scholarly journals Kinetic stability properties of relativistic nonneutral electron flow for low-frequency extraordinary-mode perturbations

1989 ◽  
Vol 7 (1) ◽  
pp. 85-109 ◽  
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Dispersion Relation ◽  
Layer Thickness ◽  
Electron Energy ◽  
Electron Flow ◽  
Low Frequency ◽  
Outer Edge ◽  
Stability Properties ◽  
System Parameters ◽  
Wide Range ◽  
Electron Layer

The kinetic stability properties of relativistic nonneutral electron flow in planar diode geometry are examined for extraordinary-mode perturbations about the self-consistent Vlasov equilibrium . Here, the cathode is located at x = 0; the anode is located at x = d the outer edge of the electron layer is located at is the equilibrium flow velocity in the x-direction; n^b is the electron density at the cathode (x = 0); and is the axial magnetic field, with const. in the vacuum region (xb < x ≤ d). The extraordinary-mode eigenvalue equation, derived in a companion paper for low-frequency, long-wavelength perturbations, is solved exactly. This leads to a formal dispersion relation, which can be used to determine the complex eigenfrequency ω over a wide range of system parameters and wavenumber k in the y-direction. The formal dispersion relation is further simplified for and , assuming low-frequency perturbations about a tenuous electron layer with and . Here, , and , where denotes the average equilibrium orbit, and [γ(x) − 1]mc2 is the average kinematic energy of an electron fluid element. The resulting approximate dispersion relation is solved numerically over a wide range of system parameters to determine the detailed dependence of stability properties on electromagnetic effects, layer thickness, and electron energy, as measured by , and γb − 1, respectively. Here, γb = γ(xb) denotes the electron energy at the outer edge of the electron layer. As a general remark, it is found that increasing the electron energy (γb − 1), increasing the strength of electromagnetic effects , and/or decreasing the layer thickness (xb/d) all have a stabilizing influence.

scholarly journals Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

1989 ◽  
Vol 7 (1) ◽  
pp. 55-84 ◽  
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Electron Flow ◽  
Low Frequency ◽  
Companion Paper ◽  
Field Configuration ◽  
Outer Edge ◽  
Eigenvalue Equation ◽  
Planar Geometry ◽  
Canonical Momentum ◽  
Stability Properties ◽  
Long Wavelength

Use is made of the Vlasov–Maxwell equations to derive an eigenvalue equation describing the extraordinary–mode stability properties of relativistic, non-neutral electron flow in high-voltage diodes. The analysis is based on well-established theoretical techniques developed in basic studies of the kinetic equilibrium and stability properties of nonneutral plasmas characterized by intense self fields. The formal eigenvalue equation is derived for extraordinary-mode flute perturbations in a planar diode. As a specific example, perturbations are considered about the choice of self-consistent Vlasov equilibrium , where . is the electron density at the cathode (x = 0), H is the energy, and Py is the canonical momentum in the Y-direction (the direction of the equilibrium electron flow). As a limiting case, the planar eigenvalue equation is further simplified for low-frequency long-wavelength perturbations with |ω − kvd, ≪ ωυ where and and ⋯c = eB0/mc, and B0ệz is the applied magnetic field in the vacuum region xb < x ≤ d. Here, the outer edge of the electron layer is located at x = xb; ω is complex oscillation frequency; k is the wavenumber in the y-direction; ωυ is the characteristic betatron frequency for oscillations in the x′-orbit about the equilibrium value x′ = x0 = xb/2; and Vd is the average electron flow velocity in the y-direction at x = x0. In simplifying the orbit integrals, a model is adopted in which the eigenfunction approximated by , where x′(t′) is the x′-orbit in the equilibrium field configuration. A detailed analysis of the resulting eigenvalue equation for , derived for low-frequency long-wavelength perturbations, is the subject of a companion paper.

