Ion beams flowing downward, into the ionosphere, along the Earth's magnetic field have frequently been observed by the FAST satellite in the auroral zone. These discrete downward moving ion beams (DFI) have been characterized by Klumpar et al. [1999] who interpreted the horseshoe‐shaped distributions as being consistent with acceleration in a parallel potential drop above the satellite, followed by motion into a region of increased magnetic field strength. The down‐flowing ion beams are associated with an intense narrowband electrostatic emission at the lower hybrid frequency, polarized perpendicular to the geomagnetic field. Hydrogen cyclotron harmonics both above and below the lower hybrid frequency are also very common. These are the first observations of down‐flowing ions and associated waves outside of the cusp, and the physical mechanism producing the ions is very different from the one associated with cusp ion injections. The DFI events that had a monotonic increase in energy were associated with a clear field‐aligned current signature. The DFI densities were usually ∼5–10/cc, whereas the background plasma had densities up to 100/cc. The wave and DFI observations are consistent with linear dispersion relation calculations and simulations with ion ring distributions that show that the instability is due to coupling of the ion Bernstein waves to the lower hybrid wave. In addition, for a few events, electrostatic ion cyclotron waves were observed. Such waves are usually associated with up‐going ion beams and have not previously been seen with DFI, which have a very different shape in the distribution.
The plasma sheet boundary, at distances intermediate between the auroral acceleration region and the regions where energy conversion associated with substorms occurs, is very dynamic with electron and ion beams, field-aligned currents and many types of waves and non-linear structures. We discuss electric and magnetic fields observations of waves occurring at two very different time-scales. At the longer scales (10's of seconds), Wygant (2000) have shown that the observed fields are associated with Alfvenic fluctuations which have their largest electric field normal to the average plane of the plasma sheet (δEN). The simultaneously observed magnetic field perturbations are azimuthal(δBT), resulting in a Poynting flux along the geomagnetic field. The observations are consistent with an incompressible, transverse electromagnetic surface shear Alfven mode at the surface of the plasma sheet boundary. The local δEN/δBT is consistent with VA. The waves provide an intense earthward Poynting flux sufficient to provide the energy necessary for the energization of auroral electron beams. In addition, the large amplitude surface waves are magnetically conjugate (to within 1 degree) to intense auroral emission as determined from the UVI imager, whereas weak aurora are correlated with small amplitude electric fields. Particle detectors simultaneously observe ions flowing up the field line away from the earth, providing further evidence that low altitude acceleration is occurring on conjugate magnetic field lines. At small scales, large amplitude solitary waves are frequently observed, and ion acoustic, lower hybrid, and Langmuir wave packets are sometimes seen. There are clear differences between the solitary wave observations at the plasma sheet boundary and in the low altitude auroral zone. At high altitudes, only electron mode solitary waves have been identified and they occur both in regions of upward and downward field-aligned current, in contrast to the auroral zone where ion solitary waves occur in upward currents and electron solitary waves occur primarily in downward currents. This difference may because the growth of ion acoustic solitons requires that the plasma be strongly magnetized (fce/fpe >>1) which is not the case for the observed high altitude plasma sheet boundary crossings. The high altitude events are associated with a wide variety of electron distribution types, whereas the low altitude events occur in regions of flat-top electron beam distributions. Preliminary evidence suggests that the high altitude events may be BGK electron holes, as has been shown for the low altitude events. For the parameter regime usually observed at high attitudes, electron holes would be stable. In addition, initial work on electron acoustic solitons suggests that these compressive waves would occur only for a limited range of parameters, so they are unlikely to explain the high altitude solitary waves.
FAST particle and wave data for a single nightside auroral zone crossing are utilized to examine the free energy source for electrostatic ion cyclotron (EIC) waves. Comparisons of the unstable wave modes, obtained by an electrostatic linear dispersion relation solver, to the observed waves for two intervals with upflowing ion beams and two with upflowing electron beams are consistent with the conclusion that the observed waves near the cyclotron frequencies are EIC which are driven by the electron drift both in the upgoing ion beam regions and in the upgoing electron regions. A limitation is that the drifting bi‐Maxwellian model used in the dispersion relation is not a good match to the observed upflowing electron distributions. The observed ion beams do not drive EIC waves; however, the relative drift of the various ion species comprising the ion beam can drive low frequency (<∼50 Hz) waves unstable. The electron drift, during some intervals, also destabilizes electron acoustic waves.
