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DOE OSTI2024

Approximating accelerator impedances with resonator networks

It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a general manner for excitations that are not necessarily Gaussian in nature. Here, the conventional method for doing this involves taking the inverse Fourier Transform of the component impedance, obtaining the Green's Function, and then convolving it with the desired excitation distribution. This method can prove numerically cumbersome, for a convolution integral must be evaluated for each individual point in time when the wake function is desired. An alternative to this method would be to compute the wake function analytically, which would sidestep the need for repetitive integration. Only a handful of cases, however, are simple enough for this method to be tenable. One of these cases is the case where the component in question is an RLC resonator, which has a closed-form analytical wake function solution. This means that a component which can be represented in terms of resonators can leverage this solution. As it happens, common network synthesis techniques may be used to map arbitrary impedance profiles to RLC resonator networks in a manner the accelerator community has yet to take advantage of. In this work, we will use Foster Canonical Resonator Networks and partial derivative descent optimization to develop a technique for synthesizing resonator networks that well approximate the impedances of real-world accelerator components. We will link this synthesis to the closed-form resonator wake function solution, giving rise to a powerful workflow that may be used to streamline beam dynamics simulations.

43 PARTICLE ACCELERATORS↗

NASA NTRS2003

The cumulative cost of additional wakefulness: dose-response effects on neurobehavioral functions and sleep physiology from chronic sleep restriction and total sleep deprivation

OBJECTIVES: To inform the debate over whether human sleep can be chronically reduced without consequences, we conducted a dose-response chronic sleep restriction experiment in which waking neurobehavioral and sleep physiological functions were monitored and compared to those for total sleep deprivation. DESIGN: The chronic sleep restriction experiment involved randomization to one of three sleep doses (4 h, 6 h, or 8 h time in bed per night), which were maintained for 14 consecutive days. The total sleep deprivation experiment involved 3 nights without sleep (0 h time in bed). Each study also involved 3 baseline (pre-deprivation) days and 3 recovery days. SETTING: Both experiments were conducted under standardized laboratory conditions with continuous behavioral, physiological and medical monitoring. PARTICIPANTS: A total of n = 48 healthy adults (ages 21-38) participated in the experiments. INTERVENTIONS: Noctumal sleep periods were restricted to 8 h, 6 h or 4 h per day for 14 days, or to 0 h for 3 days. All other sleep was prohibited. RESULTS: Chronic restriction of sleep periods to 4 h or 6 h per night over 14 consecutive days resulted in significant cumulative, dose-dependent deficits in cognitive performance on all tasks. Subjective sleepiness ratings showed an acute response to sleep restriction but only small further increases on subsequent days, and did not significantly differentiate the 6 h and 4 h conditions. Polysomnographic variables and delta power in the non-REM sleep EEG-a putative marker of sleep homeostasis--displayed an acute response to sleep restriction with negligible further changes across the 14 restricted nights. Comparison of chronic sleep restriction to total sleep deprivation showed that the latter resulted in disproportionately large waking neurobehavioral and sleep delta power responses relative to how much sleep was lost. A statistical model revealed that, regardless of the mode of sleep deprivation, lapses in behavioral alertness were near-linearly related to the cumulative duration of wakefulness in excess of 15.84 h (s.e. 0.73 h). CONCLUSIONS: Since chronic restriction of sleep to 6 h or less per night produced cognitive performance deficits equivalent to up to 2 nights of total sleep deprivation, it appears that even relatively moderate sleep restriction can seriously impair waking neurobehavioral functions in healthy adults. Sleepiness ratings suggest that subjects were largely unaware of these increasing cognitive deficits, which may explain why the impact of chronic sleep restriction on waking cognitive functions is often assumed to be benign. Physiological sleep responses to chronic restriction did not mirror waking neurobehavioral responses, but cumulative wakefulness in excess of a 15.84 h predicted performance lapses across all four experimental conditions. This suggests that sleep debt is perhaps best understood as resulting in additional wakefulness that has a neurobiological "cost" which accumulates over time.

