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Results for “modulational instability”

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NASA NTRS1998

Constraints on Nonlinear and Stochastic Growth Theories for Type 3 Solar Radio Bursts from the Corona to 1 AU

Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for modulational instability or parametric decay to proceed in type III sources at any heliocentric distance: theories for type III bursts based on modulational instability or parametric decay are therefore not viable in general. In contrast, the constraint on SGT can be satisfied and random phase ES decay can proceed at all heliocentric distances under almost all circumstances. (The contrary circumstances involve unusually slow, broad beams moving through unusually hot regions of the Corona.) The analyses presented here strongly justify extending the existing SGT-based model for interplanetary type III bursts (which includes SGT physics, random phase ES decay, and specific electromagnetic emission mechanisms) into a general theory for type III bursts from the corona to beyond 1 AU. This extended theory enjoys strong theoretical support, explains the characteristics of specific interplanetary type III bursts very well, and can account for the detailed dynamic spectra of type III bursts from the lower corona and solar wind.

Cairns, Iver H.↗

NASA NTRS1998

Evidence for Langmuir Envelope Solitons in Solar Type III Burst Source Regions

We present observational evidence for the generation of Langmuir envelope solitons in the source regions of solar type III radio bursts. The solitons appear to be formed by electron beams which excite either the modulational instability or oscillating two-stream instability (OTSI). Millisecond data from the Ulysses Unified Radio and Plasma Wave Experiment (URAP) show that Langmuir waves associated with type III bursts occur as broad intense peaks with time scales ranging from 15 to 90 milliseconds (6 - 27 km). These broad field structures have the properties expected of Langmuir envelope solitons, viz.: the normalized peak energy densities, W(sub L)/n(sub e)T(sub e) approximately 10(exp -5), are well above the modulational instability threshold; the spatial scales, L, which range from 1 - 5 Langmuir wavelengths, show a high degree of inverse correlation with (W(sub L)/n(sub e)T(sub e))(sup 1/2); and the observed widths of these broad peaks agree well with the predicted widths of envelope solitons. We show that the orientation of the Langmuir field structures is random with respect to the ambient magnetic field, indicating that they are probably isotropic structures that have evolved from initially pancake-like solitons. These observations suggest that strong turbulence processes, such as the modulational instability or the OTSI, stabilize the electron beams that produce type III bursts.

Thejappa, G.↗

NASA NTRS1984

Solitons versus parametric instabilities during ionospheric heating

Various effects associated with ionospheric heating are investigated by numerically solving the modified Zakharov (1972) equations. It is shown that, for typical ionospheric parameters, the modulational instability is more important than the parametric decay instability in the spatial region of strongest heater electric field. It is concluded that the modulational instability leads to the formation of solitons, as originally predicted by Petviashvili (1976).

Nicholson, D. R.↗

NASA NTRS2012

In Situ Detection of Strong Langmuir Turbulence Processes in Solar Type III Radio Bursts

The high time resolution observations obtained by the WAVES experiment of the STEREO spacecraft in solar type III radio bursts show that Langmuir waves often occur as intense localized wave packets. These wave packets are characterized by short durations of only a few ms and peak intensities, which well exceed the supersonic modulational instability (MI) thresholds. These timescales and peak intensities satisfy the criterion of the solitons collapsed to spatial scales of a few hundred Debye lengths. The spectra of these wave packets consist of primary spectral peaks corresponding to beam-resonant Langmuir waves, two or more sidebands corresponding to down-shifted and up-shifted daughter Langmuir waves, and low frequency enhancements below a few hundred Hz corresponding to daughter ion sound waves. The frequencies and wave numbers of these spectral components satisfy the resonance conditions of the modulational instability (MI). Moreover, the tricoherences, computed using trispectral analysis techniques show that these spectral components are coupled to each other with a high degree of coherency as expected of the MI type of four wave interactions. The high intensities, short scale lengths, sideband spectral structures and low frequency spectral enhancements and, high levels of tricoherences amongst the spectral components of these wave packets provide unambiguous evidence for the supersonic MI and related strong turbulence processes in type III radio bursts. The implication of these observations include: (1) the MI and related strong turbulence processes often occur in type III source regions, (2) the strong turbulence processes probably play very important roles in beam stabilization as well as conversion of Langmuir waves into escaping radiation at the fundamental and second harmonic of the electron plasma frequency, fpe, and (3) the Langmuir collapse probably follows the route of MI in type III radio bursts.