Local analysis of extraordinary-mode stability properties for relativistic non-neutral electron flow in a planar diode

1987 ◽  
Vol 37 (1) ◽  
pp. 63-79
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Dispersion Relation ◽  
Cyclotron Frequency ◽  
Electron Flow ◽  
Electron Cyclotron ◽  
Local Analysis ◽  
Planar Diode ◽  
Stability Properties ◽  
Local Dispersion ◽  
Electron Cyclotron Frequency ◽  
Wide Range

The extraordinary-mode eigenvalue equation is used to investigate the local stability properties of relativistic, non-neutral electron flow in a planar diode. The local stability analysis assumes gentle equilibrium gradients and short perturbation wavelengths. The lowest-order local dispersion relation is derived assuming that localized solutions for the eigenfunction exist, and stability properties are investigated numerically over a wide range of System parameters for perturbations with frequency small in comparison with the electron cyclotron frequency. It is found that the local dispersion relation supports three solutions in this frequency regime. One of the solutions corresponds to a stable diocotron mode driven by the local density gradient. The other two branches are found to exhibit instability over a wide range of electron density. These modes are electromagnetic in nature and require relativistic electron flow with velocity shear in order for instability to exist. Moreover, the growth rate of the unstable electromagnetic mode can be substantial (a few per cent of the electron cyclotron frequency).

Filamentation instability of electron/ion beams in magnetized plasma waveguide

2013 ◽  
Vol 80 (1) ◽  
pp. 81-87 ◽  
Author(s):  
A. Hasanbeigi ◽  
S. Moghani ◽  
S. Azimi ◽  
H. Mehdian
Keyword(s):  
Dispersion Relation ◽  
Relativistic Electron ◽  
Ion Beams ◽  
Magnetized Plasma ◽  
Plasma Waveguide ◽  
Velocity Difference ◽  
System Parameters ◽  
Wide Range ◽  
Difference Factor ◽  
Filamentation Instability

AbstractThe filamentation instability due to the interaction of two relativistic electron and ion beams with magnetized plasma in a waveguide is studied within the framework of a macroscopic cold fluid description. It is assumed that the background plasma provides charge and current neutralization of the injected beams. The dispersion relation is obtained by solving wave eigenvalue equation. The resulting dispersion equation is analyzed numerically over a wide range of system parameters. It is found that the velocity difference factor can strongly affect the filamentation instability.

The finite-product method in the theory of waves and stability

2009 ◽  
Vol 466 (2114) ◽  
pp. 471-491 ◽  
Author(s):  
C. J. Chapman ◽  
S. V. Sorokin
Keyword(s):  
Dispersion Relation ◽  
Elastic Waves ◽  
Low Frequency ◽  
Wave Theory ◽  
Finite Product ◽  
High Frequencies ◽  
Polynomial Approximations ◽  
Wide Range ◽  
Product Method ◽  
Finite Products

This paper presents a method of analysing the dispersion relation and field shape of any type of wave field for which the dispersion relation is transcendental. The method involves replacing each transcendental term in the dispersion relation by a finite-product polynomial. The finite products chosen must be consistent with the low-frequency, low-wavenumber limit; but the method is nevertheless accurate up to high frequencies and high wavenumbers. Full details of the method are presented for a non-trivial example, that of anti-symmetric elastic waves in a layer; the method gives a sequence of polynomial approximations to the dispersion relation of extraordinary accuracy over an enormous range of frequencies and wavenumbers. It is proved that the method is accurate because certain gamma-function expressions, which occur as ratios of transcendental terms to finite products, largely cancel out, nullifying Runge’s phenomenon. The polynomial approximations, which are unrelated to Taylor series, introduce no spurious branches into the dispersion relation, and are ideal for numerical computation. The method is potentially useful for a very wide range of problems in wave theory and stability theory.

scholarly journals Calculation and comparative analysis of the mean energy expended per ion pair by electrons in water and hydroxyl radical

Energetika ◽  
2017 ◽  
Vol 63 (2) ◽  
Author(s):  
Yurii V. Kovtun
Keyword(s):  
Energy Expenditure ◽  
Water Molecule ◽  
Plasma Physics ◽  
Hydroxyl Radical ◽  
Electron Impact ◽  
Electron Energy ◽  
Electron Flow ◽  
Electric Discharges ◽  
Wide Range ◽  
The Cost

