MODELLING OF QUASI‐CHERENKOV ELECTRON BEAM INSTABILITY IN PERIODICAL STRUCTURES

2005 ◽  
Vol 9 (1) ◽  
pp. 1-8
Author(s):  
K. Batrakov ◽  
S. Sytova
Keyword(s):  
Mathematical Model ◽  
Electron Beam ◽  
Numerical Method ◽  
Differential System ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Distributed Feedback ◽  
Beam Instability ◽  
Nonlinear Stage ◽  
Cherenkov Instability

Nonlinear stage of quasi‐Cherenkov instability of electron beam under conditions of two‐ and three‐dimensional distributed feedback is simulated. The scheme of distributed feedback with two strong coupled waves is considered. Mathematical model of quasi‐Cherenkov electron beam instability is proposed. Numerical method to solve the nonlinear integro‐differential system, describing such instability, is worked out. Results of numerical experiments are discussed. Modeliuojama elektronu spindulio kvazi‐Cherenkovo nestabilumo netiesine faze su dvimačio ir trimačio paskirstytojo grižtamojo ryšio salyga. Nagrinejama schema su grižtamuoju ryšiu su dviem susietomis stipriomis bangomis. Pateiktas kvazi‐Cherenkovo elektroninio spindulio nestabilumo matematinis modelis. Pasiūlytas veiksmingas skaitinis algoritmas, skirtas netiesinems integro‐diferencialinems lygčiu sistemoms su tokio tipo nestabilumu, spresti. Apžvelgti skaitinio eksperimento rezultai.

scholarly journals NONSTATIONARY STAGE OF QUASI‐CHERENKOV BEAM INSTABILITY IN PERIODICAL STRUCTURES

2005 ◽  
Vol 12 (1) ◽  
pp. 1-8
Author(s):  
K. Batrakov ◽  
S. Sytova
Keyword(s):  
Electron Beam ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Numerical Experiments ◽  
Distributed Feedback ◽  
Beam Instability ◽  
Nonstationary Solution ◽  
Nonstationary Stage ◽  
Cherenkov Instability

Analysis of nonstationary stage of quasi‐Cherenkov instability of electron beam in the case of two‐wave distributed feedback is carried out. Mathematical models and numerical methods of nonstationary quasi‐Cherenkov electron beam instability are proposed. Results of numerical experiments are proposed. Bifurcations of nonstationary solution are discussed. Straipsnyje analizuojama nestacionariosios fazes kvazi‐Cherenkovo elektronu spinduliuotes nestabilumas esant dvieju bangu saveikai su grižtamo ryšio pernešimu. Pasiūlyti šios elektronu spinduliuotes nestacionariosios fazes atveju matematiniai ir skaitiniai sprendimo metodai. Pateikti skaitinio eksperimento rezultatai. Aptartos nestacionariojo sprendinio bifurkacijos.

A PERTURBATIVE APPROACH TO ACOUSTIC SCATTERING FROM A VIBRATING BOUNDED OBSTACLE

2002 ◽  
Vol 10 (03) ◽  
pp. 349-384 ◽  
Author(s):  
FRANCESCA MARIANI ◽  
MARIA CRISTINA RECCHIONI ◽  
FRANCESCO ZIRILLI
Keyword(s):  
Mathematical Model ◽  
Numerical Method ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Perturbation Series ◽  
Quantitative Character ◽  
Doppler Spectrum ◽  
Test Problems ◽  
The Mathematical Model

In this paper we study a mathematical model to describe a three dimensional acoustic scattering problem associated to a "vibrating" obstacle that is a bounded simply connected domain contained in the three dimensional real Euclidean space whose shape changes in time. In particular we propose a numerical method based on a perturbation series and the operator expansion method to solve the mathematical model considered. This method makes possible to obtain highly parallelizable algorithms able to compute the solution of the problem considered order by order in perturbation theory, and able to obtain the required solution of the scattering problem summing up the perturbation series. Really impressive speed up factors are observed and reported when the algorithm is executed on the Chiba Cluster, a parallel machine of the Argonne National Laboratory, USA. We validate the mathematical model and the numerical method proposed solving some test problems. The quantitative character of the numerical results obtained is established. The results obtained on the test problems are discussed both from the numerical and the physical point of view. In particular we show that the Doppler spectrum associated to the far field patterns of the scattered acoustic fields depends mainly from the incoming wave and from the excited vibrational modes (Figs. 9–13). The website: shows some Applets relative to the numerical examples.

scholarly journals MATHEMATICAL MODELLING OF MULTIWAVE VOLUME FREE ELECTRON LASER: BASIC PRINCIPLES AND NUMERICAL EXPERIMENTS

2006 ◽  
Vol 11 (1) ◽  
pp. 13-22 ◽  
Author(s):  
K. Batrakov ◽  
S. Sytova
Keyword(s):  
Mathematical Modelling ◽  
Key Words ◽  
Differential System ◽  
Free Electron ◽  
Free Electron Laser ◽  
Numerical Experiments ◽  
Computer Code ◽  
Basic Principles ◽  
Cherenkov Instability

