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Results for “nonlinear saturation”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Structure in the nonlinear saturation spectrum of parametric instabilities.

The nonlinear saturation spectrum of the decay instability is obtained in the limit of small spontaneous emission, for comparable ion and electron temperatures, from numerical solutions of a kinetic equation based on an accurate expression for the nonlinearity. The spectral energy occupies several pairs of isolated saucer-shaped regions in wave-vector space. The regions increase in thickness, angular diameter, and number as the pump power is increased. The theory thus predicts the generation of waves propagating in directions which can differ substantially from the direction of the pump field. Ionospheric observations confirm this prediction; they were difficult to reconcile with the predictions of previous theories based on an approximated expression for the nonlinearity. The present work also corrects the results of previous one-dimensional theories that used an accurate expression for the nonlinearity and predicted 'spectral lines' in the limit of vanishing spontaneous emission.

Fejer, J. A.↗
DOE OSTI2022

Nonlinear saturation of reverse shear Alfvén eigenmodes induced by kinetic electrons

A strong nonlinear saturation mechanism of the reverse shear Alfvén eigenmode (RSAE) induced by thermal electrons is observed in gyrokinetic $\delta$$f$ particle-in-cell simulation. This nonlinear effect occurs at moderate mode amplitude, $\delta$$B$ ⟂ /$B$ < 10 -3 , and is associated with the electron parallel streaming along the perturbed magnetic field lines, the term v $\|$ $\frac{δΒ_{⟂}}{B}$ ∙ ∇$\delta$$f$, in the electron drift-kinetic equation. In the case of an n = 4 RSAE, where n is the toroidal mode number, this magnetic fluttering nonlinearity leads to strong mode coupling and broadening of the saturation spectrum. The nonlinear components, which are highly damped through the interaction between thermal electrons and the parallel electric field, modifies the RSAE mode structure and suppresses energetic particle drive significantly. The split-weight scheme (Chen and Parker 2007 J. Comput. Phys. 220 839–55) is used to simulate kinetic electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1979

Predicting dynamic performance limits for servosystems with saturating nonlinearities

A generalized treatment for a system with a single saturating nonlinearity is presented and compared with frequency response plots obtained from an analog model of the system. Once the amplitude dynamics are predicted with the limit lines, an iterative technique is employed to determine the system phase response. The saturation limit line technique is used in conjunction with velocity and acceleration limits to predict the performance of an electro-hydraulic servosystem containing a single-stage servovalve. Good agreement was obtained between predicted performance and experimental data.

Webb, J. A., Jr.↗
DOE OSTI2023

Nonlinear saturation of whistler modes driven by runaway electrons

Runaway electrons exhibit kinetic instabilities with potentially beneficial consequences. The anomalous Doppler resonance between the electrons and whistler modes is a primary underlying mechanism. These instabilities require a first-principle nonlinear theoretical analysis, which would ultimately enable assessment of their impact on disruption mitigation and diagnostics, especially in ITER-relevant conditions. This paper presents recent progress in developing the required theoretical framework for isolated nonlinear resonances. By employing the generic bump-on-tail model, we predict the wave saturation levels in both near-threshold and strongly driven regimes. Remarkably, for the waves of interest, the parallel component of the wave vector dictates the parallel momentum of the resonant particles. This feature, together with the expected wave saturation level, provides a complete description of the resonance impact on the runaway electron distribution function. We show that the parametric dependence of the nonlinearly saturated mode provides a way to recover certain features of the runaway momentum distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

Design for performance enhancement in feedback control systems with multiple saturating nonlinearities

A systematic control design methodology is introduced for multi-input/multi-output systems with multiple saturations. The methodology can be applied to stable and unstable open loop plants with magnitude and/or rate control saturations and to systems in which state limitations are desired. This new methodology is a substantial improvement over previous heuristic single-input/single-output approaches. The idea is to introduce a supervisor loop so that when the references and/or disturbances are sufficiently small, the control system operates linearly as designed. For signals large enough to cause saturations, the control law is modified in such a way to ensure stability and to preserve, to the extent possible, the behavior of the linear control design. Key benefits of this methodology are: the modified compensator never produces saturating control signals, integrators and/or slow dynamics in the compensator never windup, the directional properties of the controls are maintained, and the closed loop system has certain guaranteed stability properties. The advantages of the new design methodology are illustrated by numerous simulations, including the multivariable longitudinal control of modified models of the F-8 (stable) and F-16 (unstable) aircraft.