NASA Discipline Regulatory Physiology↗

DOE OSTI2018

Evolution of plasma wakes in density up- and down-ramps

The time evolution of plasma wakes in density up- and down-ramps is examined through theory and particle-in-cell simulations. Motivated by observation of the reversal of a linear plasma wake in a plasma density upramp in a recent experiment we have examined the behaviour of wakes in plasma ramps that always accompany any plasma source used for plasma-based acceleration. In the up-ramp case it is found that, after the passage of the drive pulse, the wavnumber/wavelength of the wake starts to decrease/increase with time until it eventually tends to zero/infinity, then the wake reverses its propagation direction and the wavenunber/wavelength of the wake begins to increase/shrink. Here, the evolutions of the wavenumber and the phase velocity of the wake as functions of time are shown to be significantly different in the up-ramp and the down-ramp cases. In the latter case the wavenumber of the wake at a particular position in the ramp increases until the wake is eventually damped. It is also shown that the waveform of the wake at a particular time after being excited can be precisely controlled by tuning the initial plasma density profile, which may enable a new type of plasma-based ultrafast optics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2008

Wake Vortex Inverse Model User's Guide

NorthWest Research Associates (NWRA) has developed an inverse model for inverting landing aircraft vortex data. The data used for the inversion are the time evolution of the lateral transport position and vertical position of both the port and starboard vortices. The inverse model performs iterative forward model runs using various estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Forward model predictions of lateral transport and altitude are then compared with the observed data. Differences between the data and model predictions guide the choice of vortex parameter values, crosswind profile and circulation evolution in the next iteration. Iterations are performed until a user-defined criterion is satisfied. Currently, the inverse model is set to stop when the improvement in the rms deviation between the data and model predictions is less than 1 percent for two consecutive iterations. The forward model used in this inverse model is a modified version of the Shear-APA model. A detailed description of this forward model, the inverse model, and its validation are presented in a different report (Lai, Mellman, Robins, and Delisi, 2007). This document is a User's Guide for the Wake Vortex Inverse Model. Section 2 presents an overview of the inverse model program. Execution of the inverse model is described in Section 3. When executing the inverse model, a user is requested to provide the name of an input file which contains the inverse model parameters, the various datasets, and directories needed for the inversion. A detailed description of the list of parameters in the inversion input file is presented in Section 4. A user has an option to save the inversion results of each lidar track in a mat-file (a condensed data file in Matlab format). These saved mat-files can be used for post-inversion analysis. A description of the contents of the saved files is given in Section 5. An example of an inversion input file, with preferred parameters values, is given in Appendix A. An example of the plot generated at a normal completion of the inversion is shown in Appendix B.

Lai, David↗

NASA NTRS2008

Updated Results for the Wake Vortex Inverse Model

NorthWest Research Associates (NWRA) has developed an Inverse Model for inverting aircraft wake vortex data. The objective of the inverse modeling is to obtain estimates of the vortex circulation decay and crosswind vertical profiles, using time history measurements of the lateral and vertical position of aircraft vortices. The Inverse Model performs iterative forward model runs using estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Iterations are performed until a user-defined criterion is satisfied. Outputs from an Inverse Model run are the best estimates of the time history of the vortex circulation derived from the observed data, the vertical crosswind profile, and several vortex parameters. The forward model, named SHRAPA, used in this inverse modeling is a modified version of the Shear-APA model, and it is described in Section 2 of this document. Details of the Inverse Model are presented in Section 3. The Inverse Model was applied to lidar-observed vortex data at three airports: FAA acquired data from San Francisco International Airport (SFO) and Denver International Airport (DEN), and NASA acquired data from Memphis International Airport (MEM). The results are compared with observed data. This Inverse Model validation is documented in Section 4. A summary is given in Section 5. A user's guide for the inverse wake vortex model is presented in a separate NorthWest Research Associates technical report (Lai and Delisi, 2007a).

