Controllability of nonlinear systems
Hermann method for controllability determination of linear and nonlinear control systems
CONTROL SYSTEM↗
SEARCH · Engineering Papers
Results for “PFAFF EQUATION”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Lightning-Generated Whistler Waves Observed by Probes On The Communication/Navigation Outage Forecast System Satellite at Low Latitudes
Direct evidence is presented for a causal relationship between lightning and strong electric field transients inside equatorial ionospheric density depletions. In fact, these whistler mode plasma waves may be the dominant electric field signal within such depletions. Optical lightning data from the Communication/Navigation Outage Forecast System (C/NOFS) satellite and global lightning location information from the World Wide Lightning Location Network are presented as independent verification that these electric field transients are caused by lightning. The electric field instrument on C/NOFS routinely measures lightning ]related electric field wave packets or sferics, associated with simultaneous measurements of optical flashes at all altitudes encountered by the satellite (401.867 km). Lightning ]generated whistler waves have abundant access to the topside ionosphere, even close to the magnetic equator.
Holzworth, R. H.↗
Observations of Low-Latitude Plasma Density Enhancements and their Associated Plasma Drifts
Plasma density structures are frequently encountered in the nighttime low-latitude ionosphere by probes on the Communication/Navigation Outage Forecasting System (C/NOFS) satellite. Of particular interest to us here are plasma density enhancements, which are typically observed +/- 15 deg away from the magnetic equator. The low inclination of the C/NOFS satellite offers an unprecedented opportunity to examine these structures and their associated electric fields and plasma velocities, including their field-aligned components, along an east-west trajectory. Among other observations, the data reveal a clear asymmetry in the velocity structure within and around these density enhancements. Previous observations have shown that the peak change in drift velocity associated with a density enhancement occurs simultaneously both perpendicular and parallel to the magnetic field, while the 1results in this paper show that the peak change in parallel fl ow typically occurs 25-100 km to the east of the peak perpendicular ow. We discuss this and other aspects of the observations in relation to the characteristics of the plasma depletions formed near the magnetic equator detected by the same probes on the C/NOFS satellite and to previous observations and theories.
Klenzing, J. H.↗
Survey of the Frequency Dependent Latitudinal Distribution of the Fast Magnetosonic Wave Mode from Van Allen Probes Electric and Magnetic Field Instrument and Integrated Science Waveform Receiver Plasma Wave Analysis
We present a statistical survey of the latitudinal structure of the fast magnetosonic wave mode detected by the Van Allen Probes spanning the time interval of 21 September 2012 to 1 August 2014. We show that statistically, the latitudinal occurrence of the wave frequency (f) normalized by the local proton cyclotron frequency (f(sub cP)) has a distinct funnel-shaped appearance in latitude about the magnetic equator similar to that found in case studies. By comparing the observed E/B ratios with the model E/B ratio, using the observed plasma density and background magnetic field magnitude as input to the model E/B ratio, we show that this mode is consistent with the extra-ordinary (whistler) mode at wave normal angles (theta(sub k)) near 90 deg. Performing polarization analysis on synthetic waveforms composed from a superposition of extra-ordinary mode plane waves with theta(sub k) randomly chosen between 87 and 90 deg, we show that the uncertainty in the derived wave normal is substantially broadened, with a tail extending down to theta(sub k) of 60 deg, suggesting that another approach is necessary to estimate the true distribution of theta(sub k). We find that the histograms of the synthetically derived ellipticities and theta(sub k) are consistent with the observations of ellipticities and theta(sub k) derived using polarization analysis.We make estimates of the median equatorial theta(sub k) by comparing observed and model ray tracing frequency-dependent probability occurrence with latitude and give preliminary frequency dependent estimates of the equatorial theta(sub k) distribution around noon and 4 R(sub E), with the median of approximately 4 to 7 deg from 90 deg at f/f(sub cP) = 2 and dropping to approximately 0.5 deg from 90 deg at f/f(sub cP) = 30. The occurrence of waves in this mode peaks around noon near the equator at all radial distances, and we find that the overall intensity of these waves increases with AE*, similar to findings of other studies.
