The origin of fluctuations and cross-field transport in idealized magnetic confinement systems

1981 ◽  
Vol 300 (1456) ◽  
pp. 547-557 ◽  
Keyword(s):  
Electric Fields ◽  
High Frequency ◽  
Scaling Laws ◽  
Scaling Law ◽  
Low Frequency ◽  
Magnetic Confinement ◽  
Upper Bounds ◽  
Transport Processes ◽  
General View ◽  
Long Wavelength

The study of plasma fluctuations and confinement in idealized systems such as octupoles and levitrons has contributed to the understanding of cross-field transport processes. The linear theory of plasma instabilities that cause fluctuations is well developed and can predict growth rates γ and wavelengths θ x around lines of force. However, the theoretical prediction of cross-field transport coefficient D ± is restricted to quasilinear estimates of upper bounds (for example, D = 1 2 γ λ x 2 ) because of the complexity of the full nonlinear calculation. Such quasilinear estimates usually far exceed the measured values and are of limited worth. A general view of the results from octupole and levitron experiments shows that under collisional conditions ( λ ei / L < 0 ) the diffusion coefficient, D , scales in the same way as classical collisional diffusion ( D α n / T e 1 2 B 2 ). Agreement is closely approached in many cases, sometimes even in the presence of fluctuations. Under collisionless conditions ( D α n / T e 1 2 B 2 ), Bohm diffusion scaling ( D α T e / B ) is found in the few cases where the scaling law has been determined. This behaviour is consistent with the general scaling laws of Connor & Taylor (1977) but is not understood in detail. In addition there is evidence, both experimental and theoretical, that long-wavelength low-frequency electric fields (convection cells) can be generated nonlinearly from high-frequency fluctuations and can contribute to cross-field transport

scholarly journals Активация нейромедиаторов мозга животных интерференционными транскраниальными токами

2021 ◽  
Vol 91 (12) ◽  
pp. 2067
Author(s):  
Y. Katsnelson ◽  
А.В. Ильинский ◽  
Е.Б. Шадрин
Keyword(s):  
Electric Fields ◽  
High Frequency ◽  
Low Frequency ◽  
Mammalian Brain ◽  
Electromagnetic Stimulation ◽  
The Brain ◽  
Transcranial Electromagnetic Stimulation ◽  
Stimulation Of

A method of transcranial electromagnetic stimulation of the mammalian brain is proposed. The method is based on the interference of currents caused by high-frequency orthogonal oscillations of electric fields, which are modulated by low-frequency meander pulses. The effectiveness of the method was confirmed by the results of experiments on stimulating the brain of rats and rabbits.

Characterization of interactive force acting on colloidal particles near an electrode in presence of a high-frequency (>10 kHz) AC electric field using particle diffusometry

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Kshitiz Gupta ◽  
Dong Hoon Lee ◽  
Steven T. Wereley ◽  
Stuart J. Williams
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Particle Motion ◽  
Electrode Surface ◽  
High Frequency ◽  
Colloidal Particles ◽  
Low Frequency ◽  
Double Layers ◽  
Average Height ◽  
Ac Electric Field

Colloidal particles like polystyrene beads and metallic micro and nanoparticles are known to assemble in crystal-like structures near an electrode surface under both DC and AC electric fields. Various studies have shown that this self-assembly is governed by a balance between an attractive electrohydrodynamic (EHD) force and an induced dipole-dipole repulsion (Trau et al., 1997). The EHD force originates from electrolyte flow caused by interaction between the electric field and the polarized double layers of both the particles and the electrode surface. The particles are found to either aggregate or repel from each other on application of electric field depending on the mobility of the ions in the electrolyte (Woehl et al., 2014). The particle motion in the electrode plane is studied well under various conditions however, not as many references are available in the literature that discuss the effects of the AC electric field on their out-of-plane motion, especially at high frequencies (>10 kHz). Haughey and Earnshaw (1998), and Fagan et al. (2005) have studied the particle motion perpendicular to the electrode plane and their average height from the electrode mostly in presence of DC or low frequency AC (<1 kHz) electric field. However, these studies do not provide enough insight towards the effects of high frequency (>10 kHz) electric field on the particles’ motion perpendicular to the electrode plane.  