Robins, Robert E.↗

NASA NTRS1999

Effects of menstrual cycle phase and oral contraceptives on alertness, cognitive performance, and circadian rhythms during sleep deprivation

The influence of menstrual cycle phase and oral contraceptive use on neurobehavioral function and circadian rhythms were studied in healthy young women (n = 25) using a modified constant routine procedure during 24 h of sleep deprivation. Alertness and performance worsened across sleep deprivation and also varied with circadian phase. Entrained circadian rhythms of melatonin and body temperature were evident in women regardless of menstrual phase or oral contraceptive use. No significant difference in melatonin levels, duration, or phase was observed between women in the luteal and follicular phases, whereas oral contraceptives appeared to increase melatonin levels. Temperature levels were higher in the luteal phase and in oral contraceptive users compared to women in the follicular phase. Alertness on the maintenance of wakefulness test and some tests of cognitive performance were poorest for women in the follicular phase especially near the circadian trough of body temperature. These observations suggest that hormonal changes associated with the menstrual cycle and the use of oral contraceptives contribute to changes in nighttime waking neurobehavioral function and temperature level whereas these factors do not appear to affect circadian phase.

NASA Discipline Regulatory Physiology↗

DOE OSTI2015

Collective Effects in a Diffraction Limited Storage Ring

Our paper gives an overview of collective effects that are likely to appear and possibly limit the performance in a diffraction-limited storage ring (DLSR) that stores a high-intensity ultra-low-emittance beam. Beam instabilities and other intensity-dependent effects that may significantly impact the machine performance are covered. The latter include beam-induced machine heating, Touschek scattering, intra-beam scattering, as well as incoherent tune shifts. The general trend that the efforts to achieve ultra-low emittance result in increasing the machine coupling impedance and the beam sensitivity to instability is reviewed. The nature of coupling impedance in a DLSR is described, followed by a series of potentially dangerous beam instabilities driven by the former, such as resistive-wall, TMCI (transverse mode coupling instability), head-tail and microwave instabilities. Additionally, beam-ion and CSR (coherent synchrotron radiation) instabilities are also treated. Means to fight against collective effects such as lengthening of the bunch with passive harmonic cavities and bunch-by-bunch transverse feedback are introduced. Numerical codes developed and used to evaluate the machine coupling impedance, as well as to simulate beam instability using the former as inputs are described.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1997

Wake Vortex Sensors Requirements Overview

The presentation includes discussions of primary wake vortex system requirements, evolution models, sensor evolution, site specific sensor tradeoffs, wake sensor functions, deployment considerations, the operational test bed system and additional sensor requirements.

Hinton, David A.↗

DOE OSTI2021

Cooling and diffusion rates in coherent electron cooling concepts

We present analytic cooling and diffusion rates for a simplified model of coherent electron cooling (CEC), based on a proton energy kick at each turn. This model also allows to estimate analytically the rms value of electron beam density fluctuations in the "kicker" section. Having such analytic expressions should allow for better understanding of the CEC mechanism, and for a quicker analysis and optimization of main system parameters. Our analysis is applicable to any CEC amplification mechanism, as long as the wake (kick) function is available.

43 PARTICLE ACCELERATORS↗

NASA NTRS1985

Finite-time arbitrary-motion unsteady cascade airfoil theory for helicopter rotors in hover

A complete and detailed derivation of finite-time arbitrary-motion cascade theory is presented for both Laplace and frequency domains. This theory includes the effect of returning wakes for both single- and multibladed rotors. The generalized cascade lift-deficiency function (CLDF) is shown to be consistent with the generalized Theodorsen lift-deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity. This function predicts correct zero-reduced-frequency limit. Accurate and efficient numerical procedures are presented for the evaluation of the CLDF. Numerical examples comparing the CLDF with Loewy's lift deficiency function in frequency domain are presented. Accurate Pade approximants of the CLDF are constructed using a Bode-plot approach which allows for complex poles.