Boardsen, Scott A.↗
Focusing of nonducted whistlers by the equatorial anomaly
Impulsive ELF/VLF electric field bursts observed by the vector electric field instrument (VEFI) on the Dynamics Explorer 2 (DE 2) satellite on almost every crossing of the geomagnetic equator in the evening hours are interpreted as originating in lightning discharges. These signals that peak in intensity near the magnetic equator are observed within 5-20 deg latitude of the geomagnetic equator at altitudes of 300-500 km with amplitudes of the order of approximately mV/m in the 512- or 1024-Hz frequency band of the VEFI instrument. Whistler-mode ELF/VLF wave propagation through a horizontally stratified ionosphere predicts strong attenuation of subionospheric signals reaching the equator at low altitudes. However, ray tracing analysis shows that the presence of the equatorial density anomaly, commonly observed in the upper ionosphere during evening hours, leads to the focusing of the wave energy from lightning near the geomagnetic equator at low altitudes, thus accounting for all observed aspects of the phenomenon. The observations presented here indicate that during certain hours in the evening, almost all the energy input from lightning discharges entering the ionosphere at less than 30 deg latitude remains confined to a small region (in altitude and latitude) near the geomagnetic equator. The net wideband electric field, extrapolated from the observed electric field values in the 512- to 1024-Hz band, can be approximately 10 mV/m or higher. These strong electric fields generated in the ionosphere by lightning at local evening times may be important for the equatorial electrodynamics of the ionosphere.
Sonwalkar, Vikas S.↗
Irregularities at Sub-Auroral, Middle, and Low Latitudes in the Topside Ionosphere Observed During Geomagnetic Storms with the DEMETER and DMSP Satellites
Detailed observations of the plasma structure and irregularities that characterize the topside ionosphere at sub-auroral, middle, and low-latitudes are presented that were gathered with probes on the DEMETER and DMSP satellites during geomagnetic storms. Data from successive orbits reveal how the density structure and irregularities evolve with changes in the Dst. The observations reveal that precisely during the main phase of severe geomagnetic storms, increased ambient plasma densities and broad regions of irregularities are observed at 700 km, initially at storm commencement near the magnetic equator and then extending to mid- and sub-auroral latitudes within the approximately 8 hour period corresponding to the negative Dst excursions. Furthermore, intense, broadband electric and magnetic field irregularities are often observed at sub-auroral latitudes and are typically associated with the trough region and its poleward plasma density gradient. The observations provide a general framework showing how low, mid, and sub-auroral latitude plasma density structuring and associated irregularities respond to geomagnetic storms.
Pfaff, R.↗
The Guara Campaign: Rocket-Radar Investigations of the Earth's Upper Atmosphere at the Magnetic and Geographic Equators
The Guara Campaign consisted of a series of sounding rockets that were launched from August to October, 1994 at a new launch facility at Alcantara, Brazil, which is within one degree of the Earth's magnetic equator. The campaign was based on focused scientific experiments designed to investigate the electrodynamics and irregularities in the ionosphere and mesosphere at the Earth's magnetic equator and to study their relationship with neutral upper atmosphere motions. In all, 13 large sounding rockets and 20 small meteorological rockets were launched as part of four different experiment groups designed to investigate: (1) the daytime equatorial electrojet, (2) very high altitude Spread-F processes, (3) sunset electrodynamics, and (4) middle atmosphere-thermosphere coupling at the equator. The instrumentation on the sounding rockets varied with each investigation, but primarily included experiments to measure electric fields, currents, plasma densities,- neutral winds, neutral densities and temperatures, and ionospheric instabilities. All of the experiments utilized ground-based scientific instruments including a VHF backscatter radar interferometer, magnetometers, ionosondes, and scintillation receivers. An overview of each investigation is provided, along with a description of the launch site and the ground-based experiments. Scientific highlights of the campaign are provided.
Pfaff, Robert F., Jr.↗
Flux Transfer Event in the Subsolar Region and Near the Cusp: Simultaneous Polar and Cluster Observations
The phenomenon called flux transfer events (FTEs) is widely accepted as the manifestation of time-dependent reconnection. In this paper, we present an observational evidence of a flux transfer event observed simultaneously at low-latitude by Polar and high-latitude by Cluster. This event occurred on March 21, 2002, when both Cluster and Polar were located near the local noon but with large latitudinal distance. Cluster was moving outbound from polar cusp to the magnetosheath, and Polar was in the magnetosheath near the equatorial magnetopause. The observations show that a flux transfer event was formed between the equator and the northern cusp. Polar and Cluster observed the FTE's two open flux tubes: Polar saw the southward moving flux tube near the equator; and Cluster the , northward moving flux tube at high latitude. Unlike low-latitude FTEs, the high-latitude FTE did not exhibit the characteristic bi-polar BN signature. But the plasma data clearly showed its open flux tube configuration. Enhanced electric field fluctuations were observed within the FTE core, both at low- and high-attitudes. This event provides us a unique opportunity to understand high-latitude FTE signatures and the nature of time-varying reconnection.
