Numerische Untersuchungen charakteristischer Größen eines Plasmamodells

1968 ◽  
Vol 23 (5) ◽  
pp. 761-770
Author(s):  
Karlheinz Wilke
Keyword(s):  
Electric Field ◽  
Relaxation Times ◽  
Charged Particles ◽  
Density Fluctuations ◽  
Distribution Functions ◽  
Mean Square ◽  
3 Dimensional ◽  
Time Averages ◽  
The Mean ◽  
Predictor Corrector

A fully 3-dimensional plasma consisting of up to 96 charged particles is simulated in a computer. The plasma is confined to a sphere (or cube) with specularly reflecting walls. The forces are computed using a predictor corrector method with variable time steps. From initial configurations randomly chosen the evolution of the plasma is followed numerically. Distribution functions and moments with respect to various phase variables are obtained as time averages: the distribution of velocity, kinetic and potential energy, of the electric microfield, the micropotential as measured at a neutral point of reference (usually the center of the system) , the mean square electric field, the microfield correlation function and the particle relaxation times. As the sphere used in the experiments has dimensions only slightly larger than the Debye sphere, collective phenomena and those due to major density fluctuations cannot be expected. Despite these limitations the mean electric field is found to be high by approx. 10% compared to the Holtsmark field. Furthermore other comparisons to existing theories with respect to the variables already mentioned are carried out.

TURBULENT DIFFUSION OF TEST PARTICLES IN STRONGLY MAGNETIZED PLASMAS

1991 ◽  
Vol 05 (08) ◽  
pp. 1243-1262 ◽  
Author(s):  
MAURIZIO OTTAVIANI ◽  
MARCO PETTINI
Keyword(s):  
Electric Field ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Mean Square Displacement ◽  
Wave Model ◽  
Particle Dynamics ◽  
Suitable Parameter ◽  
Test Particles ◽  
The Mean ◽  
Parameter Values

The motion of charged particles is described in the presence of a strong magnetic field and of an electric field made of three spatial Fourier modes whose amplitudes vary in time. The dynamics of the wave amplitudes is governed by a model of three interacting drift waves. For suitable parameter values of the three-wave model, chaotic solutions are found so that the Eulerian electric field is made of three turbulent modes. The E × B motion is described for charged particles in the guiding center approximation, which brings to nonlinear Hamiltonian equations of motion. The Hamiltonian (that coincides with the electric potential) is explicitly time-dependent through the temporal variation of the mode-amplitudes of the electric field, this fact is at the origin of the intrinsic chaoticity of particle dynamics (lagrangian chaos). Diffusive behaviour of particle trajectories is due to their intrinsic chaoticity and thus it is of non-collisional origin. Some results are reported concerning the particle dynamics when the Eulerian electric field is either quasi-periodically or chaotically varying in time. In particular, one finds different diffusion laws in the two cases (anomalous and classical respectively). The scaling behaviour of the diffusion coefficients (when the mean square displacement grows linearly in time) is reported. A simple stochastic model is also used to account for some of the observed features of particle diffusion.

QUANTUM COHERENCE OF SUPERLATTICES IN TRIANGLE-WAVE ELECTRIC FIELDS

2000 ◽  
Vol 14 (01) ◽  
pp. 41-49 ◽  
Author(s):  
HAI-FENG LIU ◽  
XIAN-GENG ZHAO
Keyword(s):  
Electric Field ◽  
Exact Solutions ◽  
Electric Fields ◽  
Quantum Coherence ◽  
Mean Square Displacement ◽  
Initial Distribution ◽  
Coherent Motion ◽  
Mean Square ◽  
Long Period ◽  
The Mean

The problem of coherent motion of an electron in a long period superlattice driven by a triangle-wave electric field is studied. Exact solutions for the amplitude propagators, the field-induced polarization, the mean-square displacement, and the quasienergy spectrum of any initial distribution and long-range hopping coupling are obtained generally. Total collapse of the quasienergy spectrum is found to take place at certain field parameters, which leads to the transition between localization and delocalization. The transport property of the system is also investigated.

Kinetic theory of the diochotron instability

1968 ◽  
Vol 2 (3) ◽  
pp. 311-327 ◽  
Author(s):  
A. Nocentini ◽  
H. L. Berk ◽  
R. N. Sudan
Keyword(s):  
Kinetic Theory ◽  
Vlasov Equation ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Charged Particles ◽  
Physical Space ◽  
Distribution Functions ◽  
Velocity Spread ