63 research outputs found
Nonlinear waves in a model for silicate layers
Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggest that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based in physical principles and the silicate structure. The main characteristic of the model is that it has a hard substrate potential and two different repulsion terms, between ions and nuclei. In a previous work with this model, it was found the propagation of crowdions, i.e., lattice kinks in a lattice with substrate potential that transport mass and charge. They have a single specific velocity and energy coherent with the experimental data. In the present work we perform a much more thorough search for nonlinear excitations in the same model using the pseudospectral method to obtain exact nanopteron solutions, which are single kinks with tails, crowdions and bi-crowdions. We analyze their velocities, energies and stability or instability and the possible reasons for the latter. We relate the different excitations with their possible origin from recoils from different beta decays and with the fossil tracks. We explore the consequences of some variation of the physical parameters because their values are not perfectly known. Through a different method, we also have found stationary and moving breathers, that is, localized nonlinear excitations with an internal vibration. Moving breathers have small amplitude and energy, which is also coherent with the fossil evidence.MINECO (Spain) FIS2015-65998-C2-2-PJunta de AndalucĂa 2017/FQM-280Universidad de Sevilla (España) grants VI PPIT-US-201
Zakharov simulations of beam-induced turbulence in the auroral ionosphere
Recent detections of strong incoherent scatter radar echoes from the auroral F region, which have been explained as the signature of naturally produced Langmuir turbulence, have motivated us to revisit the topic of beam-generated Langmuir turbulence via simulation. Results from one-dimensional Zakharov simulations are used to study the interaction of ionospheric electron beams with the background plasma at the F region peak. A broad range of beam parameters extending by more than 2 orders of magnitude in average energy and electron number density is considered. A range of wave interaction processes, from a single parametric decay, to a cascade of parametric decays, to formation of stationary density cavities in the condensate region, and to direct collapse at the initial stages of turbulence, is observed as we increase the input energy to the system. The effect of suprathermal electrons, produced by collisional interactions of auroral electrons with the neutral atmosphere, on the dynamics of Langmuir turbulence is also investigated. It is seen that the enhanced Landau damping introduced by the suprathermal electrons significantly weakens the turbulence and truncates the cascade of parametric decays
Artificial ionospheric layers driven by high-frequency radiowaves : an assessment
High-power ordinary mode radio waves produce artificial ionization in the F-region ionosphere at the European Incoherent Scatter (EISCAT at TromsĂž, Norway) and High-frequency Active Auroral Research Program (HAARP at Gakona, Alaska, USA) facilities. We have summarized the features of the excited plasma turbulence and descending layers of freshly-ionized (âartificialâ) plasma. The concept of an ionizing wavefront created by accelerated suprathermal electrons appears to be in accordance with the data. The strong Langmuir turbulence (SLT) regime is revealed by the specific spectral features of incoherent radar backscatter and stimulated electromagnetic emissions. Theory predicts that the SLT acceleration is facilitated in the presence of photoelectrons. This agrees with the intensified artificial plasma production and the greater speeds of descent but weaker incoherent radar backscatter in the sunlit ionosphere. Numerical investigation of propagation of O-mode waves and the development of SLT and descending layers have been performed. The greater extent of the SLT region at the magnetic zenith than at vertical appears to make magnetic zenith injections more efficient for electron acceleration and descending layers. At high powers, anomalous absorption is suppressed, leading to the Langmuir and upper hybrid processes during the whole heater-on period. The data suggest that parametric UH interactions mitigate anomalous absorption at heating frequencies far from electron gyroharmonics and also generate SLT in the upper hybrid layer. The persistence of artificial plasma at the terminal altitude depends on how close the heating frequency is to the local gyroharmonic
Beam-plasma interactions and Langmuir turbulence in the auroral ionosphere
Incoherent scatter radar (ISR) measurements were used in conjunction with plasma simulations to study two micro-scale plasma processes that commonly occur in the auroral ionosphere. These are 1) ion acoustic turbulence and 2) Langmuir turbulence.
Through an ISR experiment we investigated the dependence of ion acoustic turbulence on magnetic aspect angle. The results showed a very strong aspect angle sensitivity which could be utilized to classify the turbulence according to allowable generation mechanisms and sources of free energy.
In addition, this work presents results that led to the discovery of a new type of ISR echo, explained as a signature of cavitating Langmuir turbulence. A number of incoherent scatter radar experiments, exploiting a variety of beam and pulse patterns, were designed or revisited to investigate the Langmuir turbulence underlying the radar echoes. The experimental results revealed that Langmuir turbulence is a common feature of the auroral ionosphere. The experimental efforts also led to uncovering a relationship between Langmuir turbulence and one type of natural electromagnetic emission that is sometimes detected on the ground, so-called âmedium frequency burstâ, providing an explanation for the generation mechanism of these emissions.
In an attempt to gain insights into the source mechanism underlying Langmuir turbulence, 1-dimensional Zakharov simulations were employed to study the interactions of ionospheric electron beams with a broad range of parameters with the background plasma at the F region peak. A variety of processes were observed, ranging from a cascade of parametric decays, to formation of stationary wave packets and density cavities in the condensate region, and to direct nucleation and collapse at the initial stage of the turbulence.
