scholarly journals Two-Parametric, Mathematically Undisclosed Solitary Electron Holes and Their Evolution Equation

Plasma ◽  
2020 ◽  
Vol 3 (4) ◽  
pp. 166-179
Author(s):  
Hans Schamel
Keyword(s):  
Mutual Influence ◽  
Particle Interaction ◽  
Phase Speed ◽  
Solitary Wave Solutions ◽  
Mathematical Background ◽  
Phase Velocities ◽  
Coherent Wave ◽  
At Resonance ◽  
Continuous Band ◽  
Electron Holes

The examination of the mutual influence of the two main trapping scenarios, which are characterized by B and D and which in isolation yield the known sech4 (D=0) and Gaussian (B=0) electron holes, show generalized, two-parametric solitary wave solutions. This increases the variety of hole solutions considerably beyond the two cases previously discussed, but at the expense of their mathematical disclosure, since ϕ(x), the electrical wave potential, can no longer be expressed analytically by known functions. Therefore, they belong to a variety with a partially hidden mathematical background, a hitherto unexplored world of structure formation, the origin of which is the chaotic individual particle dynamics at resonance in the coherent wave particle interaction. A third trapping scenario Γ, being independent of (B, D) and representing the perturbative trapping scenarios in lowest order, provides a broad, continuous band of associated phase velocities v0. For structures propagating near CSEA=1.307, the slowelectronacousticspeed, a Generalized Schamel equation is derived: φτ+[A−B158φ+Dlnφ]φx−φxxx=0, which governs their evolution. A is associated with the phase speed and τ:=CSEAt and φ:=ϕ/ψ≥0 are the renormalized time and electric potential, respectively, where ψ is the amplitude of the structure.

scholarly journals Formation of electron holes in the long-time evolution of the bump-on-tail instability

2017 ◽  
Vol 35 (4) ◽  
pp. 706-721 ◽  
Author(s):  
Magdi Shoucri
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Electron Density ◽  
Plasma Frequency ◽  
Unstable Wave ◽  
Trapped Particles ◽  
Phase Velocities ◽  
Inflection Points ◽  
Electron Holes ◽  
Fine Resolution

AbstractAn Eulerian Vlasov code is applied for the numerical solution of the one-dimensional Vlasov–Poisson system of equations for electrons, and with ions forming an immobile background. We study the non-linear evolution of the bump-on-tail instability in the case when the system length L is greater than the wavelength λ of the unstable mode, with a beam density of 10% of the total density, nb = 0.1. We follow the growth and the saturation of an initially unstable wave perturbation, and the formation of a traveling Bernstein–Greene–Kruskal (BGK) mode, which evolves out of the instability. This first stage is followed by sidebands growing from round-off errors which develop and disrupt the BGK equilibrium. In the excited spectrum, mode coupling is mediated by the oscillating resonant particles and results in the electric energy of the system flowing to the longest wavelengths (inverse cascade), and reaching in the asymptotic state a steady state with constant amplitude oscillation modulated by the persistent oscillation of the trapped particles. Coherent phase-space electron holes are formed, which are localized phase-space regions of reduced density on trapped electron orbits, where the electron density is lower than the surrounding plasma electron density. The distribution function evolves to a shape with stationary inflection points of zero slope, at the phase velocities of the excited waves. The longest wavelengths show oscillations at frequencies below the plasma frequency, with phase velocities higher than that of the injected beam, which can accelerate electrons to energies in excess of the initial beam energy. The present work makes a connection between the formation of electron holes, the existence of inflection points of zero slopes in the electron distribution function at the phase velocities of the dominant waves, and at frequencies below the plasma frequency. A fine resolution grid is used in the Eulerian Vlasov code in the phase space and time to allow an accurate calculation of the time history of the system and of the dynamic and oscillation of the trapped particles in the low-density regions of the phase space, and of those particles at the separatrix regions of the vortex structures which evolve periodically between trapping and untrapping states and which can only be accurately studied using a fine-resolution phase-space grid.

