Electrostatic velocity-space instabilities stimulated near the harmonics of the electron cyclotron frequency in the ionosphere

Data are presented on observations made in the ionospheric plasma that provide evidence for the stimulation of Harris type instabilities at nf sub H in a single electron transition. An illustration is also given of the change in shape of the dispersion curve for a given nf sub H as the upper hybrid frequency crosses the nf sub H value. It was concluded that the instability can exist near nf sub H only when the hybrid frequency nf sub H

Field-aligned electron density irregularities near 500 km. Equator to polar cap topside sounder Z mode observations

In addition to spread F, evidence for field-aligned electron density irregularities is commonly observed on Alouette 2 topside sounder ionograms recorded near perigee (500 km). This evidence is provided by distinctive signal returns from sounder-generated Z mode waves. At low latitudes these waves become guided in wave ducts caused by field-aligned electron density irregularities and give rise to strong long-duration echoes. At high latitudes, extending well into the polar cap, these Z mode waves (and stimulated electrostatic waves at the plasma frequency) produce a series of vertical bars on the ionogram display as the satellite traverses discrete field-aligned density structures. The radio frequency (RF) noise environment to be expected in the 400 to 500 km altitude region from low to high latitudes was examined by analyzing perigee Alouette 2 topside sounder data. All observed noise bands were scaled on nearly 200 topside sounder ionograms recorded near perigee at low, mid, and high latitude telemetry stations. The minimum and maximum frequencies of each noise band were entered into a data base or compuer analysis. The signals of primary interest in the perigee study were found to be sounder-generated

Ion effects on ionospheric electron resonance phenomena

Ion effects are often observed on topside-sounder stimulated electron plasma wave phenomena. A commonly observed effect is a spur, appearing after a time delay corresponding to the proton gyro period, attached to the low frequency side of an electron plasma resonance. The spurs are often observed on the resonances at the electron plasma frequency f sub N, the harmonics nf sub H of the electron cyclotron frequency f sub H (n = 2, 3, 4, ...), and occasionally on the upper hybrid frequency. The spurs on the f sub N resonance are usually quite small unless the f sub N resonance overlaps with an nf sub H resonance; very large spurs are observed during such overlap conditions. Proton spurs are only observed on the nf sub H resonances when the electron plasma waves associated with these resonances are susceptible to the Harris instability and when the electromagnetic z wave can be initiated by the sounderpulse. This instability is the result of a sounder stimulated anisotropic electron velocity distribution. The observations suggest that energy is fed into the nf sub H longitudinal plasma wave from the z wave via wave-mode coupling. The magnitude of the nf sub H spurs for large n is much greater than for small n

Ordinary mode auroral kilometric radiation, with harmonics, observed by ISIS 1

Topside-sounder receiver observations by ISIS 1 that reveal examples of o-mode auroral kilometric radiation (AKR) are presented. They correspond to locations outside of the low density source region of intense AKR x-mode emission. The propagation modes are identified by comparing the natural radiation wave cutoffs with the local resonant and wave cutoff phenomena stimulated by the sounder transmitter. The o-mode AKR is the dominant emission in these regions of relatively high electron density, but it is considerably weaker than the intense x-mode AKR observed to emanate from low density cavities above the auroral regions. In addition to the fundamental o-mode, 2nd and 3rd harmonic bands of radiation have also been detected. Harmonics associated with these o-mode AKR are less intense than the harmonics associated with x-mode AKR. It is difficult to explain the variety of harmonic AKR observations (x as well as o-mode) based on present AKR theories

Ionospheric nf sub H resonances: Frequency shifts versus plasma conditions

The Alouette 2 resonances observed near the harmonics of the electron cyclotron frequency f sub H reveal frequency shifts (relative to the n(f sub H) values derived from model field calculations) which can be interpreted in terms of plasma wave dispersion effects. These effects are observed on the 2(f sub H) resonance when it is near the resonance observed close to the upper hybrid frequency f sub T. The observations suggest that an oblique echo model may be required to give a proper interpretation of the 2(f sub H) resonance. Cyclotron damping can be ignored only when the angle between the propagation vector and the direction perpendicular to the earth's magnetic field B is less than a few degrees for the 2(f sub H) wave, and less than a few tenths of a degree for the n(f sub H) waves with n 2. The negative offset of the absolute value of B inferred from the plasma resonance observations is consistent with expectations based on recent OGO 3 and OGO 5 rubidium magnetometer observations at higher altitudes in the equatorial regions

Nonlinear Landau damping in the ionosphere

A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere

Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures

The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factorization. It has been used in traditional high performance computing and grid computing environments. For MapReduce environments, existing methods to compute the QR decomposition use a numerically unstable approach that relies on indirectly computing the Q factor. In the best case, these methods require only two passes over the data. In this paper, we describe how to compute a stable tall-and-skinny QR factorization on a MapReduce architecture in only slightly more than 2 passes over the data. We can compute the SVD with only a small change and no difference in performance. We present a performance comparison between our new direct TSQR method, a standard unstable implementation for MapReduce (Cholesky QR), and the classic stable algorithm implemented for MapReduce (Householder QR). We find that our new stable method has a large performance advantage over the Householder QR method. This holds both in a theoretical performance model as well as in an actual implementation

Tensor Spectral Clustering for Partitioning Higher-order Network Structures

Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.Comment: SDM 201

Auroral kilometric radiation/aurora correlation

Auroral kilometric radiation (AKR) observations from the ISIS 1 topside sounder receiver were compared with visual auroral observations from the network of Alaskan all-sky camera stations. The goal was to relate AKR source region encounters to specific auroral forms on the same magnetic field line. Thirty-eight simultaneous data sets were identified and analyzed. In general, intense AKR was associated with bright auroral arcs and conditions of weak or no AKR corresponded to times when either no aurora or only a faint arc or weak diffuse aurora were observed. Five cases, when both intense AKR and bright visual aurora were present, were analyzed in detail. Complete electron density N sub e contours, from the satellite altitude down to the F region ionization peak, were obtained along N-S traversals of the AKR source region. In addition, the ISIS 1 orbital tracks were projected down the magnetic field lines to the auroral altitude and compared to auroral features on a map derived from the all sky camera images. Density cavities (regions where N sub e 100/cu cm) were encountered on each of these passes