Search NASA⌕ Search

SEARCH · Search NASA

Results for “fast frequency response”

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.

At least 181 records · Page 10

Coupled wave model for large magnet coils

A wave coupled model based on field theory is evolved for analysis of fast electromagnetic transients on superconducting coils. It is expected to play a useful role in the design of protection methods against damage due to high voltages or any adverse effects that might arise from unintentional transients. The significant parameters of the coil are identified to be the turn to turn wave coupling coefficients and the travel time of an electromagnetic disturbance around a single turn. Unlike circuit theoretic inductor, the coil response evolves in discrete steps having durations equal to this travel time. It is during such intervals that high voltages are likely to occur. The model also bridges the gap between the low and high ends of the frequency spectrum.

Gabriel, G. J.↗

Interaction of global merged interaction region shock with the heliopause and its relation to the 2- and 3-kHz radio emissions

We use the Voyager 2 plasma and magnetic field data together with a one-fluid magnetohydrodynamics model to study the interactions of the 1991 global merge interaction region (GMIR) shock with the termination shock and the heliopause. The 1991 GMIR is an extraordinarily large global solar wind structure in radial, longitudinal, and latitudinal extents. It has a strong shock at the leading edge. After its penetration through the termination shock, the GMIR shock first propagates through the subsonic solar wind, then interacts with the heliopause. The interaction produces a transmitted shock propagating outward in the interstellar medium, and a reflected shock propagating backward in the subsonic solar wind. We identify the reflected shock and the transmitted shock as the possible source of the radio noise detected at Voyagers (Gurnett, et al., 1993). The plasma frequency behind the reflected and the transmitted shock can be responsible for the 2- and 3-kHz radio emissions, respectively. The two bands of radio noise are emitted from sources on both sides of the heliopause starting at about the same time. If the emissions picked up by Voyager are due to f(sub P) radiation, then the heliopause is located at R is approximately = 130 AU. If the emissions are due to 2f(sub P) radiation, the R is approximately 150 AU. Because the relative speed of the interstellar plasma with respect to the sun appears to be sub-Alfvenic, it is very unlikely there is a fast-mode bow shock of the heliosphere.

Whang, Y. C.↗

Control Oriented Models for Co-Design: Technical Overview of MT HVDC, MVDC, and Solid State Transformer Building Blocks

The electric power system is shifting toward a power electronics–enabled grid, where converter based “building blocks” (e.g., high voltage direct current (HVDC) links, multi terminal HVDC (MT HVDC) networks, medium voltage DC (MVDC) links, and solid state transformers (SSTs)) provide fast, precise control of power flows, voltage, and frequency. This report develops and applies publicly shareable electromagnetic transient (EMT) and phasor models to examine how such building blocks can be composed and coordinated to support offshore wind integration, inter area transfers, feeder support, and resilience. Section 2 documents a modular multilevel converter (MMC)–based MT HVDC modeling framework and two use cases: a compact WSCC/IEEE 9 bus test system and a 240 bus “mini WECC” case with five offshore wind plants (OWFs). Phasor to EMT transfer, initialization, and sanity checks are summarized, and neutral demonstrations of normal and contingency operation are reported. Section 3 frames the problem of wind plant inertial frequency response (IFR): shaping energy release and recovery to improve nadir while avoiding aerodynamic stall; representative simulations illustrate the issues without disclosing proprietary control. Section 4 develops MVDC concepts through an IEEE 16 bus loop and an Olympic Peninsula case study that compares AC vs. MVDC corridors and shows how feeder headroom can be pooled via DC couplers. Section 5 surveys SST architectures and identifies a gap: scalable, communication free coordination of multiple SSTs for islanded feeder networks. Across the report, novel methods and configurations under separate publication and IP review are not disclosed; only topic oriented, replicable setups and non proprietary results are shown. These models and use cases are intended as foundations for future publications and co design studies on architecture, control, and coordination of PE enabled grids.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Development and Validation of a Fast, Accurate and Cost-Effective Aeroservoelastic Method on Advanced Parallel Computing Systems

Progress to date towards the development and validation of a fast, accurate and cost-effective aeroelastic method for advanced parallel computing platforms such as the IBM SP2 and the SGI Origin 2000 is presented in this paper. The ENSAERO code, developed at the NASA-Ames Research Center has been selected for this effort. The code allows for the computation of aeroelastic responses by simultaneously integrating the Euler or Navier-Stokes equations and the modal structural equations of motion. To assess the computational performance and accuracy of the ENSAERO code, this paper reports the results of the Navier-Stokes simulations of the transonic flow over a flexible aeroelastic wing body configuration. In addition, a forced harmonic oscillation analysis in the frequency domain and an analysis in the time domain are done on a wing undergoing a rigid pitch and plunge motion. Finally, to demonstrate the ENSAERO flutter-analysis capability, aeroelastic Euler and Navier-Stokes computations on an L-1011 wind tunnel model including pylon, nacelle and empennage are underway. All computational solutions are compared with experimental data to assess the level of accuracy of ENSAERO. As the computations described above are performed, a meticulous log of computational performance in terms of wall clock time, execution speed, memory and disk storage is kept. Code scalability is also demonstrated by studying the impact of varying the number of processors on computational performance on the IBM SP2 and the Origin 2000 systems.