Dynamic Variational-Asymptotic Procedure for Laminated Composite Shells—Part II: High-Frequency Vibration Analysis

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Chang-Yong Lee ◽  
Dewey H. Hodges
Keyword(s):  
High Frequency ◽  
Vibration Analysis ◽  
Shell Theory ◽  
Low Frequency ◽  
Normal Displacement ◽  
Difficult Situation ◽  
Long Wavelength ◽  
First Approximation ◽  
Low Frequency Vibration ◽  
Characteristic Wavelength

Shell theories intended for low-frequency vibration analysis are frequently constructed from a generalization of the classical shell theory in which the normal displacement (to a first approximation) is constant through the thickness. Such theories are not suitable for the analysis of complicated high-frequency effects in which displacements may change rapidly along the thickness coordinate. Clearly, to derive by asymptotic methods, a shell theory suitable for high-frequency behavior requires a different set of assumptions regarding the small parameters associated with the characteristic wavelength and timescale. In Part I such assumptions were used to perform a rigorous dimensional reduction in the long-wavelength low-frequency vibration regime so as to construct an asymptotically correct energy functional to a first approximation. In Part II the derivation is extended to the long-wavelength high-frequency regime. However, for short-wavelength behavior, it becomes very difficult to represent the three-dimensional stress state exactly by any two-dimensional theory; and, at best, only a qualitative agreement can be expected. To rectify this difficult situation, a hyperbolic short-wave extrapolation is used. Unlike published shell theories for this regime, which are limited to homogeneous and isotropic shells, all the formulas derived herein are applicable to shells in which each layer is made of a monoclinic material.

Turbulent bremsstrahlung instability of whistler mode in the presence of enhanced ion-acoustic fluctuations

1984 ◽  
Vol 31 (3) ◽  
pp. 477-485 ◽  
Author(s):  
S. N. Sarma ◽  
M. Nambu ◽  
S. Bujarbarua
Keyword(s):  
Growth Rate ◽  
Electric Fields ◽  
High Frequency ◽  
Low Frequency ◽  
Resonant Interaction ◽  
Plasma Instability ◽  
Whistler Mode ◽  
Acoustic Fluctuations ◽  
Ion Acoustic ◽  
Nonlinear Force

In the presence of a low-frequency ion-acoustic turbulence and a high-frequency whistler-mode test wave, a new plasma instability occurs owing to a nonlinear force which originates from the resonant interaction between electrons and modulated nonlinear electric fields. The growth rate of the whistler mode is calculated and compared with observations.

scholarly journals Double layer (DL) formation in laser-produced plasma

1983 ◽  
Vol 1 (3) ◽  
pp. 251-269 ◽  
Author(s):  
Shalom Eliezer ◽  
Ariold Ludmirsky
Keyword(s):  
Heat Flux ◽  
Electric Fields ◽  
Scaling Laws ◽  
Laser Energy ◽  
Scaling Law ◽  
Feedback Mechanism ◽  
High Irradiance ◽  
Laser Produced Plasma ◽  
Temperature Scaling ◽  
Wave Instabilities

It is shown that appropriate conditions for DL formation may be created in laser produced plasma. In particular, a ‘feedback’ mechanism is suggested:Wave instabilities → absorption of laser energy → inward heat flux → DL formation → heat flux inhibition → wave instabilitiesPlasma-target potentials and plasma-currents, produced by Nd. laser intensities (IL) between 1012 to 1015 W/cm2, were measured in situ. These measurements seem to be the first direct evidence of DLs in laser produced plasma. Electric fields of EDL ∼ 5 × 105 to 5 × 106 Volts/cm and widths of 10 to 100 Debye lengths are estimated for the DL.Scaling laws are derived for the measured extremum potentials (V) and currents (I): . Two different slopes were obtained experimentally, one slope equal to α = β = 1·0 for IL < 1014 W/cm2 and another of α = β = 0·4 for IL > 1014 W/cm2. These data are explained for temperature scaling law for the low irradiance and for the high irradiance. While the first scaling law is consistent with inverse bremsstrahlung absorption, the second scaling necessitates other absorption processes. Potential and current probes are suggested as useful devices in detecting wave plasma instabilities.