Langmuir↗

NASA NTRS1994

Beat, modulational, and decay instabilities of a circularly polarized Alfven wave

A circulary polarized low-frequency electomagnetic pump wave propoagating along an ambient magnetic field is known to be unstable to the growth of several parallel-propagating parametric instabilties. If ion-cyclotron effects are retained in a two-fluid description, the dispersion relation is a sixth-order polynomial. We present a series of new analytical approximations to this dispersion relation. We emphasize new results for the beat instability that occurs as an interaction of the forward prpagating upper sideband with the backward propagating lower sideband. The nature of the beat instabitlity depends on beta = (v(sub sound)/v(sub A)(exp 2) and on the sense of polarization of the pump wave. The beat and decay instabilities can occur together if the pump is left-handed (i.e., ion resonant) and if beta is less than or approximately 1, but they cannot occur together if the pump is right-handed. For a left-handed pump the beat mode is the only instability if beta is greater than or approximately 1. If the pump is right-handed and beta is greater than or approximately 1, then the beat instability exists only when the pump amplitude exceeds a threshold value, and the beat will be the only instability if the pump amplitude is large enough to stabilize the modulational instability. If the pump is left-handed and beta is less than or approximately 1, then the beat mode is stabilized when the pump amplitude becomes sufficiently large. The beat instability primarily produces a forward propagating transverse wave in the upper sideband. Thus if beta is greater than or approximately 1, the instabilities considered here do not produce the backward propagating waves which are thought to affect turbulence and the evolution of cross helicity in the solar wind. New analytical results are presented also for the decay and modulational instabilites when beta is approximately equal to 1.

Hollweg, Joseph V.↗

DOE OSTI2020

Structure formation in turbulence as an instability of effective quantum plasma

Structure formation in turbulence can be understood as an instability of “plasma” formed by fluctuations serving as effective particles. These “particles” are quantumlike in the sense that their wavelengths are non-negligible compared to the sizes of background coherent structures. The corresponding “kinetic equation” describes the Wigner matrix of the turbulent field, and the coherent structures serve as collective fields. This formalism is usually applied to manifestly quantumlike or scalar waves. Here, we show how to systematically extend it to more complex systems using compressible Navier–Stokes turbulence as an example. In this case, the fluctuation Hamiltonian is a five-dimensional matrix operator and diverse modulational modes are present. As an illustration, we calculate these modes for a sinusoidal shear flow and find two modulational instabilities. One of them is specific to supersonic flows, and the other one is a Kelvin–Helmholtz-type instability that is a generalization of the known zonostrophic instability. Our calculations are readily extendable to other types of turbulence, for example, magnetohydrodynamic turbulence in plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Pseudospectral Landau-Lifshitz description of magnetization dynamics

Magnetic materials host a wealth of nonlinear dynamics, textures, and topological defects. This is possible due to the competition between strong nonlinearity and dispersion, which act at the atomic scale, as well as long-range interactions. However, these features are difficult to study analytically and numerically because of the vastly different temporal and spatial scales involved. Here, in this work, we present a pseudospectral approach for the Landau-Lifshitz equation that invokes energy and momentum conservation embodied in the magnon dispersion relation to accurately describe both atomic and continuum limits. Furthermore, this approach enables analytical study at every scale. We show the applicability of this model in both the continuum and atomic limit by investigating modulational instability and ultrafast evolution of magnetization due to transient grating, respectively, in a one-dimensional ferromagnetic chain with perpendicular magnetic anisotropy. This model provides the possibility of grid-independent multiscale numerical approaches that will enable the description of singularities within a single framework.

