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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 343 records · Page 19

Nonlinear wave particle interaction in the Earth's foreshock

The possibility that ion beams could provide a free energy source for driving an ion/ion instability responsible for the ULF wave occurrence is investigated. For this, the wave dispersion relation with the observed parameters is solved. Secondly, it is shown that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered around a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions with the observations are compared.

Mazelle, C.↗

Maneuver simulations of flexible spacecraft by solving TPBVP

The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.

Bainum, Peter M.↗

Gradient-based constrained optimization using a database of linear reduced-order models

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential Equation (PDE). A key component of this methodology is the construction, during an offline phase, of a database of pointwise, linear, Projection-based Reduced-Order Models (PROM)s associated with a design parameter space and the linear PDE(s). A parameter sampling procedure based on an appropriate saturation assumption is proposed to maximize the efficiency of such a database of PROMs. A real-time method is also presented for interpolating at any queried but unsampled parameter vector in the design parameter space the relevant sensitivities of a PROM. The practical feasibility, computational advantages, and performance of the proposed methodology are demonstrated for several realistic, nonlinear, aerodynamic shape optimization problems governed by linear aeroelastic constraints.

97 MATHEMATICS AND COMPUTING↗

On the Behavior of Three-dimensional Wave Packets in Viscously Spreading Mixing Layers

We consider analytically the evolution of a three-dimensional wave packet generated by an impulsive source in a mixing layer. The base flow is assumed to be spreading due to viscous diffusion. The analysis is restricted to small disturbances (linearized theory). A suitable high-frequency ansatz is used to describe the packet; the key elements of this description are a complex phase and a wave action density. It is found that the product of this density and an infinitesimal material volume convecting at the local group velocity is not conserved: there is a continuous interaction between the base flow and the wave action. This interaction is determined by suitable mode-weighted averages of the second and fourth derivatives of the base-flow velocity profile. Although there is some tendency for the dominant wave number in the packet to shift from the most unstable value toward the neutral value, this shift is quite moderate. In practice, wave packets do not become locally neutral in a diverging base flow (as do instability modes), therefore, they are expected to grow more suddenly than pure instability modes and do not develop critical layers. The group velocity is complex; the full significance of this is realized by analytically continuing the equations for the phase and wave action into a complex domain. The implications of this analytic continuation are discussed vis-a-vis the secondary instabilities of the packet: very small scale perturbations on the phase can grow very rapidly initially, but saturate later because most of the energy in these perturbations is convected away by the group velocity. This remark, as well as the one regarding critical layers, has consequences for the nonlinear theories.

Balsa, Thomas F.↗

Kinetic-ballooning-mode turbulence in low-average-magnetic-shear equilibria

In this work, kinetic-ballooning-mode (KBM) turbulence is studied via gyrokinetic flux-tube simulations in three magnetic equilibria that exhibit small average magnetic shear: the Helically Symmetric eXperiment (HSX), the helical-axis Heliotron-J and a circular tokamak geometry. For HSX, the onset of KBM being the dominant instability at low wavenumber occurs at a critical value of normalized plasma pressure $\beta ^{\rm KBM}_{\rm crit}$ that is an order of magnitude smaller than the magnetohydrodynamic (MHD) ballooning limit $\beta ^{\rm MHD}_{\rm crit}$ when a strong ion temperature gradient (ITG) is present. However, $\beta ^{\rm KBM}_{\rm crit}$ increases and approaches the MHD ballooning limit as the ITG tends to zero. For these configurations, $\beta ^{\rm KBM}_{\rm crit}$ also increases as the magnitude of the average magnetic shear increases, regardless of the sign of the normalized magnetic shear. Simulations of Heliotron-J and a circular axisymmetric geometry display behaviour similar to HSX with respect to $\beta ^{\rm KBM}_{\rm crit}$ . Despite large KBM growth rates at long wavelengths in HSX, saturation of KBM turbulence with $\beta > \beta _{\rm crit}^{\rm KBM}$ is achievable in HSX and results in lower heat transport relative to the electrostatic limit by a factor of roughly five. Nonlinear simulations also show that KBM transport dominates the dynamics when KBMs are destabilized linearly, even if KBM growth rates are subdominant to ITG growth rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonlinear dynamic theory for photorefractive phase hologram formation

A nonlinear dynamic theory is developed for the formation of photorefractive volume phase holograms. A feedback mechanism existing between the photogenerated field and free-electron density, treated explicitly, yields the growth and saturation of the space-charge field in a time scale characterized by the coupling strength between them. The expression for the field reduces in the short-time limit to previous theories and approaches in the long-time limit the internal or photovoltaic field. Additionally, the phase of the space charge field is shown to be time-dependent.