Kapasouris, Petros↗
NASA NTRS1982

Nonlinear saturation spectra of electric fields and density fluctuations in drift wave turbulence

The detection of drift waves in the nonlinear evolution of a space plasma process driven at long wavelengths is considered, adducing measurements of the electric field and density fluctuation power spectra as evidence. Since the driving mechanism is clearly at long wavelengths, the detection of drift waves suggests that they may play an important role in the transfer of wave energy from long to short wavelengths in a low beta plasma. The saturated spectral density is compared with theoretical results in order to estimate the anomalous diffusion rate. The observed spectral form and amplitude is in excellent agreement with drift wave predictions.

Kelley, M. C.↗
DOE OSTI2026

Nonlinear saturation of ballooning modes in stellarators

Ballooning mode saturation is investigated in realistic stellarator configurations using the flux tube approach of Ham et al (2018 Plasma Phys. Control. Fusion 60 075017), Ham et al (2016 Phys. Rev. Lett. 116 235001). The method is adapted to account for the lack of exact force balance in stellarator equilibrium solvers that assume existence of nested flux surfaces. A variational approach for calculating flux tube energy is developed to overcome this force error problem in stellarator numerical equilibria. Saturated (equilibrium) flux tube states that cross 10%–20% of the plasma minor radius are shown to exist for linearly ballooning unstable profiles. It is shown that several features of the displaced flux tube structure in a full nonlinear MHD simulation of Wendelstein 7X are reproduced by our model. Saturated states are found in a compact stellarator equilibrium close but below the marginal ballooning linear instability, i.e. the unperturbed equilibrium is metastable. This suggests that edge-localized-mode-like explosive MHD behavior may be possible in stellarators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1972

Spectral-line structures of saturated parametric instabilities.

The nonlinear saturation spectrum of parametric instabilities is shown to be restricted to discrete values of the propagation vector if spontaneous emission is neglected and a one-dimensional analysis is used. The purely growing instability is not excited for equal ion and electron temperatures if the power is less than 3.5 times the threshold power. The inadequacy of the present one-dimensional treatment is pointed out, and it is shown that waves with propagation vectors that are not parallel to the pump field must be present even if spontaneous emission is neglected.

Kuo, Y.-Y.↗
NASA NTRS2002

The Semicircular Canal Microphonic

Present experiments were designed to quantify the alternating current (AC) component of the semicircular canal microphonic for angular motion stimulation as a function of stimulus frequency and amplitude. The oyster toadfish, Opsanus tau, was used as the experimental model. Calibrated mechanical indentation of the horizontal canal duct was used as a stimulus to generate hair-cell and afferent responses reproducing those present during head rotation. Sensitivity to polarization of the endolymph DC voltage re: perilymph was also investigated. Modulation of endolymph voltage was recorded using conventional glass electrodes and lock-in amplification over the frequency range 0.2-80 Hz. Access to the endolymph for inserting voltage recording and current passing electrodes was obtained by sectioning the anterior canal at its apex and isolating the cut ends in air. For sinusoidal stimulation below approx.10 Hz, the horizontal semicircular canal AC microphonic was nearly independent of stimulus frequency and equal to approximately 4 microV per micron indent (equivalent to approx. 1 microV per deg/s). A saturating nonlinearity decreasing the microphonic gain was present for stimuli exceeding approx.3 micron indent (approx. 12 deg/s angular velocity). The phase was not sensitive to the saturating nonlinearity. The microphonic exhibited a resonance near 30Hz consistent with basolateral current hair cell resonance observed previously in voltage-clamp records from semicircular canal hair cells. The magnitude and phase of the microphonic exhibited sensitivity to endolymphatic polarization consistent with electro-chemical reversal of hair cell transduction currents.