Dinyavari, M. A. H.↗

NASA NTRS1997

Change in Ion Distribution Function While Crossing the Space Shuttle Wake

During the space shuttle/Spacelab 2 mission (STS-5]F) the Plasma Diagnostic Package (PDP) was placed in free flight in the vicinity of the Orbiter and provided the first opportunity to measure the midwake and far-wake regions of an orbiting spacecraft. During this period the PDP crossed the wake 4 times at downstream distances ranging from 40 m to 240 m. During each crossing a definite change in the ion-retarding potential curves was measured when the PDP was in the shuttle wake compared to the ambient ionosphere. These measurements were obtained by both the differential ion flux probe and the retarding potential analyzer instruments on the PDP. The temperature of the ions, derived from fitting the data to a Maxwellian distribution, are consistent with an enhancement during each wake crossing of as much as a factor of 2.5 (from about 0.08 eV to 0.2 eV). Such studies of plasma wakes were never before performed.

Sorensen, J. E.↗

NASA NTRS1994

Subsidence of aircraft engine exhaust in the stratosphere: Implications for calculated ozone depletions

The deposition altitude of nitrogen oxides and other exhaust species emitted by stratospheric aircraft is a crucial parameter in determining the impact of these emissions on stratospheric ozone. We have utilized a model for the wake of a High-Speed Civil Transport (HSCT) to estimate the enhancements in water and reductions in ozone in these wakes as a function of time. Radiative calculations indicate differential cooling rates as large as -5K/day at the beginning of the far-wake regime, mostly due to the enhanced water abundance. These cooling rates would imply a net sinking of the wakes of about 1.2 km after three days in the limit of no mixing. Calculated mid-latitude column ozone reductions due to emissions from a Mach 2.4 HSCT would then change from about -1% to -06%. However, more realistic calculations adopting moderate mixing for the wake reduce the net sinking to less than 0.2 km, making the impact of radiative subsidence negligible.

Rodriguez, J. M.↗

NASA NTRS2000

Evolution of Rotor Wake in Swirling Flow

A theory is presented for modeling the evolution of rotor wakes as a function of axial distance in swirling mean flows. The theory, which extends an earlier work to include arbitrary radial distributions of mean swirl, indicates that swirl can significantly alter the wake structure of the rotor especially at large downstream distances (i.e., for moderate to large rotor-stator spacings). Using measured wakes of a representative scale model fan stage to define the mean swirl and initial wake perturbations, the theory is used to predict the subsequent evolution of the wakes. The results indicate the sensitivity of the wake evolution to the initial profile and the need to have complete and consistent initial definition of both velocity and pressure perturbations.

El-Haldidi, Basman↗

DOE OSTI2025

A Comparison of Pre‐Construction and Operational Wake Loss Estimates for Land‐Based Wind Plants

The overall bias between pre‐construction energy yield assessment (EYA) estimates of wind plant energy production and the achieved operational production is improving in the wind industry, but uncertainty remains high for individual wind plants. Wake effects within wind plants are one of the largest sources of energy loss considered in the EYA process, and previous work shows wake loss estimates to be a major source of disagreement among wind energy consultants who perform EYAs. To better understand the accuracy of wake loss predictions, we compare overall operational wake loss estimates based on supervisory control and data acquisition data to pre‐construction estimates provided by six wind energy consultants for five land‐based wind plants in North America. By augmenting existing approaches for quantifying operational wake losses, we estimate wake losses during the period of record for which operational data are available as well as the expected long‐term wake losses, based on historical reanalysis weather data, to which the EYA estimates are compared. To account for power variations at different turbine locations caused by terrain‐induced wind resource heterogeneity, we correct the operational wake loss estimates using predicted freestream wind speed variations from the Wind Systems Engineering Reynolds‐averaged Navier–Stokes (RANS) tool. We identify long‐term corrected operational wake losses between 1.9% and 6.4% for the five plants, with a mean loss of 4%. For the project deemed most acceptable for operational wake loss assessment, which is located in the simplest terrain and isolated from neighboring plants, the mean EYA wake loss estimate is within 0.7 percentage points of the operational value of 6.4%. For most of the remaining plants, results suggest that wake losses are generally overpredicted by 2.6–6.3 percentage points. However, operational wake losses may be underestimated for many of these projects because of spatial wind resource variations not captured by the RANS model, external wake effects that are unaccounted for in the estimation process, and wind plant blockage effects. To better understand factors that contribute to the observed wake losses, we investigate operational wake losses as a function of wind direction and wind speed. As expected, wake losses are generally concentrated near wind directions that are aligned with rows of closely spaced turbines and at below‐rated wind speeds; however, for some projects, the energy produced by the wind plant exceeds the estimated potential energy of the plant without wake interactions for certain wind directions and wind speeds, suggesting inaccurate assumptions in the wake loss estimation method for those plants. Lastly, we compare predicted and operational wake losses for individual wind turbines, finding that even when overall wake losses are predicted accurately, large uncertainty exists at the turbine level.

