Test charge potential in the presence of trapped electrons

1979 ◽  
Vol 22 (3) ◽  
pp. 443-451 ◽  
Author(s):  
M. Nambu ◽  
K. H. Spatschek ◽  
H. Akama
Keyword(s):  
Test Particle ◽  
Turbulent Plasma ◽  
Characteristic Parameters ◽  
Single Wave ◽  
Trapped Particles ◽  
Charge Potential ◽  
Test Charge ◽  
The Many ◽  
Trapped Electron ◽  
Particle Approach

Using a test particle approach, the potential of a trapped electron is calculated outside the Debye sphere in the electrostatic limit. The potential strongly depends on some characteristic parameters, such as bounce frequencies of the test and background trapped particles, the total number of trapped particles, etc. In some cases, the potential falls off as the inverse of the distance r. The model is limited to the single-wave case; possible generalizations to the many-wave situation in a turbulent plasma are discussed.

scholarly journals THE DYNAMIC RESPONSE OF OFFSHORE STRUCTURES TO TIME-DEPENDENT FORCES

1964 ◽  
Vol 1 (9) ◽  
pp. 29
Author(s):  
William S. Gaither ◽  
David P. Billington
Keyword(s):  
Degrees Of Freedom ◽  
Wind Waves ◽  
Offshore Structures ◽  
Time Dependent ◽  
Wave Forces ◽  
Ocean Bottom ◽  
Single Wave ◽  
Single Degree Of Freedom ◽  
The Many ◽  
Floating Objects

This paper is addressed to the problem of structural behavior in an offshore environment, and the application of a more rigorous analysis for time-dependent forces than is currently used. Design of pile supported structures subjected to wave forces has, in the past, been treated in two parts; (1) a static analysis based on the loading of a single wave, and (2) a dynamic analysis which sought to determine the resonant frequency by assuming that the structure could be approximated as a single-degree-of-freedom system. (Ref. 4 and 6) The behavior of these structures would be better understood if the dynamic nature of the loading and the many degrees of freedom of the system were included. A structure which is built in the open ocean is subjected to periodic forces due to wind, waves, floating objects, and due occasionally to machinery mounted on the structure. To resist motion, the structure relies on the stiffness of the elements from which it is built and the restraints of the ocean bottom into which the supporting legs are driven.

scholarly journals Particle acceleration in three-dimensional reconnection regions: A new test particle approach

1999 ◽  
Vol 6 (11) ◽  
pp. 4318-4327 ◽  
Author(s):  
Rüdiger Schopper ◽  
Guido T. Birk ◽  
Harald Lesch
Keyword(s):  
Particle Acceleration ◽  
Test Particle ◽  
Three Dimensional ◽  
Particle Approach

scholarly journals A many-particle approach to the gyro-kinetic theory

2007 ◽  
Vol 73 (5) ◽  
pp. 757-772 ◽  
Author(s):  
ALEXEY MISHCHENKO ◽  
AXEL KÖNIES
Keyword(s):  
Kinetic Equation ◽  
Kinetic Theory ◽  
First Principles ◽  
Conventional Approach ◽  
The Self ◽  
Collision Term ◽  
Lie Transform ◽  
Self Consistent ◽  
The Many ◽  
Particle Approach

AbstractA systematic first-principles approach to the many-particle formulation of the gyro-kinetic theory is suggested. The gyro-kinetic many-particle Hamiltonian is derived using the Lie transform technique. The generalized gyro-kinetic equation is obtained following the Born–Bogoliubov–Green–Kirkwood–Yvon approach. The microscopic expression for the self-consistent potential and the polarization density is obtained. It is shown that new terms appear in the gyro-kinetic polarization that can not be derived in the conventional approach. An expression for the collision term is obtained in the Landau approximation.

scholarly journals Plasma Diagnostic Methods: Test Charge Response in Lorentzian Dusty Plasmas

2020 ◽  
Author(s):  
Shahid Ali ◽  
Yas Al-Hadeethi
Keyword(s):  
Dusty Plasmas ◽  
Diagnostic Methods ◽  
Charged Dust ◽  
Dust Grains ◽  
Plasma Diagnostic ◽  
Acoustic Oscillations ◽  
Plasma Parameters ◽  
Charge Potential ◽  
Test Charge ◽  
Electrons And Ions

Different plasma diagnostic methods are briefly discussed, and the framework of a test charge technique is effectively used as diagnostic tool for investigating interaction potentials in Lorentzian plasma, whose constituents are the superthermal electrons and ions with negatively charged dust grains. Applying the space-time Fourier transformations to the linearized coupled Vlasov-Poisson equations, a test charge potential is derived with a modified response function due to energetic ions and electrons. For a test charge moving much slower than the dust-thermal speed, there appears a short-range Debye-Hückel (DH) potential decaying exponentially with distance and a long-range far-field (FF) potential as the inverse cube of the distance from test charge. The FF potentials exhibit more localized shielding curves for low-Kappas, and smaller effective shielding length is observed in dusty plasma compared to electron-ion plasma. However, a wakefield (WF) potential is formed behind the test charge when it resonates with dust-acoustic oscillations, whereas a fast moving test charge leads to the Coulomb potential having no shielding around. It is revealed that superthermality and plasma parameters significantly alter the DH, FF, and WF potentials in space plasmas of Saturn’s E-ring, where power-law distributions can be used for energetic electrons and ions in contrast to Maxwellian dust grains.

scholarly journals VARIATIONAL FORMULATION OF THE FOKKER–PLANCK EQUATION WITH DECAY: A PARTICLE APPROACH

2013 ◽  
Vol 15 (05) ◽  
pp. 1350017 ◽  
Author(s):  
MARK A. PELETIER ◽  
D. R. MICHIEL RENGER ◽  
MARCO VENERONI
Keyword(s):  
Variational Formulation ◽  
Large Deviation ◽  
Particle System ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Stochastic Particle System ◽  
Deviation Rate ◽  
The Many ◽  
Particle Approach ◽  
Fokker Planck

We introduce a stochastic particle system that corresponds to the Fokker–Planck equation with decay in the many-particle limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an energy-dissipation functional in a Mosco-convergence sense. Moreover, we prove that the resulting functional, which involves entropic terms and the Wasserstein metric, is again a variational formulation for the Fokker–Planck equation with decay.

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