Rabbitt, R. D.↗
NASA NTRS1989

Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities

The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation-theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave-wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the prturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave-wave resonance condition which, in turn, causes the wave amplitude to cease its growth.

Hoshino, M.↗
NASA NTRS1960

The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity

A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case.

Schmidt, Stanley F.↗
DOE OSTI2021

A modal wave-packet model for the multi-mode Richtmyer–Meshkov instability

In this work, a model for multimode perturbations subject to the Richtmyer–Meshkov (RM) instability is presented and compared with simulations and experiments for conditions relevant to inertial confinement fusion. The model utilizes the single mode response to the RM impulse whereby its amplitude h(k, t) first grows with an initial velocity V 0 ∝ kh(k, 0) that eventually decays in time as 1/kV 0 t. Both the growth and saturation stages are subject to nonlinearities since they depend explicitly on the initial amplitude. However, rather than using the individual mode amplitude h(k, t), nonlinearity is taken to occur when the root-mean-square amplitude h rms (k, t) of a wave-packet within wavenumbers k ± δk becomes comparable to 1/k. This is done because nearby sidebands can act in unison for an auto-correlation distance 1/δk beyond nonlinearity as observed in the beam-plasma instability. Thus, the nonlinear saturation amplitude for each mode is reduced from the usual 1/k by a phase space factor that depends on the physical dimensionality, as in the Haan model for the Rayleigh–Taylor instability. In addition, for RM, the average value of kh rms for the initial spectrum is used to calculate a nonlinear factor F NL that reduces V 0 , as observed for single modes. For broadband perturbations, the model describes self-similar growth ∝t θ as successively longer wavelength modes reach saturation. The growing and saturated modes must be discerned because only the former promote θ and are enhanced by reshock and spherical convergence. All of these flows are described here by the model in good agreement with simulations and experiments.

42 ENGINEERING↗
NASA NTRS1974

The saturation spectrum of parametric instabilities

Recent calculations on the nonlinear saturation spectrum of the parametric decay instability are described. The initial calculations did not use the correct expression for the spontaneous emission term and were aimed at obtaining the distribution of spectral energy in the unstable part of wave vector space. Results of those initial calculations are combined here with the correct expression for the spontaneous emission term to obtain the distribution of spectral energy in the stable part of wave vector space. These latter calculations are believed to be relevant to the interpretation of the so called plasma line spectra obtained in ionospheric heating experiments at Arecibo, Puerto Rico.

Fejer, J. A.↗
NASA NTRS1981

Chaotic /strange/ and periodic behavior in instability saturation by the oscillating two-stream instability

The nonlinear Schroedinger equation with linear growth and damping is truncated to three waves. The resulting system of nonlinear ordinary differential equations describes the excitation of linearly damped waves by the oscillating two-stream instability driven by a linearly unstable pump wave. This system represents a simple model for the nonlinear saturation of a linearly unstable wave. The model is examined analytically and numerically as a function of the dimensionless parameters of the system. It is found that the model can exhibit a wealth of characteristic dynamical behavior including stationary equilibria, Hopf bifurcations to periodic orbits, period doubling bifurcations, chaotic solutions characteristic of a strange attractor, tangent bifurcations from chaotic to periodic solutions, transient chaos, and hysteresis. Many of these features are shown to be explainable on the basis of one-dimensional maps. In the case of chaotic solutions, evidence for the presence of a strange attractor is provided by demonstrating Cantor set-like structure (i.e., scale invariance) in the surface of section.

Russell, D. A.↗