The Magneto-Dimensional Transformation Properties of the Ultradispersed Metallic Media as a Mechanism for Managing the Macrodynamic Features of Crystallizing Thermoplastic Nanocomposites

2021 ◽  
Vol 899 ◽  
pp. 292-299
Author(s):  
N.I. Mashukov ◽  
Albina M. Altueva ◽  
Galina M. Danilova-Volkovskaya ◽  
Gennady B. Shustov
Keyword(s):  
Chemical Potential ◽  
Mutual Influence ◽  
Three Dimensional ◽  
Polymeric Materials ◽  
Condensed State ◽  
Structural Elements ◽  
Structure Property ◽  
Coherent Wave ◽  
Thermoplastic Matrix ◽  
Dimensional Parameters

The work considers the main elements of the magneto-dimensional transformation properties in the ultradispersed metallic media (UDM) as a nanomodifier in the process of the formation of nanocompositional polymeric materials (NCPM) based on polyolefins () from a melt. It has been shown that UDM nanoparticles in a melt under the influence and interaction with a thermoplastic matrix are capable of transforming their magnetic properties (to the level of superparamagnetic), structural-dimensional parameters, and chemical potential. With this mutual influence, the nanomodifier has an active effect on the thermoplastic melt at all stages of the formation of the structure-property relationship: structureless ensembles of macromolecules → formation of clusters (domains), lamellas, crystallites → formation of a network of intermolecular entanglements → crystallization of the thermoplastic matrix → transition to a condensed state. An important component of the formation of a fine-crystalline anisotropic NCPM structure is the intramatrix orientation of the structural elements of the thermoplastic in the melt under the influence of the magneto-dimensional transformable manifestations of the nanomodifier. A consequence of the formation of a fine-crystalline anisotropic structure of the NCPM is an increased level of a complex of physicochemical properties (such as deformation-strength, rheological, etc.). An assumption is made about the possibility of the formation of coherent wave packets from clusters (domains) and lamellas of crystallites of matrix thermoplastic with a minimum three-dimensional geometry under the action of superparamagnetic forces of nanoparticles of the nanomodifier.

Convectively Coupled Equatorial Waves. Part II: Propagation Characteristics

2007 ◽  
Vol 64 (10) ◽  
pp. 3424-3437 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian Hoskins ◽  
Julia Slingo
Keyword(s):  
Rossby Wave ◽  
Phase Speed ◽  
Kelvin Waves ◽  
Equatorial Waves ◽  
Propagation Characteristics ◽  
Upper Troposphere ◽  
Ambient Flow ◽  
Vertical Coupling ◽  
Convectively Coupled Equatorial Waves ◽  
Coherent Wave

Abstract Following the description of the horizontal and vertical structures of convectively coupled equatorial waves presented in Part I, here their propagation characteristics are investigated. Linear lagged regressions are used to produce their composite evolution, and the Radon transform technique is used to calculate their phase speeds. It is shown that coherent wave structures with convective coupling generally exist for about 1–2 weeks. Typical zonal wavenumbers are 6–8, wavelengths are 42°–64° of longitude, and typical periods are 4–8 days. The eastward phase speed of convectively coupled Kelvin waves is between 10 and 17 m s−1. The westward phase speed of the coupled mixed Rossby–gravity wave is between 10 and 15 m s−1, and the westward phase speed of the coupled n = 1 Rossby wave is between 7 and 9 m s−1. It is found that convection can produce stronger vertical coupling of phase speeds, and Doppler shifting by the ambient flow can modify phase speeds. There is further evidence that some waves tend to act as forcing agents for convection whereas others tend to be forced by convection. Eastward propagation of some n = 0 and 1 modes in the upper troposphere is also examined.