Le, G.↗
A Topside Equatorial Ionospheric Density and Composition Climatology During and After Extreme Solar Minimum
During the recent solar minimum, solar activity reached the lowest levels observed during the space age. This extremely low solar activity has accompanied a number of unexpected observations in the Earth's ionosphere and thermosphere when compared to previous solar minima. Among these are the fact that the ionosphere is significantly contracted beyond expectations based on empirical models. Climatological altitude profiles of ion density and composition measurements near the magnetic dip equator are constructed from the C/NOFS satellite to characterize the shape of the top side ionosphere during the recent solar minimum and into the new solar cycle. The variation of the profiles with respect to local time, season, and solar activity are compared to the IRI-2007 model. Building on initial results reported by Heelis et al. [2009], here we describe the extent of the contracted ionosphere, which is found to persist throughout 2009. The shape of the ionosphere during 2010 is found to be consistent with observations from previous solar minima.
Klenzing, J. H.↗
Topside Equatorial Ionospheric Density and Composition During and After Extreme Solar Minimum
During the recent solar minimum, solar activity reached the lowest levels observed during the space age. This extremely low solar activity has accompanied a number of unexpected observations in the Earth s ionosphere-thermosphere system when compared to previous solar minima. Among these are the fact that the ionosphere is significantly contracted beyond expectations based on empirical models. Altitude profiles of ion density and composition measurements near the magnetic dip equator are constructed from the Communication/Navigation Outage Forecast System (C/NOFS) satellite to characterize the shape of the topside ionosphere during the recent solar minimum and into the new solar cycle. The variation of the profiles with respect to local time, season, and solar activity are compared to the IRI-2007 model. Building on initial results reported by Heelis et al. (2009), here we describe the extent of the contracted ionosphere, which is found to persist throughout 2009. The shape of the ionosphere during 2010 is found to be consistent with observations from previous solar minima.
Klenzing, J.↗
Electron density distribution in the magnetosphere
Eight months of differential potential measurements from the POLAR satellite were used to study the electron density distribution in the magnetosphere and its dependence on the level of geomagnetic activity identified by the Kp index. The differential potential measurement is directly proportional to the electron density, and this technique can be used for detecting fast electron density variation in low-density plasmas with a good accuracy. The inner magnetospheric regions are particularly investigated in this study. The cusp is found to be denser during low Km, and it moves equator-ward with increasing Km. The plasmapause is quite asymmetric, as expected. In particular, on the nightside, the plasmapause is compressed closer to the earth with increasing Kp. While the density gradients at the dayside plasmapause are usually not very steep, they can be quite large at other time sectors. A particularly pronounced sharpening of the plasmapause occurs at the dusk sector with increasing Kp. The density in the region between the dayside plasmapause and magnetopause is relatively high during all Kp levels; the average densities are several electrons per cubic meter. During disturbed periods, the density in the near-earth plasma sheet near midnight increases and becomes higher than the densities towards the flanks of the plasma sheet.
Laakso, H.↗
Highly Structured Plasma Density and Associated Electric and Magnetic Field Irregularities at Sub-Auroral, Middle, and Low Latitudes in the Topside Ionosphere Observed with the DEMETER and DMSP Satellites
Detailed observations of the plasma structure and irregularities that characterize the topside ionosphere at sub-auroral, middle, and low-latitudes are gathered with probes on the DEMETER and DMSP satellites. In particular, we present DEMETER observations near 700 km altitude that reveal: (1) the electric field irregularities and density depletions at mid-latitudes are remarkably similar to those associated with equatorial spread-F at low latitudes; (2) the mid-latitude density structures contain both depletions and enhancements with scale lengths along the spacecraft trajectory that typically vary from 10's to 100's of km; (3) in some cases, ELF magnetic field irregularities are observed in association with the electric field irregularities on the walls of the plasma density structures and appear to be related to finely-structured spatial currents and/or Alfven waves; (4) during severe geomagnetic storms, broad regions of nightside plasma density structures are typically present, in some instances extending from the equator to the subauroral regions; and (5) intense, broadband electric and magnetic field irregularities are observed at sub-auroral latitudes during geomagnetic storm periods that are typically associated with the trough region. Data from successive DEMETER orbits during storm periods in both the daytime and nighttime illustrate how enhancements of both the ambient plasma density, as well as sub-auroral and mid-latitude density structures, correlate and evolve with changes in the Dst. The DEMETER data are compared with near simultaneous observations gathered by the DMSP satellites near 840 km. The observations are related to theories of sub-auroral and mid-latitude plasma density structuring during geomagnetic storms and penetration electric fields and are highly germane to understanding space weather effects regarding disruption of communication and navigation signals in the near-space environment.