Characteristics of acoustic phonon transport and thermal conductance in multi-frame graphene nanoribbons

2018 ◽  
Vol 32 (26) ◽  
pp. 1850307
Author(s):  
Bengang Bao ◽  
Fei Li ◽  
Xin Zhou
Keyword(s):  
High Frequency ◽  
Acoustic Phonon ◽  
Graphene Nanoribbons ◽  
Cutoff Frequency ◽  
Thermal Conductance ◽  
Low Frequency ◽  
Frame Structure ◽  
Phonon Modes ◽  
Long Wavelength ◽  
Single Frame

Using non-equilibrium Green’s function method and maintaining the zigzag carbon chains unchanged, we investigate the transmission rate of acoustic phonon and the reduced thermal conductance through multi-frame graphene nanoribbons (GNRs). The results show that the reduced thermal conductance approaches [Formula: see text] in the limit [Formula: see text]. Due to the fact that only long wavelength acoustic phonons with zero cutoff frequency are excited at such low temperatures, the scattering influence on the long wavelength acoustic phonons by the multi-frame in GNRs can be ignored and these phonons can go through the scattering region perfectly. As the temperature goes up, the reduced thermal conductance decreases. This is because the high-frequency phonons are excited and these high-frequency phonons are scattered easily by the scattering structures. With the further rise in temperature, acoustic phonon modes with the cutoff frequency greater than zero are excited, which leads to a rapid increase of the reduced thermal conductance. This study shows that changing the frame structure by a small length can lead to a significant change of transmission probability. In the higher frequency region, the transmission spectra display complex peak-dip structures, which results from the fact that in higher frequency region more phonon modes are excited and scattered in the middle scattering region with multi-frames, and the scattering phonons are coupled with the incident phonons, with the increase of the length of frame structure, the scattering of the phonon is also enhanced, which leads to the decrease in the phonon transmission; by changing the frame structure, the parameters can effectively adjust the position of low-frequency phonon transmission valley. The frame structure can induce high-frequency phonon blocking effect and the blocking effect depending on the structure parameter of the frame. When the single frame and double frame GNRs are narrowest, the scattering from low-frequency phonons by the scattering structure is largest, which leads to the fact that the reduced thermal conductance is smallest at low temperatures; however, at high temperature, the reduced thermal conductance is biggest when the single frame and double frame GNRs are narrowest. This is because the scattering from high-frequency phonons by the scattering structure is the smallest. When the length of the frame structure is unchanged, a graphite chain is inserted in which the reduced thermal conductance is always reduced. These results provide an effective theoretical basis for designing the thermal transport quantum devices based on GNRs.

Dynamic Variational-Asymptotic Procedure for Laminated Composite Shells—Part I: Low-Frequency Vibration Analysis

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Chang-Yong Lee ◽  
Dewey H. Hodges
Keyword(s):  
High Frequency ◽  
Short Wavelength ◽  
Vibration Analysis ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Low Frequency ◽  
Long Wavelength ◽  
Energy Functionals ◽  
Wide Range ◽  
Variational Asymptotic

An asymptotically correct dynamic shell theory, valid over a wide range of frequencies and wavelengths, is rigorously derived from an analytical point of view. The derivation provides insight and guidance for the numerical modeling of layered shells. This work is based on three essential theoretical foundations: (a) the concept of decomposition of the rotation tensor, which is to establish the dynamic three-dimensional elasticity problem in a compact and elegant intrinsic form for application to the complex geometry of shells; (b) the variational-asymptotic method, which is to perform a systematic and mathematical dimensional reduction in the long-wavelength regime for both low- and high-frequency vibration analysis; and (c) hyperbolic short-wavelength extrapolation, which is to achieve simple, accurate, and positive definite energy functionals for all wavelengths. Based on these, unlike most established shell theories that are limited to the long-wavelength low-frequency regime, the present theory describes in an asymptotically correct manner not only the low-frequency but also some of the first high-frequency branches of vibrations in the long-wave range. Moreover, it recovers the approximate three-dimensional stress state in both long- and short-wavelength ranges.