Goodwin, Sabine A.↗

Delayed Alumina Scale Spallation on Rene'n5+y: Moisture Effects and Acoustic Emission

The single crystal superalloy Rene'N5 (with or without Y-doping and hydrogen annealing) was cyclically oxidized at 1150 C for 1000 hours. After considerable scale growth (>= 500 hours), even the adherent alumina scales formed on Y-doped samples exhibited delayed interfacial spallation during subsequent water immersion tests, performed up to one year after oxidation. Spallation was characterized by weight loss, the amount of spalled area, and acoustic emission response. Hydrogen annealing (prior to oxidation) reduced spallation both before and after immersion, but without measurably reducing the bulk sulfur content of the Y-doped alloys. The duration and frequency of sequential, co-located acoustic emission events implied an interfacial crack growth rate at least 10(exp -3) m/s, but possibly higher than 10(exp 2) m/s. This is much greater than classic moisture-assisted slow crack growth rates in bulk alumina (10(exp -6) to 10(exp -3) m/s), which may still have occurred undetected by acoustic emission. An alternative failure sequence is proposed: an incubation process for preferential moisture ingress leads to a local decrease in interfacial toughness, thus allowing fast fracture driven by stored strain energy.

Smialek, James L.↗

Characterization of MgB2 Superconducting Hot Electron Bolometers

Hot-Electron Bolometer (HEB) mixers have proven to be the best tool for high-resolution spectroscopy at the Terahertz frequencies. However, the current state of the art NbN mixers suffer from a small intermediate frequency (IF) bandwidth as well as a low operating temperature. MgB2 is a promising material for HEB mixer technology in view of its high critical temperature and fast thermal relaxation allowing for a large IF bandwidth. In this work, we have fabricated and characterized thin-film (approximately 15 nanometers) MgB2-based spiral antenna-coupled HEB mixers on SiC substrate. We achieved the IF bandwidth greater than 8 gigahertz at 25 degrees Kelvin and the device noise temperature less than 4000 degrees Kelvin at 9 degrees Kelvin using a 600 gigahertz source. Using temperature dependencies of the radiation power dissipated in the device we have identified the optical loss in the integrated microantenna responsible as a cause of the limited sensitivity of the current mixer devices. From the analysis of the current-voltage (IV) characteristics, we have derived the effective thermal conductance of the mixer device and estimated the required local oscillator power in an optimized device to be approximately 1 microwatts.

Superconducting Devices↗

NASA SETI microwave observing project: Sky Survey element

The SETI Sky Survey Observing Program is one of two complimentary strategies that NASA plans to use in its microwave Search for Extraterrestrial Intelligence (SETI). The primary objective of the sky survey is to search the entire sky over the frequency range of 1.0 to 10.0 GHz for evidence of narrow band signals of extraterrestrial intelligent origin. Frequency resolutions of 30 Hz or narrower will be used across the entire band. Spectrum analyzers with upwards of ten million channels are required to keep the survey time approximately 6 years. Data rates in excess of 10 megabits per second will be generated in the data taking process. Sophisticated data processing techniques will be required to determine the ever changing receiver baselines, and to detect and archive potential SETI signals. Existing radio telescopes, including several of NASA's Deep Space Network (DSN) 34 meter antennas located at Goldstone, CA and Tidbinbilla, Australia will be used for the observations. The JPL has the primary responsibility to develop and carry out the sky survey. In order to lay the foundation for the full scale SETI Sky Survey, a prototype system is being developed at the JPL. The system will be installed at the new 34-m high efficiency antenna at the Deep Space Station (DSS) 13 research and development station, Goldstone, CA, where it will be used to initiate the observational phase of the NASA SETI Sky Survey. It is anticipated that the early observations will be useful to test signal detection algorithms, scan strategies, and radio frequency interference rejection schemes. The SETI specific elements of the prototype system are: (1) the Wide Band Spectrum Analyzer (WBSA); a 2-million channel fast Fourier transformation (FFT) spectrum analyzer which covers an instantaneous bandpass of 40 MHz; (2) the signal detection processor; and (3) the SETI Sky Survey Manager, a network-based C-language environment that provides observatory control, performs data acquisition and analysis algorithms. A high level description of the prototype hardware and software systems will be given and the current status of the system development will be reported.