Pfaff, Robert F.↗
Flux Transfer Events Simultaneously Observed by Polar and Cluster: Flux Rope in the Subsolar Region and Flux Tube Addition to the Polar Cusp
The phenomenon called flux transfer events (FTEs) is widely accepted as the manifestation of time-dependent reconnection. In this paper, we present observational evidence of a flux transfer event observed simultaneously at low-latitude by Polar and at high-latitude by Cluster. This event occurs on March 21, 2002, when both Cluster and Polar are located near local noon but with a large latitudinal separation. During the event, Cluster is moving outbound from the polar cusp to the magnetosheath, and Polar is in the magnetosheath near the equatorial magnetopause. The observations show that a flux transfer event occurs between the equator and the northern cusp. Polar and Cluster observe the FTE s two open flux tubes: Polar encounters the southward moving flux tube near the equator; and Cluster the northward moving flux tube at high latitude. The low latitude FTE appears to be a flux rope with helical magnetic field lines as it has a strong core field and the magnetic field component in the boundary normal direction exhibits a strong bi-polar variation. Unlike the low-latitude FTE, the high-latitude FTE observed by Cluster does not exhibit the characteristic bi-polar perturbation in the magnetic field. But the plasma data clearly reveal its open flux tube configuration. It shows that the magnetic field lines have straightened inside the FTE and become more aligned to the neighboring flux tubes as it moves to the cusp. Enhanced electrostatic fluctuations have been observed within the FTE core, both at low- and high-latitudes. This event provides a unique opportunity to understand high-latitude FTE signatures and the nature of time-varying reconnection.
Le, G.↗
DC Electric Fields, Associated Plasma Drifts, and Irregularities Observed on the C/NOFS Satellite
Results are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. The VEFI instrument includes a vector DC electric field detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux gate magnetometer, an optical lightning detector, and associated electronics including a burst memory. Compared to data obtained during more active solar conditions, the ambient DC electric fields and their associated E x B drifts are variable and somewhat weak, typically < 1 mV/m. Although average drift directions show similarities to those previously reported, eastward/outward during day and westward/downward at night, this pattern varies significantly with longitude and is not always present. Daytime vertical drifts near the magnetic equator are largest after sunrise, with smaller average velocities after noon. Little or no pre-reversal enhancement in the vertical drift near sunset is observed, attributable to the solar minimum conditions creating a much reduced neutral dynamo at the satellite altitude. The nighttime ionosphere is characterized by larger amplitude, structured electric fields, even where the plasma density appears nearly quiescent. Data from successive orbits reveal that the vertical drifts and plasma density are both clearly organized with longitude. The spread-F density depletions and corresponding electric fields that have been detected thus far have displayed a preponderance to appear between midnight and dawn. Associated with the narrow plasma depletions that are detected are broad spectra of electric field and plasma density irregularities for which a full vector set of measurements is available for detailed study. The VEFI data represents a new set of measurements that are germane to numerous fundamental aspects of the electrodynamics and irregularities inherent to the Earth s low latitude ionosphere.