Researches of physical and chemical processes occurring in water during the interaction with particles (electrons, ions, photons, etc.) are interesting for a wide range of physical and applied problems in astrophysics, radiation physics, chemistry, medicine and biology, plasma physics, and other branches of science and technology. One of the directions, which invokes a considerable interest in low-temperature plasma physics and its application technologies, includes researches of electric discharges in the liquid and above its surface. While developing any technology, in which electric discharges in a liquid and above its surface will be used, the determination of the main channels of energy expenditure and, accordingly, the total amount of energy expenditure comprises an important task. One of the main channels of energy expenditures are those for ionization by an electron impact, or the so-called ionization cost W. The cost of ionization by an electron impact is usually assumed to be a certain mean value of energy spent by an electron for the formation of an ion-electron pair in the substance. The paper presents the results of calculations and comparison of the cost of ionization of water and hydroxyl radical by an electron impact on the basis of two models. The calculations based on the model with the passage of a monoenergetic electron flow (beam) with an energy of 14–1000 eV through the medium show that for an electron energy of 1000 eV, the ionization cost for the water molecule is W = 25.26 eV and W = 21.65 eV for the hydroxyl radical. The results of calculations show that the ionization cost for the model taking into account the electron energy distribution function in a plasma with Te = 100 eV, this value is W = 16.85 eV for the water molecule and W = 14.5 eV for the hydroxyl radical.

The Attenuation of Very Low Frequency Brain Oscillations in Transitions from a Rest State to Active Attention

2009 ◽  
Vol 23 (4) ◽  
pp. 191-198 ◽  
Author(s):  
Suzannah K. Helps ◽  
Samantha J. Broyd ◽  
Christopher J. James ◽  
Anke Karl ◽  
Edmund J. S. Sonuga-Barke
Keyword(s):  
Brain Activity ◽  
Sampling Rate ◽  
Low Frequency ◽  
Future Research ◽  
Adhd Symptoms ◽  
Default Mode ◽  
Very Low Frequency ◽  
Wide Range ◽  
Interference Hypothesis ◽  
Mode Interference

Background: The default mode interference hypothesis ( Sonuga-Barke & Castellanos, 2007 ) predicts (1) the attenuation of very low frequency oscillations (VLFO; e.g., .05 Hz) in brain activity within the default mode network during the transition from rest to task, and (2) that failures to attenuate in this way will lead to an increased likelihood of periodic attention lapses that are synchronized to the VLFO pattern. Here, we tested these predictions using DC-EEG recordings within and outside of a previously identified network of electrode locations hypothesized to reflect DMN activity (i.e., S3 network; Helps et al., 2008 ). Method: 24 young adults (mean age 22.3 years; 8 male), sampled to include a wide range of ADHD symptoms, took part in a study of rest to task transitions. Two conditions were compared: 5 min of rest (eyes open) and a 10-min simple 2-choice RT task with a relatively high sampling rate (ISI 1 s). DC-EEG was recorded during both conditions, and the low-frequency spectrum was decomposed and measures of the power within specific bands extracted. Results: Shift from rest to task led to an attenuation of VLFO activity within the S3 network which was inversely associated with ADHD symptoms. RT during task also showed a VLFO signature. During task there was a small but significant degree of synchronization between EEG and RT in the VLFO band. Attenuators showed a lower degree of synchrony than nonattenuators. Discussion: The results provide some initial EEG-based support for the default mode interference hypothesis and suggest that failure to attenuate VLFO in the S3 network is associated with higher synchrony between low-frequency brain activity and RT fluctuations during a simple RT task. Although significant, the effects were small and future research should employ tasks with a higher sampling rate to increase the possibility of extracting robust and stable signals.

scholarly journals UV Nanoimprint Lithography: Geometrical Impact on Filling Properties of Nanoscale Patterns

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 822
Author(s):  
Christine Thanner ◽  
Martin Eibelhuber
Keyword(s):  
Layer Thickness ◽  
Process Parameters ◽  
Nanoimprint Lithography ◽  
Failure Modes ◽  
Production Method ◽  
Efficient Production ◽  
Comprehensive Overview ◽  
Replication Method ◽  
Wide Range ◽  
Pattern Size

Ultraviolet (UV) Nanoimprint Lithography (NIL) is a replication method that is well known for its capability to address a wide range of pattern sizes and shapes. It has proven to be an efficient production method for patterning resist layers with features ranging from a few hundred micrometers and down to the nanometer range. Best results can be achieved if the fundamental behavior of the imprint resist and the pattern filling are considered by the equipment and process parameters. In particular, the material properties and pattern size and shape play a crucial role. For capillary force-driven filling behavior it is important to understand the influencing parameters and respective failure modes in order to optimize the processes for reliable full wafer manufacturing. In this work, the nanoimprint results obtained for different pattern geometries are compared with respect to pattern quality and residual layer thickness: The comprehensive overview of the relevant process parameters is helpful for setting up NIL processes for different nanostructures with minimum layer thickness.