Klein, M. J.↗

UAV Path Planning for Wildfires - Sustainably Fighting Wildfires with Automated Path Planning for UAVs

As the severity and frequency of wildfires increase, infrastructure, properties, national parks, animal habitats, and human lives (civilians and firefighters) are put at greater risk. This paper examines the possible application of algorithmic path planning for UAV reconnaissance to reduce damage and safety risks, as aforementioned. When the location of a wildfire is known, UAVs are immediately dispatched from an operating base to fly to the fire and support the firefighters as quickly as possible. Then, the algorithm incrementally analyzes different environmental factors to create a path for the UAV to follow. This work focuses on generating a path for the UAV to follow given a set of polygons representing obstacles. The most important features of this algorithm are its fast response time and obstacle maneuverability. The use of an efficient path planning algorithm could potentially save lives, infrastructure, and acres of forest destruction.

UAV↗

Gradient-based surface nuclear magnetic resonance for groundwater investigation

In medical magnetic resonance imaging, spatial localization (imaging) is based upon the application of controlled magnetic field gradients on top of the main magnetic field to spatially modulate the frequency and/or phase of the nuclear magnetic resonance (NMR) signal across the volume of investigation. In this work, we have applied similar physical principles to produce controlled magnetic field gradients during surface NMR-based groundwater investigations. In this approach, a gradient pulse of variable amplitude or duration is applied immediately after the excitation pulse to cause predictable phase encoding of the NMR signal as a function of depth. This approach is also applicable to emerging surface NMR detection methods that use a prepolarization field with fast nonadiabatic turn-off to generate detectable NMR signals from the shallow subsurface. In this case, the gradient pulse is applied after terminating the prepolarization field and provides a heretofore unavailable means of localizing the NMR response as a function of depth. The application of gradients can also be combined with tip-angle-based modulation to yield higher imaging resolution than can be achieved through either gradient- or tip-angle-based imaging alone. We implemented this new gradient-based capability into a surface NMR gradient generation accessory that is compatible with the GMR-Flex instrument and developed surface NMR-specific forward modeling and linear inverse models. We validated the accuracy of this novel gradient-based sNMR technology using computer simulations, experiments using a small pool filled with a discrete layer of bulk water, and field experiments at well-characterized groundwater test sites along Ebey Island, WA, and Larned, KS. The gradient-based sNMR imaging observations were compared with high-resolution direct push NMR results observed at these sites. The results of computer simulations and field experiments indicate improvements in both the detection (signal-to-noise ratio) and spatial resolution of shallow subsurface water content using gradient-based surface NMR, compared with traditional surface NMR imaging methods.

Geochemistry & Geophysics↗

A Compact, Tunable Near-UV Source for Quantitative Microgravity Combustion Diagnostics

There is a need for improved optical diagnostic methods for use in microgravity combustion research. Spectroscopic methods with fast time response that can provide absolute concentrations and concentration profiles of important chemical species in flames are needed to facilitate the understanding of combustion kinetics in microgravity. Although a variety of sophisticated laser-based diagnostics (such as planar laser induced fluorescence, degenerate four wave mixing and coherent Raman methods) have been applied to the study of combustion in laboratory flames, the instrumentation associated with these methods is not well suited to microgravity drop tower or space station platforms. Important attributes of diagnostic systems for such applications include compact size, low power consumption, ruggedness, and reliability. We describe a diode laser-based near-UV source designed with the constraints of microgravity research in mind. Coherent light near 420 nm is generated by frequency doubling in a nonlinear crystal. This light source is single mode with a very narrow bandwidth suitable for gas phase diagnostics, can be tuned over several 1/cm and can be wavelength modulated at up to MHz frequencies. We demonstrate the usefulness of this source for combustion diagnostics by measuring CH radical concentration profiles in an atmospheric pressure laboratory flame. The radical concentrations are measured using wavelength modulation spectroscopy (WMS) to obtain the line-of-sight integrated absorption for different paths through the flame. Laser induced fluorescence (LIF) measurements are also demonstrated with this instrument, showing the feasibility of simultaneous WMS absorption and LIF measurements with the same light source. LIF detection perpendicular to the laser beam can be used to map relative species densities along the line-of-sight while the integrated absorption available through WMS provides a mathematical constraint on the extraction of quantitative information from the LIF data. Combining absorption with LIF - especially if the measurements are made simultaneously with the same excitation beam - may allow elimination of geometrical factors and effects of intensity fluctuations (common difficulties with the analysis of LIF data) from the analysis.