1-dimensional spin chains↗

DOE OSTI2021

Suppression of power losses during laser pulse propagation in underdense plasma slab

For current state-of-the-art terawatt lasers, the primary laser scattering mechanisms in plasma include Forward Raman Scattering (FRS), excitation of plasma waves, and the self-modulational instability (SMI). Using 2D PIC simulations, we demonstrate the dominance of the FRS in the regime with medium-to-low density plasma and non-relativistic laser fields. However, the use of multi-colored lasers with frequency detuning exceeding the plasma frequency, Δω > ω pe , suppresses the FRS. Finally, the laser power can then be transmitted efficiently.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Power Solitons in Inverter-based Electric Energy Systems: Observation, Analysis and Implications

The discovery of an unfamiliar class of nonlinear energy waves in electric energy systems with dominating coupled inverter-based energy resources has been reported in a recent research project. Whenever there are slight but persistent differences among the reference signals used by inverters in pulse-width modulation, i.e., a weak group modulation instability condition, the unfamiliar energy waves appear, which contain not only the familiar frequency components present in electric power systems but also self-organized components in the ultra-high frequency region of the energy spectrum. These components are found to be exploding solitary waves with concentrated energy masses, hence we call them power solitons. This paper explains the work of the discovery reported, and the implications of the presence of power solitons for grid integration of inverter-based resources and power system protection.

14 SOLAR ENERGY↗

NASA NTRS1993

Lower hybrid turbulence at cometary bow wave and acceleration of cometary protons

The wave measurements at the spacecraft encounters with Comet Halley have shown intense wave activity at the lower hybrid frequency. The excitation of the lower hybrid instability by the pickup cometary ions (protons and water group) in the bow wave region and the quasi-linear diffusion of the ions in these fluctuations are discussed. The quasi-linear diffusion of the pickup protons takes place over a scale length shorter than that of the heavier water group ions. This enhances damping of the waves by protons, and when the pickup proton density is large enough, it can result in the saturation of the instability as this damping balances the heavy ion driven growth. The observed electric field amplitude and the scale length of proton relaxation are in agreement with the theory. For small pickup proton density the instability can saturate due to the wave energy cascade arising from the modulation instability of the large-amplitude lower hybrid waves. This saturation mechanism leads to electron acceleration and suprathermal tail formation.

Shapiro, V. D.↗

NASA NTRS1988

Filamentation instability of large-amplitude Alfven waves

An instability that leads to the filamentation of large-amplitude Alfven waves and gives rise to purely growing density and magnetic field fluctuations is studied. The dispersion relation of the instability is derived, from which the threshold conditions and the growth rates of the instability are analyzed quantitatively for applications to the solar wind plasma. Their dependence on the filamentation spectrum, the plasma beta, and the pump frequency and intensity was examined for both right-hand and left-hand circularly polarized Alfven waves. The excitation of filamentation instability for certain cases of interest is discussed and compared with that of the parametric decay and modulation instability. The relevance of the proposed instability to some observations is discussed.

Kuo, S. P.↗

DOE OSTI2020

Rayleigh–Taylor Instability With Varying Periods of Zero Acceleration

We present our findings from a numerical investigation of the acceleration-driven Rayleigh–Taylor Instability, modulated by varying periods without an applied acceleration field. It is well known from studies on shock-driven Richtmyer–Meshkov instability that mixing without external forcing grows with a scaling exponent as ≈ t 0.20-0.28 When the Rayleigh–Taylor Instability is subjected to varying periods of “zero” acceleration, the structural changes to the mixing layer remain remarkably small. After the acceleration is re-applied, the mixing layer quickly resumes the profile of development it would have had if there had been no intermission. As a result, this behavior contrasts in particular with the strong sensitivity that is found to other variable acceleration profiles examined previously in the literature.

42 ENGINEERING↗

DOE OSTI2025

On reduced modelling of the modulational dynamics in magnetohydrodynamics

This paper explores structure formation in two-dimensional magnetohydrodynamic (MHD) turbulence as a modulational instability (MI) of turbulent fluctuations. We focus on the early stages of structure formation and consider simple backgrounds that allow for a tractable model of the MI while retaining the full chain of modulational harmonics. This approach allows us to systematically examine the validity of popular closures such as the quasilinear approximation and other low-order truncations. We find that, although such simple closures can provide quantitatively accurate approximations of the MI growth rates in some regimes, they can fail to capture the modulational dynamics in adjacent regimes even qualitatively, falsely predicting MI when the system is actually stable. We find that this discrepancy is due to the excitation of propagating spectral waves (PSWs) which can ballistically transport energy along the modulational spectrum, unimpeded until dissipative scales, thereby breaking the feedback loops that would otherwise sustain MIs. The PSWs can be self-maintained as global modes with real frequencies and drain energy from the primary structure at a constant rate until the primary structure is depleted. To describe these waves within a reduced model, we propose an approximate spectral closure that captures them and MIs on the same footing. We also find that introducing corrections to ideal MHD, conservative or dissipative, can suppress PSWs and reinstate the accuracy of the quasilinear approximation. In this sense, ideal MHD is a ‘singular’ system that is particularly sensitive to the accuracy of the closure within mean-field models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Thermal Weibel instability induced magnetic fields co-exist with linear wakes in laser-ionized plasmas