Kim, D. M.↗

Simulations of ion cyclotron anisotropy instabilities in the terrestrial magnetosheath

Enhanced transverse magnetic fluctuations observed below the proton cyclotron frequency in the terrestrial magnetosheath have been identified as due to the proton cyclotron and helium cyclotron instabilities driven by the T-perpendicular greater than T-parallel condition of the sheath ions. One-dimensional hybrid computer simulations are used here to examine the nonlinear properties of these two growing modes at relatively weak fluctuation energies and for wave vectors parallel to the background magnetic field. Second-order theory predicts fluctuating magnetic field energies at saturation of the proton cyclotron anisotropy instability in semiquantitative agreement with the simulation results. Introduction of the helium component enhances the wave-particle exchange rate for proton anisotropy reduction by that instability, thereby reducing the saturation energy of that mode. The simulations demonstrate that wave-particle interactions by the proton cyclotron and helium cyclotron instabilities lead to the anticorrelation observed by Anderson and Fuselier (1993).

Gary, S. P.↗

Ultrafast electron dynamics of graphene quantum dots: High harmonic generation

We study theoretically nonlinear optical properties of graphene quantum dots placed in a field of a short and strong linearly polarized optical pulse. We address the problem of high harmonic generation in quantum dots and how such nonlinear effect is affected by dephasing processes in a quantum dot. The dephasing makes the ultrafast electron dynamics more irreversible with a large residual population of the excited quantum dot levels. In relation to the high-harmonic spectrum, with increasing the dephasing time, the intensities of the low-frequency harmonics increase while the cutoff energy decreases. The dependence of the cutoff energy on the amplitude of the optical pulse is also sensitive to the frequency of the pulse. When the frequency of the optical pulse is much less than the quantum dot band gap, this dependence is almost linear, but when the frequency of the pulse is comparable to the band gap, the cutoff energy shows saturation behavior at large field amplitude, >0.4 V/Å.

36 MATERIALS SCIENCE↗

Numerical comparison of strong Langmuir turbulence models

Two models of Langmuir turbulence, the nonlinear Schroedinger equation and the Zakharov equations, are solved numerically for an initial value problem in which the electric field evolves from an almost flat initial condition via the modulational instability and finally saturates into a set of solitons. The two models agree well with each other only when the initial dimensionless electric field has an amplitude less than unity. An analytic soliton gas model consisting of equal-amplitude, randomly spaced, zero-speed solitons is remarkably good at reproducing the time-averaged Fourier spectra in both cases.

Shen, Mei-Mei↗

Not all that is β0 is β-function: the DGLAP resummation and the running coupling in NLO JIMWLK

Abstract We reanalyze the origin of the large transverse logarithms associated with the QCD one loopβfunction coefficient in the NLO JIMWLK Hamiltonian. We show that some of these terms are not associated with the running of the QCD coupling constant but rather with the DGLAP evolution. The DGLAP-like resummation of these logarithms is mandatory within the JIMWLK Hamiltonian, as long as the color correlation length in the projectile is larger than that in the target. This regime in fact covers the whole range of rapidities at which JIMWLK evolution is supposed to be applicable. We derive the RG equation that resums these logarithms to all orders inα s in the JIMWLK Hamiltonian. This is a nonlinear equation for the eikonal scattering matrixS(x). We solve this equation, and perform the DGLAP resummation in two simple cases: the dilute limit, where both the projectile and the target are far from saturation, and the saturated regime, where the target correlation length also determines its saturation momentum.

Physics↗

Phenomenological model of the third-harmonic magnetic response due to superconducting fluctuations: Application to Sr 2 RuO 4

Here, we employ the phenomenological Lawrence-Doniach model to compute the contributions of the superconducting fluctuations to the third-harmonic magnetic response, denoted here by $\bar{M_3}$, which can be measured in a precise way using ac magnetic fields and lock-in techniques. We show that, in an intermediate temperature regime, this quantity behaves as the third-order nonlinear susceptibility, which shows a power-law dependence with the reduced temperature ε = $\frac{T-T_c}{T_c}$ as ε -5/2 . Very close to T c , however, $\bar{M_3}$ saturates due to the nonzero amplitude of the ac field. We compare our theoretical results with experimental data for three conventional superconductors—lead, niobium, and vanadium—and for the unconventional superconductor Sr 2 RuO 4 (SRO). We find good agreement between theory and experiment for the elemental superconductors, although the theoretical values for the critical field systematically deviate from the experimental ones. In the case of SRO, however, the phenomenological model completely fails to describe the data, as the third-harmonic response remains sizable over a much wider reduced temperature range compared to Pb, Nb, and V. We show that an inhomogeneous distribution of T c across the sample can partially account for this discrepancy, since regions with a locally higher T c contribute to the fluctuation $\bar{M_3}$ significantly more than regions with the “nominal” T c of the clean system. However, the exponential temperature dependence of $\bar{M_3}$ first reported by Pelc et al. [Nat. Commun. 10, 2729 (2019)] is not captured by the model with inhomogeneity. We conclude that, while inhomogeneity is an important ingredient to understand the superconducting fluctuations of SRO and other perovskite superconductors, additional effects may be at play, such as non-Gaussian fluctuations or rare-region effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nonlinear theory of type I irregularities in the equatorial electrojet

By allowing for the effect of wave electric fields on electron orbits, a nonlinear dispersion relation for type I irregularities is obtained. This relation predicts (1) isotropy of the Doppler shift with elevation, (2) a limiting phase velocity equal to the ion acoustic speed, and (3) a saturation amplitude which is maximum for horizontally propagating waves and decreases with elevation. With the theory presented here, the in situ electric field measurements of Pfaff et al. (1980) in the electrojet environment could provide a quantitative check for the theory of orbit diffusion by stochastic electric fields.