scholarly journals The Band-Gap Studies of Short-Period CdO/MgO Superlattices

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Ewa Przeździecka ◽  
P. Strąk ◽  
A. Wierzbicka ◽  
A. Adhikari ◽  
A. Lysak ◽  
...  
Keyword(s):  
Band Gap ◽  
Layer Thickness ◽  
Energy Gap ◽  
Band Gaps ◽  
Short Period ◽  
Wide Range ◽  
Salt Structure ◽  
Short Period Superlattices ◽  
Direct Band ◽  
Sublayer Thickness

AbstractTrends in the behavior of band gaps in short-period superlattices (SLs) composed of CdO and MgO layers were analyzed experimentally and theoretically for several thicknesses of CdO sublayers. The optical properties of the SLs were investigated by means of transmittance measurements at room temperature in the wavelength range 200–700 nm. The direct band gap of {CdO/MgO} SLs were tuned from 2.6 to 6 eV by varying the thickness of CdO from 1 to 12 monolayers while maintaining the same MgO layer thickness of 4 monolayers. Obtained values of direct and indirect band gaps are higher than those theoretically calculated by an ab initio method, but follow the same trend. X-ray measurements confirmed the presence of a rock salt structure in the SLs. Two oriented structures (111 and 100) grown on c- and r-oriented sapphire substrates were obtained. The measured lattice parameters increase with CdO layer thickness, and the experimental data are in agreement with the calculated results. This new kind of SL structure may be suitable for use in visible, UV and deep UV optoelectronics, especially because the energy gap can be precisely controlled over a wide range by modulating the sublayer thickness in the superlattices.

scholarly journals Temporal Variations of the Turbulence Profiles at the Sayan Solar Observatory Site

Atmosphere ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 499 ◽  
Author(s):  
Artem Shikhovtsev ◽  
Pavel Kovadlo ◽  
Vladimir Lukin
Keyword(s):  
Atmospheric Turbulence ◽  
Temporal Variability ◽  
Low Frequency ◽  
Temporal Variations ◽  
Solar Observatory ◽  
Vertical Profiles ◽  
Spatial And Temporal Scales ◽  
Atmospheric Disturbances ◽  
Wide Range ◽  
The Mean

The paper focuses on the development of the method to estimate the mean characteristics of the atmospheric turbulence. Using an approach based on the shape of the energy spectrum of atmospheric turbulence over a wide range of spatial and temporal scales, the vertical profiles of optical turbulence are calculated. The temporal variability of the vertical profiles of turbulence under different low-frequency atmospheric disturbances is considered.

Quantitative Content Analysis of the United Nations Seabed Debate: Methodology and a Continental Shelf Case Study

1970 ◽  
Vol 24 (3) ◽  
pp. 479-502 ◽  
Author(s):  
R. L. Friedheim ◽  
J. B. Kadane
Keyword(s):  
United Nations ◽  
Continental Shelf ◽  
Ad Hoc ◽  
Mineral Resources ◽  
Outer Edge ◽  
General Assembly ◽  
Wide Range ◽  
The Subject ◽  
The United Nations

International arrangements for the uses of the ocean have been the subject of long debate within the United Nations since a speech made by Ambassador Arvid Pardo of Malta before the General Assembly in 1967. Issues in question include the method of delimiting the outer edge of the legal continental shelf; the spectrum of ocean arms control possibilities; proposals to create a declaration of principles governing the exploration for, and the exploitation of, seabed mineral resources with the promise that exploitation take place only if it “benefits mankind as a whole,” especially the developing states; and consideration of schemes to create international machinery to regulate, license, or own the resources of the seabed and subsoil. The discussions and debates began in the First (Political and Security) Committee of the 22nd General Assembly and proceeded through an ad hoc committee to the 23rd and 24th assembly plenary sessions. The creation of a permanent committee on the seabed as a part of the General Assembly's machinery attests to the importance members of the United Nations attribute to ocean problems. Having established the committee, they will be faced soon with the necessity of reaching decisions. The 24th General Assembly, for example, passed a resolution requesting the Secretary-General to ascertain members' attitudes on the convening of a new international conference to deal with a wide range of law of the sea problems.

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