When a moderately intense, few-picosecond-long laser pulse ionizes gas to produce an underdense plasma column, a linear relativistic plasma wave or wake can be excited by the self-modulation instability that may prove useful for multi-bunch acceleration of externally injected electrons or positrons to high energies in a short distance. At the same time, due to the anisotropic temperature distributions of the ionized plasma electrons, the Weibel instability can self-generate magnetic fields throughout such a plasma on a few picoseconds timescale that can persist even longer than the lifetime of the wake. In the present paper, we first show using simulations that both these effects do indeed co-exist in space and time in the plasma. Using our simulations, we make preliminary estimates of the contribution to the transverse emittance growth of an externally injected beam due to the Weibel magnetic fields in a few-millimeter-long plasma. We then present the results of an experiment that has allowed us to measure the spatiotemporal evolution of the magnetic fields using an ultrashort relativistic electron probe beam. Both the topology and the lifetime of the Weibel instability induced magnetic fields in the experiment are in reasonable agreement with the fields induced by the Weibel instability in the simulations.

43 PARTICLE ACCELERATORS↗

NASA NTRS1987

Simulation of amplitude-modulated circularly polarized Alfven waves for beta less than one

The nonlinear properties of the amplitude-modulated circularly polarized Alfven wave are studied for beta less than one. The temporal behavior of the wave packet of the electromagnetic hybrid simulation is compared with a numerical solution of the derivative nonlinear Schroedinger (DNLS) equation. It is shown that the left-hand-polarized mode evolves into a shocklike structure due to the modulational instability. However, both cyclotron damping and a snowplow effect near the steepened wave packet suppress its further steepening, contrary to the predictions of the DNLS equation. For the right-hand mode, formation of the shock does not take place, and the initial time development is well described by the DNLS equation. The daughter Alfven wave and ion acoustic waves are excited due to the decay instability at a later time. Heating or acceleration of the particles takes place for both left- and right-hand waves. Energy transfer from the wave to the particles occurs effectively when substantial modulation in the wave amplitude is present.

Machida, S.↗

NASA NTRS1990

Plasma waves associated with the space shuttle

Water molecules outgassed from the Space Shuttle suffer collisional charge-exchange with ionospheric oxygen ions, thereby forming unstable distributions of pick-up water ions and leading to high levels of plasma waves near the Shuttle. Liouville's equation with a charge-exchange source term is solved for the water ion distribution function as a function of position relative to the Shuttle. The observational characteristics of the near zone Shuttle waves are summarized. A linear theory in which beam like distributions of water ions drive Doppler shifted lower hybrid waves via the modified two stream instability is developed. This theory explains many characteristics of the near zone waves. Further work on the effects of wave nonlinearities and spatial inhomogeneity is required to explain the detailed frequency spectrum of the waves. The observed wave levels apparently satisfy the threshold condition for modulational instability of lower hybrid waves.

Cairns, I. H.↗

NASA NTRS1999

Whistler Solitons in Plasma with Anisotropic Hot Electron Admixture

The longitudinal and transverse modulation instability of whistler waves in plasma, with a small admixture of hot anisotropic electrons, is discussed. If the hot particles temperature anisotropy is positive, it is found that, in such plasma, longitudinal perturbations can lead to soliton formation for frequencies forbidden in cold plasma. The soliton is enriched by hot particles. The frequency region unstable to transverse modulation in cold plasma in the presence of hot electrons is divided by stable domains. For both cases the role of hot electrons is more significant for whistlers with smaller frequencies.

Khazanov, G. V.↗

NASA NTRS1999

Whistler Solitons in Plasma with Anisotropic Hot Electron Admixture

Khazanov, G. V.↗