17 WIND ENERGY↗

NASA NTRS1989

Time domain unsteady incompressible cascade airfoil theory for helicopter rotors in hover

A detailed derivation of a finite-time arbitrary-motion incompressible cascade theory is presented for both Laplace and frequency domains. The generalized cascade lift deficiency function is shown to be consistent with the generalized Theodorsen's lift deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity; it also yields a correct value for the zero reduced frequency limit. Efficient numerical procedures are presented for the evaluation of the cascade lift deficiency function. Numerical examples comparing the cascade lift deficiency function with Loewy's (1957) rotary-wing lift deficiency function in frequency domain are presented. Pade approximants of the cascade lift deficiency function are constructed using a Bode plot approach that allows for complex poles. A general-purpose optimization program is used to determine the coefficients of the approximant.

Dinyavari, M. A. H.↗

NASA NTRS1984

Unsteady aerodynamics in time and frequency domains for finite time arbitrary motion of rotary wings in hover and forward flight

Several incompressible finite-time arbitrary-motion airfoil theories suitable for coupled flap-lag-torsional aeroelastic analysis of helicopter rotors in hover and forward flight are derived. These theories include generalized Greenberg's theory, generalized Loewy's theory, and a staggered cascade theory. The generalized Greenberg's and staggered cascade theories were derived directly in Laplace domain considering the finite length of the wake and using operational methods. The load expressions are presented in Laplace, frequency, and time domains. Approximate time domain loads for the various generalized theories, discussed in the paper, are obtained by developing finite state models using the Pade approximant of the appropriate lift deficiency functions. Three different methods for constructing Pade approximants of the lift deficiency functions were considered and the more flexible one was used. Pade approximants of Loewy's lift deficiency function, for various wake spacing and radial location parameters of a helicopter typical rotor blade section, are presented.

Dinyavari, M. A. H.↗

NASA NTRS1976

Numerical studies of three-dimensional breakdown in trailing vortex wakes

The development of dangerous vortex wakes trailing between aircraft for appreciable distance downstream, and posing hazards to following aircraft, is calculated using finite-element three-dimensional relaxation methods. Near-wake, middle-wake, and far-wake conditions are delineated. Vortex system finite lifetimes can be calculated with greater facility owing to the inclusion of a self-induction term in the solution dependent upon local curvature and vortex core radius. Looping and convergence phenomena are studied for single vortex pairs, twin pairs, and multiple pairs. Proportions of flap span and wing span are shown to affect the time to convergence of vortex pairs. The self-induction term renders the convergence time of vortices a sensitive function of wavelength. Wakes trailing between wide-body ('Jumbo') aircraft are also examined.

Hackett, J. E.↗

NASA NTRS1975

On the investigation of cascade and turbomachinery rotor wake characteristics

The objective of the investigation reported in this thesis is to study the characteristics of a turbomachinery rotor wake, both analytically and experimentally. The constitutive equations for the rotor wake are developed using generalized tensors and a non-inertial frame of reference. Analytical and experimental investigation is carried out in two phases; the first phase involved the study of a cascade wake in the absence of rotation and three dimensionality. In the second phase the wake of a rotor is studied. Simplified two- and three-dimensional models are developed for the prediction of the mean velocity profile of the cascade and the rotor wake, respectively, using the principle of self-similarity. The effect of various major parameters of the rotor and the flow geometry is studied on the development of a rotor wake. Laws governing the decay of the wake velocity defect in a cascade and rotor wake as a function of downstream distance from the trailing edge, pressure gradient and other parameters are derived.

Raj, R.↗