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The relativistic interaction of a charged particle with obliquely propagating waves of arbitrary polarization is considered. It is shown that an arbitrarily small wave packet composed of waves with parallel phase velocity comparable to the speed of light (e.g., slow extraordinary mode) can, under certain conditions, accelerate particles to unlimited energy through a process of Arnold'd diffusion in two dimensions.
We present Polar plasma wave data during cusp energetic particle (CEP) events at 6-9 R(sub E). These data suggest the presence of coherent electrostatic structures that are highly localized and that have typical velocities on the order of hundreds to thousands of kilometers per second along the ambient magnetic field. Some of the wave signatures are solitary waves and some are wave packets. The Polar wave instrument also provides evidence that some of the bursts of electromagnetic waves (with frequencies of a few hundred Hz and just below the electron cyclotron frequency around 800 Hz to 1-2 kHz) that are observed are coher&nt and propagating both up and down the field lines. Electron cyclotron harmonic (ECH) waves are often detected but their duration is usually short (less than 1 second). Low Frequency (less than 1 kHz), broadband, bursty electromagnetic waves are also present. The Polar wave data results are used to obtain a better understanding of the macro/microphysics during a CEP event that takes place on September 11, 1996, by correlating various Polar (approximately 7.0 R(sub E)) and Akebono (approximately 1.4 R(sub E)) data while both spacecraft are in or near the cusp/cleft region and nearly on the same field line, and magnetometer data from the Canadian Intermagnet and Canopus ground stations, which lie near the base of the magnetic footprint passing through Polar. Solar wind and magnetic field data from the interplanetary medium and magnetosheath are provided by the Geotail and IMP-8 satellites, respectively. Some of the cusp waves may be indicators of the reconnection process taking place through the cusp, the result of mixing of magnetosheath with magnetospheric plasma, and the consequence of an anisotropic electron population in a depressed magnetic field. The low frequency electromagnetic waves are still under study to determine their role, if any, in the heating and acceleration of the MeV He ions during CEP events.
An experimental study of the transitional flow on a flat disk, rotating in still air, has been conducted. Using digitized hot-wire data, the axes of the stationary spiral vortices, which are the primary instability mechanism for the disk flow, have been mapped-out in terms of both spatial coordinates and velocity fluctuations. Data are presented for a clean disk and for a disk with a single, isolated roughness element. The data show that the disk vortices are generated at discrete roughness disturbance sites on the disk and that they propagate and grow as wave packets. The familiar vortex pattern of 30 or so vortices results only when these wave packets have merged and filled the entire circumference. The appearance of stationary, secondary vortices prior to turbulent breakdown has also been observed. Comparisons with linear stability theory show reasonable agreement with measured growth rate data.
The effects of periodic excitation on the evolution of a turbulent jet were studied experimentally. A short, wide-angle diffuser was attached to the jet exit and excitation was introduced at the junction between the jet exit and the diffuser inlet. The introduction of high amplitude periodic excitation at the jet exit enhances the mixing and promotes attachment of the jet shear-layer to the diffuser wall. Vectoring is achieved by applying the excitation over a fraction of the circumference of the circular jet, enhancing its spreading rate on the excited side and its tendency to reattach to that side. Static deflection studies demonstrate that the presence of the wide-angle diffuser increases the effectiveness of the added periodic momentum due to a favorable interaction between the excitation, the jet shear-layer and the diffuser wall. This point was further demonstrated by the evolution of a wave packet that was excited in the jet shear-layer. Strong amplification of the wave packet was measured with a diffuser attached to the jet exit. The turbulent jet responds quickly (10-20 msec) to step changes in the level of the excitation input. The response scales with the jet exit velocity and is independent of the Reynolds number. Jet deflection angles were found to be highly sensitive to the relative direction between the excitation and the jet flow and less sensitive to the excitation frequency. The higher jet deflection angles were obtained for a diffuser length of about two diameters and for diffusers with half-angles greater than 15 degrees.
Recent Ulysses observations of millisecond spikes superposed on broader Langmuir wave packets in type 3 radio sources are compared quantitatively with constraints from the theory of wave collapse. It is found that both the millisecond spikes and the wave packets have fields at least 10 times too small to be consistent with collapse, contrary to previous interpretations in terms of this process. Several alternative explanations are considered and it is argued that the spikes should be interpreted as either non-collapse phenomena or observational artifacts. To the extent the observations are representative, this rules out theories for type 3 bursts at approx. 1 - 4 AU that rely on collapse.
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.
Integrations of the linear stability problem, in the present numerical investigation of weakly nonparallel zonal flows barotropic instability having localized intense shear regions, reveal the existence of unstable localized wave packets. The spatial structure and eigenfrequencies of these packets depend on two parameters measuring the degree of supercriticality and the zonal length scale of the shear region. It is found that instability structure is defined by conditions ensuring the decay of the wave packet at infinity, and the transition from long to short waves across a turning point region that is controlled by nonparallel effects.