Peterson, K. A.↗

A study of dynamic measurements made in the settling chamber of the Langley 0.3-meter transonic cryogenic tunnel

Tests have been conducted in a cryogenic wind tunnel settling chamber using a fast response instrumentation to measure the possible existence of temperature fronts due to a sudden or step change in the rate of liquid nitrogen injection into the circuit. No indications of such fronts were obtained using three different techniques to change the rate of nitrogen injection. The normalized pressure and velocity fluctuations at two total temperatures and over a large range of Mach numbers and Reynolds numbers were about 2 x 10 to the -7th to 2 x 10 to the -6th and about 1.8 to 3 percent, respectively. There was no evidence of liquid nitrogen droplets in the flow down to a total temperature of 140 K. The pressure fluctuation power spectra from a pressure transducer correlated with the fan blade passage through the eighth harmonic of the fundamental frequency.

Johnson, C. B.↗

Effect of altered thyroid state on the in situ mechanical properties of adult cat soleus

To determine the responsiveness of cat hindlimb muscles to thyroid manipulation, adult female cats were made hypothyroid (thyroidectomy plus tapazole treatment), hyperthyroid (synthroid pellets), or maintained euthyroid. After 4 months, the hypothyroid soleus had slower time-to-peak (TPT, 80%) and half-relaxation (HRT) times, whereas the hyperthyroid soleus had faster TPT (20%) and HRT than euthyroid cats. The tension at low stimulation frequencies (5-15 Hz) was higher in hypothyroid and lower in hyperthyroid cats compared to euthyroid cats. Muscle weight, maximum twitch and tetanic (Po) tensions, and maximum rates of shortening (Vmax) were similar across groups. The soleus of hypothyroid cats was more fatigable than normal. The myosin heavy chain (MHC) composition, based on gel electrophoresis, was unaffected by thyroid hormone manipulation. Based on the reaction of monoclonal antibodies for specific MHCs, some fast fibers in the hypothyroid cats coexpressed developmental MHC. These data indicate that 4 months of an altered thyroid state result in changes in the isometric twitch speed properties of the cat soleus, but not the tension-related or isotonic properties. Further, a chronic decrease in thyroid hormone had a greater impact than a chronic increase in thyroid hormone on the mechanical properties of the adult cat soleus. Copyright 2003 S. Karger AG, Basel.

Non-NASA Center↗

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

Probabilistic Aeroelastic Analysis Developed for Turbomachinery Components

Aeroelastic analyses for advanced turbomachines are being developed for use at the NASA Glenn Research Center and industry. However, these analyses at present are used for turbomachinery design with uncertainties accounted for by using safety factors. This approach may lead to overly conservative designs, thereby reducing the potential of designing higher efficiency engines. An integration of the deterministic aeroelastic analysis methods with probabilistic analysis methods offers the potential to design efficient engines with fewer aeroelastic problems and to make a quantum leap toward designing safe reliable engines. In this research, probabilistic analysis is integrated with aeroelastic analysis: (1) to determine the parameters that most affect the aeroelastic characteristics (forced response and stability) of a turbomachine component such as a fan, compressor, or turbine and (2) to give the acceptable standard deviation on the design parameters for an aeroelastically stable system. The approach taken is to combine the aeroelastic analysis of the MISER (MIStuned Engine Response) code with the FPI (fast probability integration) code. The role of MISER is to provide the functional relationships that tie the structural and aerodynamic parameters (the primitive variables) to the forced response amplitudes and stability eigenvalues (the response properties). The role of FPI is to perform probabilistic analyses by utilizing the response properties generated by MISER. The results are a probability density function for the response properties. The probabilistic sensitivities of the response variables to uncertainty in primitive variables are obtained as a byproduct of the FPI technique. The combined analysis of aeroelastic and probabilistic analysis is applied to a 12-bladed cascade vibrating in bending and torsion. Out of the total 11 design parameters, 6 are considered as having probabilistic variation. The six parameters are space-to-chord ratio (SBYC), stagger angle (GAMA), elastic axis (ELAXS), Mach number (MACH), mass ratio (MASSR), and frequency ratio (WHWB). The cascade is considered to be in subsonic flow with Mach 0.7. The results of the probabilistic aeroelastic analysis are the probability density function of predicted aerodynamic damping and frequency for flutter and the response amplitudes for forced response.