The simulation results were then compared with the ISR measurements where inconsistencies were found in the spectral details and intensity of the simulated and measured Langmuir turbulence echoes, suggesting the possibility that the direct energy for the turbulence was provided by unstable low-energy (5âââ20âeV) electron populations produced locally in the F region of the ionosphere rather than by electron beams originating from the magnetosphere
Dispersive shock waves and modulation theory
There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G. B. Whithamâs seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whithamâs averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Kortewegâde Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs
Approximate techniques for dispersive shock waves in nonlinear media
Many optical and other nonlinear media are governed by dispersive, or diffractive, wave equations, for which initial jump discontinuities are resolved into a dispersive shock wave. The dispersive shock wave smooths the initial discontinuity and is a modulated wavetrain consisting of solitary waves at its leading edge and linear waves at its trailing edge. For integrable equations the dispersive shock wave solution can be found using Whitham modulation theory. For nonlinear wave equations which are hyperbolic outside the dispersive shock region, the amplitudes of the solitary waves at the leading edge and the linear waves at the trailing edge of the dispersive shock can be determined. In this paper an approximate method is presented for calculating the amplitude of the lead solitary waves of a dispersive shock for general nonlinear wave equations, even if these equations are not hyperbolic in the dispersionless limit. The approximate method is validated using known dispersive shock solutions and then applied to calculate approximate dispersive shock solutions for equations governing nonlinear optical media, such as nematic liquid crystals, thermal glasses and colloids. These approximate solutions are compared with numerical results and excellent comparisons are obtained
Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal
The nonlinear aspects of longitudinal motion of interacting point masses in a
lattice are revisited, with emphasis on the paradigm of charged dust grains in
a dusty plasma (DP) crystal. Different types of localized excitations,
predicted by nonlinear wave theories, are reviewed and conditions for their
occurrence (and characteristics) in DP crystals are discussed. Making use of a
general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or
else) analytic potential form and arbitrarily long site-to-site range
of interactions, it is shown that dust-crystals support nonlinear kink-shaped
localized excitations propagating at velocities above the characteristic DP
lattice sound speed . Both compressive and rarefactive kink-type
excitations are predicted, depending on the physical parameter values, which
represent pulse- (shock-)like coherent structures for the dust grain relative
displacement. Furthermore, the existence of breather-type localized
oscillations, envelope-modulated wavepackets and shocks is established. The
relation to previous results on atomic chains as well as to experimental
results on strongly-coupled dust layers in gas discharge plasmas is discussed.Comment: 21 pages, 12 figures, to appear in Eur. Phys. J.
Nonlinear Evolution of the KelvinâHelmholtz Instability of Supersonic Tangential Velocity Discontinuities
AbstractA nonlinear stability analysis using a multiple-scales perturbation procedure is performed for the instability of two layers of immiscible, inviscid, arbitrarily compressible fluids in relative motion. Such configurations are of relevance in a variety of astrophysical and space configurations. For modes ofallwavenumbers on, or in the stable neighborhood of, the linear neutral curve, the nonlinear evolution of the amplitude of the linear fields on the slow first-order scales is shown to be governed by a complicated nonlinear KleinâGordon equation. Both the spatially dependent and space-independent versions of this equation are considered to obtain the regimes of physical parameter space where the linearly unstable solutions either evolve to final permanent envelope wave patterns resembling the ensembles of interacting vortices observed empirically, or are disrupted via nonlinear modulation instability
Ultra-Low Frequency Standing Alfven Waves: Global Magnetospheric Modeling of Resonant Wave-Wave Interactions.
Alfven waves are an important energy transport modality in the collisionless plasmas that dominate Earth's magnetosphere. While wave-particle interactions are well understood, the mechanisms that govern wave-wave interactions and their associated phenomenological impacts are still poorly understood and have received little attention. To examine both linear and nonlinear resonant mode coupling, we use the Space Weather Modeling Framework (SWMF) with a resistive, ionospheric inner boundary with ideal MHD governing equations in order to explore the excitation of field line resonances and the stability of standing Alfven waves along the magnetopause by using synthetic upstream solar wind drivers. In reproducing the essential features of broadband FLRs, we found multi-faceted local time FLR asymmetries not exclusively determined by correlated asymmetries in the compressional driver. In examining the stability of transverse magnetopause surface waves, we found evidence of an oblique parametric decay instability exciting large-scale, counterpropagating magnetotail kink modes via ponderomotive forces mediated by transverse magnetic beat waves. The latter is responsible for a backward-propagating compressional wave along the magnetopause. These magnetotail waves bear the signature of slow magnetosonic-shear Alfvenic coupling with associated density holes and soliton-like transverse waves with strong field-aligned currents. Our results have significant implications for magnetotail dynamics and the energization of radiation belts in the dayside magnetospheric cavity and is the first study to examine a) negative energy surface waves, b) parametric decay instability of transverse magnetopause surface waves, c) ponderomotive forces via magnetic beat waves, d) the coupling of MP surface waves to magnetotail kink mode waves, e) counterpropagating kink mode waves, and f) the coupling of slow magnetosonic and transverse wave modes.PhDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133424/1/sidneye_1.pd
Ionospheric plasma outflow in response to transverse ion heating: Self-consistent macroscopic treatment
We examined the various likely processes for creating the cavities and found that the mirror force acting on the transversely heated ions is the most likely mechanism. The pondermotive force causing the wave collapse was found to be a much weaker force than the mirror force on the transversely heated ions observed inside the cavities along with the lower hybrid waves. Using a hydrodynamic model for the polar wind we modeled the cavity formation and found that for the heating rate obtained from the observed waves, the mirror force does create cavities with depletions as observed. Some initial results from this study were published in a recent Geophysical Research Letters and were reported in the Fall AGU meeting in San Francisco. We have continued this investigation using a large-scale semikinetic model
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