scholarly journals Asymptotics for metamaterials and photonic crystals

2013 ◽  
Vol 469 (2152) ◽  
pp. 20120533 ◽  
Author(s):  
T. Antonakakis ◽  
R. V. Craster ◽  
S. Guenneau
Keyword(s):  
High Frequency ◽  
Negative Refraction ◽  
Low Frequency ◽  
Neumann Boundary ◽  
Ring Resonators ◽  
Split Ring ◽  
Long Wavelength ◽  
Physical Effects ◽  
Directive Antenna ◽  
High Frequency Waves

Metamaterial and photonic crystal structures are central to modern optics and are typically created from multiple elementary repeating cells. We demonstrate how one replaces such structures asymptotically by a continuum, and therefore by a set of equations, that captures the behaviour of potentially high-frequency waves propagating through a periodic medium. The high-frequency homogenization that we use recovers the classical homogenization coefficients in the low-frequency long-wavelength limit. The theory is specifically developed in electromagnetics for two-dimensional square lattices where every cell contains an arbitrary hole with Neumann boundary conditions at its surface and implemented numerically for cylinders and split-ring resonators. Illustrative numerical examples include lensing via all-angle negative refraction, as well as omni-directive antenna, endoscope and cloaking effects. We also highlight the importance of choosing the correct Brillouin zone and the potential of missing interesting physical effects depending upon the path chosen.

ANALYTICAL STUDY OF VIBRATIONAL RESONANCE IN AN OVERDAMPED BISTABLE OSCILLATOR

2008 ◽  
Vol 18 (06) ◽  
pp. 1767-1773 ◽  
Author(s):  
V. N. CHIZHEVSKY
Keyword(s):  
High Frequency ◽  
Analytical Study ◽  
Scaling Laws ◽  
Low Frequency ◽  
Approximate Solutions ◽  
Gain Factor ◽  
Bistable System ◽  
Vibrational Resonance ◽  
Periodic Signals ◽  
Good Agreement

The results of analytical study of vibrational resonance (VR) occurring in overdamped bistable system driven by two periodic signals with very different frequencies are presented. Approximate solutions for responses at the low-frequency as a function of the amplitude, and the frequency of the additional high frequency modulation which describe well the main features of vibrational resonance are obtained. Scaling laws for the gain factor and the switching threshold in VR are also found. Analytical results are compared with results of the numerical simulation, showing a good agreement.

scholarly journals Magnetic Temporal Interference for Noninvasive Focal Brain Stimulation

2022 ◽  
Author(s):  
Adam Khalifa ◽  
Seyed Mahdi Abrishami ◽  
Mohsen Zaeimbashi ◽  
Alexander D. Tang ◽  
Brian Coughlin ◽  
...  
Keyword(s):  
Electric Fields ◽  
Brain Stimulation ◽  
High Frequency ◽  
Low Frequency ◽  
Brain Regions ◽  
Strong Increase ◽  
Non Invasive ◽  
Frequency Magnetic Field ◽  
Fos Expression ◽  
The Brain

Non-invasive stimulation of deep brain regions has been a major goal for neuroscience and neuromodulation in the past three decades. Transcranial magnetic stimulation (TMS), for instance, cannot target deep regions in the brain without activating the overlying tissues and has a poor spatial resolution. In this manuscript, we propose a new concept that relies on the temporal interference of two high-frequency magnetic fields generated by two electromagnetic solenoids. To illustrate the concept, custom solenoids were fabricated and optimized to generate temporal interfering electric fields for rodent brain stimulation. C-Fos expression was used to track neuronal activation. C-Fos expression was not present in regions impacted by only one high-frequency magnetic field indicating ineffective recruitment of neural activity in non-target regions. In contrast, regions impacted by two fields that interfere to create a low-frequency envelope display a strong increase in c-Fos expression. Therefore, this magnetic temporal interference solenoid-based system provides a framework to perform further stimulation studies that would investigate the advantages it could bring over conventional TMS systems.

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