This contribution is devoted to investigation of multiwave Volume Free Electron Laser (VFEL) by methods of mathematical modelling. Special emphasis is placed on consideration of three‐wave VFEL. Mathematical modelling carried out confirmed some preliminary physical estimates. Computer code VOLC for simulation of different schemes of two‐ and three‐wave VFEL is described. Key words: free electron laser, quasi‐Cherenkov instability, simulation, nonlinear integro‐differential system.

scholarly journals GEODYNAMICS

GEODYNAMICS ◽  
2011 ◽  
Vol 2(11)2011 (2(11)) ◽  
pp. 84-85
Author(s):  
L. M. Zhuravchak ◽  
◽  
Yu. O. Fedoryshyn ◽  
Keyword(s):  
Mathematical Model ◽  
Electromagnetic Field ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Algorithm ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Steady Oscillations ◽  
Dimensional Object ◽  
The Mathematical Model

The mathematical model for steady oscillations of electromagnetic field in the three-dimensional object is built. For calculating of the distribution of the electromagnetic field the numerical algorithm based on the boundary element method is developed. Numerical experiments are performed.

scholarly journals Periodic Orbits for a Three-Dimensional Biological Differential Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Renato Colucci ◽  
Daniel Nuñez
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Differential System ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Differential Systems

We study the existence of periodic orbit for a differential system describing the effects of indirect predation over two preys. Besides discussing a generalized version of the model, we present some remarks and numerical experiments for the nonautonomous version of the two models.

Voids in Quenched Nickel

1968 ◽  
Vol 26 ◽  
pp. 266-267
Author(s):  
J. J. Laidler
Keyword(s):  
Electron Beam ◽  
Ambient Temperature ◽  
Cooling Rate ◽  
Three Dimensional ◽  
Cooling Curve ◽  
Polycrystalline Nickel ◽  
Quenching Temperature ◽  
Long Tail ◽  
Diffusion Pump

The presence of three-dimensional voids in quenched metals has long been suspected, and voids have indeed been observed directly in a number of metals. These include aluminum, platinum, and copper, silver and gold. Attempts at the production of observable quenched-in defects in nickel have been generally unsuccessful, so the present work was initiated in order to establish the conditions under which such defects may be formed.Electron beam zone-melted polycrystalline nickel foils, 99.997% pure, were quenched from 1420°C in an evacuated chamber into a bath containing a silicone diffusion pump fluid . The pressure in the chamber at the quenching temperature was less than 10-5 Torr . With an oil quench such as this, the cooling rate is approximately 5,000°C/second above 400°C; below 400°C, the cooling curve has a long tail. Therefore, the quenched specimens are aged in place for several seconds at a temperature which continuously approaches the ambient temperature of the system.

Nanoscale Self-Assembly Using Ion and Electron Beam Techniques: A Rapid Review

MRS Advances ◽  
2020 ◽  
Vol 5 (64) ◽  
pp. 3507-3520
Author(s):  
Chunhui Dai ◽  
Kriti Agarwal ◽  
Jeong-Hyun Cho
Keyword(s):  
Electron Beam ◽  
Self Assembly ◽  
Ion Beam ◽  
Three Dimensional ◽  
The Self ◽  
Stress Generation ◽  
Rapid Review ◽  
High Yield ◽  
3D Nanostructures ◽  
Self Assembled

AbstractNanoscale self-assembly, as a technique to transform two-dimensional (2D) planar patterns into three-dimensional (3D) nanoscale architectures, has achieved tremendous success in the past decade. However, an assembly process at nanoscale is easily affected by small unavoidable variations in sample conditions and reaction environment, resulting in a low yield. Recently, in-situ monitored self-assembly based on ion and electron irradiation has stood out as a promising candidate to overcome this limitation. The usage of ion and electron beam allows stress generation and real-time observation simultaneously, which significantly enhances the controllability of self-assembly. This enables the realization of various complex 3D nanostructures with a high yield. The additional dimension of the self-assembled 3D nanostructures opens the possibility to explore novel properties that cannot be demonstrated in 2D planar patterns. Here, we present a rapid review on the recent achievements and challenges in nanoscale self-assembly using electron and ion beam techniques, followed by a discussion of the novel optical properties achieved in the self-assembled 3D nanostructures.

A Real-Time Mathematical Model for Three-Dimensional Tidal Flow and Water Quality

1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Real Time ◽  
Control Volume ◽  
Tidal Flow ◽  
Three Dimensional ◽  
River Estuary ◽  
Pearl River Estuary ◽  
Practical Application ◽  
The Pearl River

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.

scholarly journals Computer Modeling of Aerosol Emissions Spread in the Atmosphere

2019 ◽  
Vol 97 ◽  
pp. 05023 ◽  
Author(s):  
Daler Sharipov ◽  
Sharofiddin Aynakulov ◽  
Otabek Khafizov
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Atmospheric Boundary Layer ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Climatic Factors ◽  
Numerical Algorithms ◽  
Aerosol Emissions ◽  
The Given ◽  
And Diffusion

The paper deals with the development of mathematical model and numerical algorithms for solving the problem of transfer and diffusion of aerosol emissions in the atmospheric boundary layer. The model takes into account several significant parameters such as terrain relief, characteristics of underlying surface and weather-climatic factors. A series of numerical experiments were conducted based on the given model. The obtained results presented here show how these factors affect aerosol emissions spread in the atmosphere.

Sign in / Sign up

Export Citation Format

Share Document