A test particle computer model of the precipitation of radiation belt electrons is extended to compute the dynamic energy spectrum of transient electron fluxes induced by short-duration VLF wave packets traveling along the geomagnetic field lines. The model is adapted to estimate the count rate and associated spectrum of precipitated electrons that would be observed by satellite-based particle detectors with given geometric factor and orientation with respect to the magnetic field. A constant-frequency wave pulse and a lightning-induced whistler wave packet are used as examples of the stimulating wave signals. The effects of asymmetry of particle mirror heights in the two hemispheres and the atmospheric backscatter of loss cone particles on the computed precipitated fluxes are discussed.
The free evolution of a non-relativistic charged particle is manipulated using time-dependent magnetic fields. It is shown that the application of a programmed sequence of magnetic pulses can invert the free evolution process, forcing an arbitrary wave packet to 'go back in time' to recover its past shape. The possibility of more general operations upon the Schrodinger wave packet is discussed.
A test particle approach is used to compare gyroresonant pitch angle scattering of energetic electrons by coherent versus incoherent whistler mode waves, for the case in which the coherent wave amplitude is below the nonlinear phase trapping threshold. Wave packets of 400 ms duration propagating along the magnetic field at L = 4 within the plasmasphere are considered, and the wave-induced pitch angle scattering along the propagation path from one hemisphere to the other and the resulting precipitation flux are computed. An incoherent wave spectrum is simulated by random modulation of the wave frequency at intervals of 1 ms, thereby generating signals with nearly constant power spectral density over a bandwidth of 2 kHz centered at 5.5 kHz. The associated pitch angle scattering is compared with that of a monochromatic 5.5-kHz signal of 400 ms duration. Results of the test particle analysis are compared with those expected on the basis of a classical diffusion treatment, and an expression is derived for an effective “diffusion” coefficient for pitch angle scattering by coherent waves. The trajectory followed by a particle when interacting with incoherent waves essentially represents a random walk in velocity space, while for coherent waves the pitch angle of the particle varies in a well-defined manner. In spite of the fact that individual particle scatterings are typically larger for coherent waves, the peak precipitation fluxes induced by incoherent waves are found to be approximately the same as those for coherent waves having the same total power. This results from the fact that incoherent waves interact with particles over a wider range of energies. As a consequence, the energy spectrum and the temporal extent of transient precipitation pulses due to incoherent wave packets are broader than those for equivalent coherent ones.
Freestream turbulence of weak but adjustable intensity incident upon a flat plate test model induced Tollmien-Schichting (TS) waves and wave packets. These were studied using a newly-developed sensor by which the packets could be followed from a station nearly as far forward as the minimum critical Reynolds number to the onset of transition. Conclusions reached from these studies were: (1) weak freestream turbulence induced TS wave packets in a Blasius boundary-layer, (2) packets gained strength during propagation through expansion of lateral and longitudinal scales, and through an increase in peak amplitude, (3) the average wave strength at stations of observation was not related to the freestream velocity fluctuation in a linear manner, and (4) packets typically evolved into turbulent spots.
Highly energetic electrons in the Earths Van Allen radiation belts can cause serious damage to spacecraft electronic systems and affect the atmospheric composition if they precipitate into the upper atmosphere. Whistler mode chorus waves have attracted significant attention in recent decades for their crucial role in the acceleration and loss of energetic electrons that ultimately change the dynamics of the radiation belts. The distribution of these waves in the inner magnetosphere is commonly presented as a function of geomagnetic activity. However, geomagnetic indices are nonspecific parameters that are compiled from imperfectly covered ground based measurements. The present study uses wave data from the two Van Allen Probes to present the distribution of lower band chorus waves not only as functions of single geomagnetic index and solar wind parameters but also as functions of combined parameters. Also the current study takes advantage of the unique equatorial orbit of the Van Allen Probes to estimate the average scale size of chorus wave packets, during close separations between the two spacecraft, as a function of radial distance, magnetic latitude, and geomagnetic activity, respectively. Results show that the average scale size of chorus wave packets is approximately 13002300 km. The results also show that the inclusion of combined parameters can provide better representation of the chorus wave distributions in the inner magnetosphere and therefore can further improve our knowledge of the acceleration and loss of radiation belt electrons.
This paper investigates the nonlinear instability of internal gravity waves and the effects of their nonlinear interaction on momentum flux, using simple theoretical and numerical models. From the result of an analysis of parametric instability of a two-dimensional internal gravity wave as discussed by Yeh and Liu (1981) and Klostermeyer (1982), a group trajectory length scale for a gravity wave packet was determined, expressed in terms of the dominant vertical wavelenght and the degree of convective saturation. It is shown that this analysis justifies the Eikonal saturation method for relatively transient packets, that are well below the saturation amplitude, propagating in a slowly varying mean flow. Conversely, linear theory fails for persistent disturbances and trasient wave packets near convective saturation.