Particle in cell plasma simulation technique has been used to study the effect of the ion two‐stream instability on hydrogen and oxygen distributions at small relative drifts (vH+−vo+<2cH, the hydrogen sound speed). We investigate whether heating due to parallel modes which are unstable at low drifts might be sufficient to quench oblique modes which are unstable at higher drifts. We find that this is not the case and that the oblique modes contribute significantly to heating.
The ion two‐stream instability develops between upflowing H+ and O+ in the auroral acceleration region, if the two species are accelerated to different velocities in a semistationary electrostatic potential. Parallel propagating modes are unstable only for small relative drifts, while oblique modes remain unstable at larger drifts and, consequently, higher altitudes. The effects of oblique modes on ion heating are investigated, and it is found that O+ heats primarily by trapping in the direction of wave propagation during the early, coherent phase of wave growth in the temporal evolution problem. After undergoing trapping along the magnetic field direction, H+ heats primarily by quasi‐linear diffusion when the spectrum broadens nonlinearly. The parallel ion distributions evolve by formation of a high‐energy (low‐energy) tail on oxygen (hydrogen) along with bulk slowing of hydrogen, which results in more energetic oxygen than hydrogen. Total heating is greatest in the direction of wave propagation, and this effect is greater for hydrogen than for oxygen.
The H+ ‐ O+ two‐stream instability in a magnetized plasma is examined for application to ion beam heating in the auroral electron acceleration region. In the fluid limit (zero ion temperature) it is found that the most unstable mode coupling is between the obliquely propagating fast O+ and slow H+ cyclotron modes, even for relative ion beam velocities where parallel propagating modes are unstable. The most unstable mode has properties analogous to those of a beam‐plasma instability. Once a relative velocity is reached where obliquely propagating modes dominate, the growth rate becomes independent of the perpendicular wave vector and so there is no particular angle of maximum wave growth. Upon adding a finite ion temperature it is found that the gross features of the H+ ‐ O+ fluid interaction are retained but finite gyroradius effects cause the appearance of an angle of maximum growth. The tangent of this angle is proportional to the velocity difference between the ion beams, for large enough relative velocity, and is also a function of the H+ to O+ density ratio. The qualitative behavior of the maximum growth rate and its frequency and wave vector versus relative velocity and density ratio are examined. The implications of this behavior for H+ and O+ beam heating in the auroral electron acceleration region are discussed.
The coherent three‐wave decay of a linearly unstable electrostatic hydrogen cyclotron (EHC) wave into stable EHC and ion acoustic modes is considered. Possible triads of parent and daughter waves are identified, and the coupling strength between the waves is calculated in two plasma models. The first model is the fluid limit of an electron‐hydrogen plasma, and the second is a three‐species kinetic model of the plasma in the evening auroral electron acceleration region. It is found that EHC waves commonly observed on auroral field lines are of sufficient amplitude to exceed the threshold for decay to weakly damped EHC modes. Further, frequency and wave number matching can be satisified only if the acoustic mode is oblique to the geomagnetic field. This decay is proposed to be a saturation mechanism for the linearly unstable coherent EHC mode. The temporal dependence of the amplitudes of the three interacting modes, as predicted by the four coupled wave kinetic equations, indicates that the coherent decay can act to saturate the parent wave. Further, it indicates that observed EHC waves may actually be linearly marginally stable daughter EHC modes.
A general electrostatic coupling coefficient which satisfies the Manley-Rowe relations is used to derive an explicit expression for the resonant three-wave coupling coefficient between electrostatic normal modes of a uniformly magnetized, infinite, homogeneous plasma with species described by drifting bi-Maxwellian distribution functions. The limit of this expression is taken when the phase velocities of the three waves are much larger than a species thermal speed, and also when the phase velocities are much smaller than the thermal speed. These are fluid limits and are applicable to the three-wave interaction between some low-frequency electrostatic waves, such as ion acoustic and ion cyclotron modes, in a plasma where Te ≫ Ti.