize for k⊥ρ i ≥ 1, where 2π/k⊥ is the mode scale size perpendicular to the magnetic field and ρi the ion gyroradius. Realistic plasma density and temperature profiles typical of the high‐latitude ionosphere are used to compute the altitude dependence of the linear growth rate of the maximally growing modes and critical drift velocity of the EIC instability. The maximally growing modes correspond to observed tens of meter size irregularities, and the threshold drift velocity required for the excitation of EIC instability is lower for heavier ions (NO+, O+) than that for the lighter ions (H+). Dupree's resonance‐broadening theory is used to estimate nonlinear saturated amplitudes for the ion cyclotron instability in the high‐latitude ionosphere. Comparison with experimental observations is also made. It is conjectured that the EIC instability in the bottomside ionosphere could be a source of transversely accelerated heavier ions and energetic heavy‐ion conic distributions at higher altitudes.

Low‐altitude field‐aligned electrons

Since some of the earliest measurements of the auroral electron spectrum at rocket altitudes were made, there has been a question about how two very distinct features of the spectrum can occur simultaneously. These features are (1) a spectrum peaked in energy and isotropic over all pitch angles directed into the atmosphere (the isotropic peak) and (2) intense fluxes of field aligned (FA) electrons which are usually observed at pitch angles of 10° or less. Recent rocket measurements with improved temporal and pitch angle resolution have added considerably to the data set on the FA component and are discussed in this paper. A summary of the characteristics of FA electrons is as follows: (1) Field‐aligned electrons are associated with evening, midnight, and cusp auroras. Field aligned electrons are a common feature, seen in 8 out of 10 University of New Hampshire evening auroral rocket flights and in half of the AE satellite orbits through the cusp over a six‐year period. About 80% of the S3‐3 passes through the statistical auroral oval recorded field aligned electron beams. (2) Rocket data associate the field aligned electrons with active auroral forms and on the edges of moving discrete arcs, predominantly the leading edge. Occasionally they are observed between bright auroral forms. (3) The spatial/temporal scale of field aligned events seen by satellites is a few seconds or tens of kilometers. The rocket data time scale extends from seconds to hundreds of seconds. When bursts of field aligned electrons appear, they may be due to incomplete energy and/or pitch angle coverage by the detectors. The intensity of field aligned electrons has been observed to oscillate at a few hertz. (4) At any given time the electrons are field aligned over a wide range of energies, often extending from the peak energy in the isotropic Maxwellian population that coexists with the field aligned electrons to very low energies. On occasion the field aligned electrons terminate at low energies in an isotropic halo. (5) Because of the high degree of field alignment and the restriction to low energies, the field aligned population does not deposit appreciable energy into the ionosphere but can be a significant current carrier. (6) At satellite altitudes of 3000–8000‐km, precipitating field aligned electrons are often associated with up streaming field aligned electrons and conic ion distributions. At satellite altitudes, field aligned electrons are also observed on the edges of ion inverted‐V structures. Recent rocket data have revealed field alignment of auroral electrons up to 15‐keV energy. The differential intensity of these electrons is very intense and gives no evidence for acceleration by static field aligned electric fields. These field aligned electrons are observed to have a distribution function very similar to that for electrons injected at synchronous orbit during substorms. Recent acceleration mechanisms involving turbulence are discussed.

Generation of electrostatic shocks and turbulence through the interaction of conics with the background plasma

Experimental results, obtained during the PORCUPINE experiment and dealing with the interaction of an artificial ion conic with the background auroral plasma, are presented. In addition, these results are compared to the measurements performed by the S3‐3 satellite when natural ion conies are present. This comparison shows that the physical processes associated with the neutralization of conical ion distributions and with their interaction with the background plasma induce the same kind of electrostatic shocks and turbulence as those recorded by S3‐3.

Direct evidence for two‐stage (bimodal) acceleration of ionospheric ions

New measurements from the energetic ion composition spectrometer on the Dynamics Explorer 1 satellite reveal the existence of hybrid conical distributions which are interpreted as the first direct observation of a two‐stage acceleration of ionospheric ions. The ions display characteristics of having experienced both transverse and parallel acceleration in the process of being injected into the magnetosphere. This signature consists of field alignment of the ions at energies just above a lower energy cutoff below which no fluxes are measured. At increasing energy the field‐aligned distribution gradually becomes a conical one whose apex angle widens with increasing energy. The lower energy cutoff gradually increases and then decreases as the satellite moves in latitude in a manner like that found in ion inverted V's. In one case analyzed in detail transversely accelerated oxygen ions having energies to 5 keV were observed while the lower energy ions were primarily field‐aligned between 430 and 870 eV. It is concluded that ions were accelerated from the ionospheric plasma by a mechanism acting primarily transverse to the geomagnetic field at an altitude near 18,000 km and additionally accelerated through a parallel potential that exceeded 300 volts in the core of the inverted V. The heating mechanism produced a bi‐Maxwellian distribution of oxygen ions with transverse and parallel temperatures of ∼1.2 keV and ∼260 eV, respectively. The deduced O+ density was on the order of 0.5 cm−3 in the source.

The production of ion conics by oblique double layers

Magnetized test ions are subjected to acceleration through a numerically simulated oblique double layer in order to determine whether they emerge with velocity vectors aligned with or oblique to the ambient magnetic field. A criterion for oblique alignment, depending on the double‐layer parameters and on the external magnetization, is obtained. When it is applied to observed and theoretical auroral double layers, this criterion predicts that accelerated heavy ions will be substantially less magnetic field aligned than will accelerated hydrogen ions, thus suggesting auroral double layers as a source of high‐energy ion conies. Test particle simulations are also used to investigate the perpendicular heating of ions at low altitudes by the electric fields associated with moving auroral arcs. The rapid motion of small‐scale structures in the arcs is suggested as a source of low‐energy conical ion distributions, and the slow drifts of the entire arc forms are inferred to heat ionospheric ions.

On ion harmonic structure in auroral zone waves: The effect of ion conic damping of auroral hiss

Several low‐altitude auroral wave observations exhibiting ion harmonic frequency structure have been reported. We present here recent S3‐3 wave and particle data that illustrate examples of ion harmonic structure in auroral hiss and the associated energetic ion distributions. Such harmonic features have previously been attributed to either hot ion absorption or emission processes. We model the observed ion conic distributions to evaluate their effect on auroral hiss near the lower hybrid resonance frequency where harmonic features are seen. The calculations indicate that resonant ion damping of auroral hiss can indeed account for this distinct class of observed harmonic feature. The concomitant heating of the ion tail, however, appears insufficient to significantly energize the ion distribution.

The properties of ionospheric O+ ions as observed in the magnetotail boundary layer and northern plasma lobe

The ISEE 2 plasma experiment data are used to investigate the properties of the O+ ions streams flowing in the earth's magnetotail low latitude boundary layer and northern plasma lobe. The E × B filter is seen to be the organizer of the flow of these ions, after their acceleration in the topside ionosphere. Between XSE=−15 RE and −23 RE the velocity of the O+ ions is a function of the distance from the center magnetotail axis, the slower flowing closer to this and the faster closer to the magnetopause. The O+ stream density is observed to vary with this distance as well. The temperature of the streaming ions is shown to be anisotropic with respect to the ambient magnetic field; a generally unresolved narrow conic pitch angle distribution of the O+ ions is suggested to be the cause of this anisotropy. The properties of the O+ ions are shown to be consistent with an acceleration mechanism, or a combination of mechanisms, that act orthogonally and parallel to the magnetic field.