A quantitative model is developed to account for the distribution in magnitude and location of the intense plasma waves observed in the earth's electron foreshock given the observed rms levels of waves. In this model, nonlinear strong-turbulence effects cause solitonlike coherent wave packets to form and decouple from incoherent background beam-excited weak turbulence, after which they convect downstream with the solar wind while collapsing to scales as short as 100 m and fields as high as 2 V/m. The existence of waves with energy densities above the strong-turbulence wave-collapse threshold is inferred from observations from IMP 6 and ISEE 1 and quantitative agreement is found between the predicted distribution of fields in an ensemble of such wave packets and the actual field distribution observed in situ by IMP 6. Predictions for the polarization of plasma waves and the bandwidth of ion-sound waves are also consistent with the observations. It is shown that strong-turbulence effects must be incorporated in any comprehensive theory of the propagation and evolution of electron beams in the foreshock. Previous arguments against the existence of strong turbulence in the foreshock are refuted.
The role of geostrophic adjustment in the middle atmosphere for given wave packet forcing by a three-dimensional hydrostatic model is examined. It is shown that the induced fields consist of two different kinds of modes. One, produced by forcing vorticity only, is steady quasi-geostrophic flow; this is restricted to the forcing region. The other, produced by both forcing vorticity and forcing divergence, is oscillatory, and is in the form of gravity waves propagating out of the forcing region plus inertial oscillations in the forcing region. The scales and amplitudes of the induced gravity waves are determined by the forcing. For a typical example, a 200 km x 200 km gravity wave packet of momentum flux 0.5 N/sq m absorbed in a layer of 5 km thickness centered near 18 km altitude, the gravity waves spread to a larger region about 1000 km x 1000 km at a level 7 km above the forcing region. At that level, the horizontal and vertical wavelengths of the induced waves are about 300 km and 7 km respectively, and the momentum flux is substantially reduced to 0.0004 N/sq m. The results suggest that geostrophic adjustment processes may play an important role in specifying the gravity wave spectrum in the middle atmosphere.
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.
We present the high time resolution in situ observations of Langmuir waves, likely excited by an electron beam accelerated by a coronal-mass ejection-driven super-critical quasi-perpendicular interplanetary shock into its upstream solar wind, which happens to be the source region of a solar type II radio burst. We show that (1) these waves occur as coherent localized magnetic-field-aligned, one-dimensional wave packets with durations of a few milliseconds and with peak intensities well in excess of the threshold for strong turbulence processes, (2) they provide what is believed to be the first evidence for: (a) the oscillating two-stream instability (OTSI) L(sub 1) + L(sub 2) S/⟶ U + D, where L(sub 1) and L(sub 2), U and D, and S are the pump Langmuir waves, up- and down-shifted side bands, and ion sound waves, respectively, (b) a three-wave interaction U + D ⟶ T(sub 2f(sub pe)), where T(sub 2f(sub pe)) is the second harmonic electromagnetic wave, (3) they satisfy the threshold condition for formation of collapsing solitons, and (4) they are accompanied by their ponderomotive force induced density cavities with δn(sub p)/n(sub e) > δn(sub b)/n(sub e), where δn(sub p)/n(sub e) is the level of ponderomotive force induced density fluctuations and δn(sub b)/n(sub e) is that of the ambient fluctuations. These findings strongly suggest that the observed wave packets provide evidence for the collapsing solitons formed as a result of OTSI. The implication is that the strong turbulence processes probably play very important roles in excitation of type II radio emissions as well as in stabilization of shock-accelerated electron beams.
A methodology combining Large Eddy Simulation (LES) trained data and a physics driven wave packet model to obtain a reduced order reconstruction for broadband, three-dimensional, temporally stationary but spatially inhomogeneous, incompressible turbulence. Wake turbulence generated by an axisymmetric dragging disk with a turbulent co-flow serves as the benchmark test case. We begin by studying the proper-orthogonal decomposition of the turbulent fluctuations taken from a high-resolution LES to first identify whether the fields demonstrate a low-rank character. It is argued that the presence of the turbulent co-flow results in a largely broadband character lacking any tonal properties. This is especially true for Strouhal numbers greater than 1 and only a small fraction of energy is contained in the leading order Kelvin-Helmholtz modes. As such reconstructions and reduced order modeling purely relying on data from LES does not appear to be a lucrative solution - contrary to problems with strongly tonal character. To supplement the missing energy from a low order truncated mode expansion, we utilize a physics based super-resolution (enrichment) algorithm that relies on spatio-temporally localized Gabor wave packets whose time evolution is described using a set of ordinary differential equations. The reconstructed flow has single- and two-point correlations that are consistent with the reference high resolution simulation data.