Discussion following the presentation by F. Deubner

1977 ◽  
Vol 36 ◽  
pp. 69-74
Keyword(s):  
List Type ◽  
The Sun ◽  
Type Number ◽  
Harmonic Motion ◽  
Locally Excited ◽  
Long Period ◽  
Coherent Wave ◽  
Short Period ◽  
Global Modes

The discussion was separated into 3 different topics according to the separation made by the reviewer between the different periods of waves observed in the sun :1) global modes (long period oscillations) with predominantly radial harmonic motion.2) modes with large coherent - wave systems but not necessarily global excitation (300 s oscillation).3) locally excited - short period waves.

Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

1990 ◽  
Vol 48 (2) ◽  
pp. 110-111 ◽  
Author(s):  
F. Hasselbach ◽  
A. Schäfer
Keyword(s):  
Group Velocity ◽  
Wave Packets ◽  
Index Of Refraction ◽  
Electron Wave ◽  
Fringe Contrast ◽  
Faraday Cage ◽  
Optical Index ◽  
Wien Filter ◽  
Coherent Wave ◽  
Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

Direct imaging of charge transfer

1996 ◽  
Vol 54 ◽  
pp. 680-681
Author(s):  
Yimei Zhu ◽  
J. Tafto
Keyword(s):  
Charge Transfer ◽  
Electron Diffraction ◽  
Scattering Amplitude ◽  
High Temperature Superconductors ◽  
Charge Carriers ◽  
Image Charge ◽  
Net Charge ◽  
Long Time ◽  
Electron Holes ◽  
First Time

The electron holes confined to the CuO2-plane are the charge carriers in high-temperature superconductors, and thus, the distribution of charge plays a key role in determining their superconducting properties. While it has been known for a long time that in principle, electron diffraction at low angles is very sensitive to charge transfer, we, for the first time, show that under a proper TEM imaging condition, it is possible to directly image charge in crystals with a large unit cell. We apply this new way of studying charge distribution to the technologically important Bi2Sr2Ca1Cu2O8+δ superconductors.Charged particles interact with the electrostatic potential, and thus, for small scattering angles, the incident particle sees a nuclei that is screened by the electron cloud. Hence, the scattering amplitude mainly is determined by the net charge of the ion. Comparing with the high Z neutral Bi atom, we note that the scattering amplitude of the hole or an electron is larger at small scattering angles. This is in stark contrast to the displacements which contribute negligibly to the electron diffraction pattern at small angles because of the short g-vectors.

Infant Responses to Recorded Sounds

1968 ◽  
Vol 11 (4) ◽  
pp. 811-816 ◽  
Author(s):  
Maurice I. Mendel
Keyword(s):  
White Noise ◽  
Narrow Band ◽  
Limited Bandwidth ◽  
Broadband Spectrum ◽  
Continuous Band

Thirty infants, ranging in age from 4 to 11 months, were tested with five different recorded sounds that varied in bandwidth and temporal configuration: a continuous band of white noise, the same band of noise interrupted twice per second, the crinkling of onionskin paper, a narrow band of noise centered at 3000 Hz, and a warbled 3000 Hz tone. With loudness and duration of the stimuli held constant, more responses occurred to sounds composed of a broadband spectrum than to those of a limited bandwidth. Temporal configuration of the sound had no effect on the number of responses elicited.

The codevelopment of group relationships: The role of individual group member’s and other group members’ mutual influence and shared group environment.

2019 ◽  
Vol 66 (5) ◽  
pp. 640-649 ◽  
Author(s):  
Gianluca Lo Coco ◽  
Salvatore Gullo ◽  
Gabriele Profita ◽  
Chiara Pazzagli ◽  
Claudia Mazzeschi ◽  
...  
Keyword(s):  
Mutual Influence ◽  
Individual Group ◽  
Group Environment ◽  
Group Members ◽  
Group Relationships
Sign in / Sign up

Export Citation Format

Share Document