Reddy, T. S. R.↗

Combined Meteorological and Hydrologic Uncertainties Shape Projections of Future Soil Moisture in the Eastern United States

Physical hazards pose risks to many critical systems. Designing adaptive measures to mitigate these risks is challenging due to large uncertainties in modeling future hazards and the associated sectoral responses. Here, we help address this challenge in a hydrologic context by examining the combined role of meteorological forcing and hydrologic parameter uncertainties in shaping projections of future soil moisture. By encoding a simple conceptual water balance model in a differentiable programming framework, we facilitate fast runtimes and an efficient calibration, enabling an improved uncertainty analysis. We characterize uncertainty in model parameters by calibrating against different target data sets and by using several loss functions. We then convolve the resulting parameter ensemble with a set of Earth system model projections to produce a large ensemble (2,340 members) of daily soil moisture simulations. Focusing on the eastern United States, we find that most ensemble members project a drying of soils across the region, although some simulate wetter conditions throughout this century. Our ensemble shows an increase in the frequency and intensity of dry extremes while there is less agreement for wet extremes. We conduct sensitivity analyses on several soil moisture signatures to measure the relative influence of meteorological and hydrologic uncertainties across space and time. Both meteorological and hydrologic factors contribute consistently to uncertainty surrounding long-term trends, while changes to both wet and dry soil extremes are typically more sensitive to hydrologic parameter uncertainty. Our results underscore the need to account for varied sources of uncertainty when developing long-term hydrometeorological projections.

Lafferty, David C. [University of Illinois Urbana‐↗

Estimation of Time-Varying Pilot Model Parameters

Human control behavior is rarely completely stationary over time due to fatigue or loss of attention. In addition, there are many control tasks for which human operators need to adapt their control strategy to vehicle dynamics that vary in time. In previous studies on the identification of time-varying pilot control behavior wavelets were used to estimate the time-varying frequency response functions. However, the estimation of time-varying pilot model parameters was not considered. Estimating these parameters can be a valuable tool for the quantification of different aspects of human time-varying manual control. This paper presents two methods for the estimation of time-varying pilot model parameters, a two-step method using wavelets and a windowed maximum likelihood estimation method. The methods are evaluated using simulations of a closed-loop control task with time-varying pilot equalization and vehicle dynamics. Simulations are performed with and without remnant. Both methods give accurate results when no pilot remnant is present. The wavelet transform is very sensitive to measurement noise, resulting in inaccurate parameter estimates when considerable pilot remnant is present. Maximum likelihood estimation is less sensitive to pilot remnant, but cannot detect fast changes in pilot control behavior.

Zaal, Peter M. T.↗

Dynamic of Langmuir and Ion-Sound Waves in Type 3 Solar Radio Sources

The evolution of Langmuir and ion-sound waves in type 3 sources is investigated, incorporating linear growth, linear damping, and nonlinear electrostatic decay. Improved estimates are obtained for the wavenumber range of growing waves and the nonlinear coupling coefficient for the decay process. The resulting prediction for the electrostatic decay threshold is consistent with the observed high-field cutoff in the Langmuir field distribution. It is shown that the conditions in the solar wind do not allow a steady state to be attained; rather, bursty linear and nonlinear interactions take place, consistent with the highly inhomogeneous and impulsive waves actually observed. Nonlinear growth is found to be fast enough to saturate the growth of the parent Langmuir waves in the available interaction time. The resulting levels of product Langmuir and ion-sound waves are estimated theoretically and shown to be consistent with in situ ISEE 3 observations of type 3 events at 1 AU. Nonlinear interactions slave the growth and decay of product sound waves to that of the product Langmuir waves. The resulting probability distribution of ion-sound field strengths is predicted to have a flat tail extending to a high-field cutoff. This prediction is consistent with statistics derived here from ISEE 3 observations. Agreement is also found between the frequencies of the observed waves and predictions for the product S waves. The competing processes of nonlinear wave collapse and quasilinear relaxation are discussed, and it is concluded that neither is responsible for the saturation of Langmuir growth. When wave and beam inhomogeneities are accounted for, arguments from quasi-linear relaxation yield an upper bound on the Langmuir fields that is too high to be relevant. Nor are the criteria for direct wave collapse of the beam-driven waves met, consistent with earlier simulation results that imply that this process is not responsible for saturation of the beam instability. Indeed, even if the highest observed Langmuir fields are assumed to he part of a long-wavelength 'condensate' produced via electrostatic decay, they still fall short of the relevant requirements for wave collapse. The most stringent requirement for collapse is that collapsing wave packets not be disrupted by ambient density fluctuations in the solar wind. Fields of several mV m(exp -1) extending over several hundred km would be needed to satisfy this requirement; at 1 AU such fields are rare at best.

Robinson, P. A.↗