Sudan, R. N.↗

Nonlinear mode coupling theory of the lower-hybrid-drift instability

A nonlinear mode coupling theory of the lower-hybrid-drift instability is presented. A two-dimensional nonlinear wave equation is derived which describes lower-hybrid drift wave turbulence in the plane transverse to B (k.B = 0), and which is valid for finite beta, collisional and collisionless plasmas. The instability saturates by transferring energy from growing, long wavelength modes to damped, short wavelength modes. Detailed numerical results are presented which compare favorably to both recent computer simulations and experimental observations. Applications of this theory to space plasmas, the earth's magnetotail and the equatorial F region ionosphere, are discussed. Previously announced in STAR as N84-17734

Drake, J. F.↗

Effect of radial pressure corrugations and profile shearing on turbulence in Fusion plasmas

Microturbulence can produce stationary fine-scale radial corrugations on the plasma density and temperature gradients in magnetic confinement fusion devices. We show that these structures play a significant role in regulating turbulent transport. We focus on the pedestal, studying electron-temperature-gradient (ETG) mode destabilisation and saturation in the presence of radial corrugations on the electron temperature gradient that could result from microtearing turbulence. A linear dispersion relation is derived for a shearless slab case, which indicates that in the presence of a sinusoidal background corrugation, each ETG mode splits into three distinct eigenvalues, with one being the original, one being more unstable and one being less unstable. However, despite the presence of more unstable linear modes, nonlinear gyrokinetic simulations of ETG with corrugated background electron temperature show a reduction of fluxes. Our investigation reveals a radial variation of the phase velocity of the modes that is proportional to the diamagnetic drift velocity and the local pressure gradient. The associated profile shearing breaks the turbulent eddies apart, reducing the transport level. This profile shearing resulting from fine-scale pressure corrugations could be a ubiquitous turbulence saturation mechanism not just in Fusion plasmas, but in Astrophysics and other areas.

FOS: Physical sciences↗

Viscous effects on plasmoid formation from nonlinear resistive tearing growth in a Harris sheet

Abstract In this work, the evolution of a highly unstable m = 1 resistive tearing mode, leading to plasmoid formation in a Harris sheet, is studied in the framework of full MHD model using the Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion simulation. Following the initial nonlinear growth of the primary m = 1 island, the X-point develops into a secondary elongated current sheet that eventually breaks into plasmoids. Two distinctive viscous regimes are found for the plasmoid formation and saturation. In the low viscosity regime (i.e. P r ≲ 1), the plasmoid width increases sharply with viscosity, whereas in the viscosity dominant regime (i.e. P r ≳ 1), the plasmoid size gradually decreases with viscosity. Such a finding quantifies the role of viscosity in modulating the plasmoid formation process through its effects on the plasma flow and the reconnection itself.

Physics↗

Safe microburst penetration techniques: A deterministic, nonlinear, optimal control approach

A relatively large amount of computer time was used for the calculation of a optimal trajectory, but it is subject to reduction with moderate effort. The Deterministic, Nonlinear, Optimal Control algorithm yielded excellent aircraft performance in trajectory tracking for the given microburst. It did so by varying the angle of attack to counteract the lift effects of microburst induced airspeed variations. Throttle saturation and aerodynamic stall limits were not a problem for the case considered, proving that the aircraft's performance capabilities were not violated by the given wind field. All closed loop control laws previously considered performed very poorly in comparison, and therefore do not come near to taking full advantage of aircraft performance.

Psiaki, Mark L.↗

Experimental study of outdoor propagation of spherically speading periodic acoustic waves of finite amplitude

The outdoor propagation of spherically spreading sound waves of finite amplitude was investigated. The main purpose of the experiments was to determine the extent to which the outdoor environment, mainly random inhomogeneity of the medium, affects finite amplitude propagation. Periodic sources with fundamental frequencies in the range 6 to 8 kHz and source levels SPLlm from 140 to 149 dB were used. The sources were an array of 7 to 10 horn drivers and a siren. The propagation path was vertical and parallel to an 85 m tower, whose elevator carried the traveling microphone. The general conclusions drawn from the experimental results were as follows. The inhomogeneities caused significant fluctuations in the instantaneous acoustic signal, but with sufficient time averaging of the measured harmonic levels, the results were comparable to results expected for propagation in a quiet medium. Propagation data for the fundamental of the siren approached within 1 dB of the weak shock saturation levels. Extra attenuation on the order of 8 dB was observed. The measurements generally confirmed the predictions of several theoretical models. The maximum propagation distance was 36 m. The narrowbeam arrays were much weaker sources. Nonlinear propagation distortion was produced, but the maximum value of extra attenuation measured was 1.5 dB. The maximum propagation distance was 76 m. The behavior of the asymetric waveforms received in one experiment qualitatively suggested that beam type diffraction effects were present. The role of diffraction of high intensity sound waves in radiation from a single horn was briefly investigated.

Theobald, M. A.↗