Pfaff, R.↗
Initial Results of DC Electric Fields, Associated Plasma Drifts, Magnetic Fields, and Plasma Waves Observed on the C/NOFS Satellite
Initial results are presented from the Vector Electric Field Investigation (VEFI) on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite, a mission designed to understand, model, and forecast the presence of equatorial ionospheric irregularities. The VEFI instrument includes a vector DC electric field detector, a fixed-bias Langmuir probe operating in the ion saturation regime, a flux gate magnetometer, an optical lightning detector, and associated electronics including a burst memory. Compared to data obtained during more active solar conditions, the ambient DC electric fields and their associated E x B drifts are variable and somewhat weak, typically < 1 mV/m. Although average drift directions show similarities to those previously reported, eastward/outward during day and westward/downward at night, this pattern varies significantly with longitude and is not always present. Daytime vertical drifts near the magnetic equator are largest after sunrise, with smaller average velocities after noon. Little or no pre-reversal enhancement in the vertical drift near sunset is observed, attributable to the solar minimum conditions creating a much reduced neutral dynamo at the satellite altitude. The nighttime ionosphere is characterized by larger amplitude, structured electric fields, even where the plasma density appears nearly quiescent. Data from successive orbits reveal that the vertical drifts and plasma density are both clearly organized with longitude. The spread-F density depletions and corresponding electric fields that have been detected thus far have displayed a preponderance to appear between midnight and dawn. Associated with the narrow plasma depletions that are detected are broad spectra of electric field and plasma density irregularities for which a full vector set of measurements is available for detailed study. Finally, the data set includes a wide range of ELF/VLF/HF oscillations corresponding to a variety of plasma waves, in particular banded ELF hiss, whistlers, and lower hybrid wave turbulence triggered by lightning-induced sferics. The VEFI data represents a new set of measurements that are germane to numerous fundamental aspects of the electrodynamics and irregularities inherent to the Earth's low latitude ionosphere.
Pfaff, R.↗
The PetitSat Mission – Science Goals and Instrumentation
The mid- and low-latitude ionosphere is home to a variety of plasma density irregularities, including depletions (bubbles), enhancements (blobs), and small-scale scintillation. Previous studies of plasma density enhancements observed using ROCSAT data have posited that these structures are the direct result of the formation of bubbles near the geomagnetic equator. However, more recent observations from the C/NOFS satellite suggest that multiple mechanisms are responsible for forming plasma enhancements, with wave action in the ionosphere and thermosphere as a significant driver of the enhanced densities. Indeed, statistical analysis of enhancements observed from satellites resembles the statistics of Medium-Scale Traveling Ionosphere Disturbances (MSTIDs) with respect to seasonal variability and solar activity. petitSat is a CubeSat mission designed to examine the link between MSTIDs and plasma enhancements. The mission will provide in situ measurements of the plasma density, 3D ion drift, as well as ion and neutral composition. The instrument suite includes a combined retarding potential analyzer and cross-track drift meter and an ion-neutral mass spectrometer. This instrument suite will provide comprehensive information about the fluctuations in plasma, as well as changes in the neutral profile. petitSat will launch into a 51 deg inclination orbit at 400 km (consistent with an International Space Station deployment), allowing for numerous conjunctions with the Boston University All-Sky Imager network over the mission lifetime.
J. Klenzing↗
Coordinated Satellite Observations of the Very Low Frequency Transmission Through the Ionospheric D Layer at Low Latitudes, Using Broadband Radio Emissions from Lightning
Both ray theory and full-wave models of very low frequency transmission through the ionospheric D layer predict that the transmission is greatly suppressed near the geomagnetic equator. We use data from the low-inclination Communication/Navigation Outage Forecast System satellite to test this semiquantitatively, for broadband very low frequency emissions from lightning. Approximate ground-truthing of the incident wavefields in the Earth-ionosphere waveguide is provided by the World Wide Lightning Location Network. Observations of the wavefields at the satellite are provided by the Vector Electric Field Instrument aboard the satellite. The data set comprises whistler observations with the satellite at magnetic latitudes<26deg. Thus, our conclusions, too, must be limited to the near-equatorial region and are not necessarily predictive of midlatitude whistler properties. We find that in most broadband recordings of radio waves at the satellite, very few of the lightning strokes result in a detectable radio pulse at the satellite. However, in a minority of the recordings, there is enhanced transmission of very low frequency lightning emissions through the D layer, at a level exceeding model predictions by at least an order of magnitude. We show that kilometric-scale D-layer irregularities may be implicated in the enhanced transmission. This observation of sporadic enhancements at low magnetic latitude, made with broadband lightning emissions, is consistent with an earlier review of D-layer transmission for transmission from powerful man-made radio beacons.
Jacobson, Abram R.↗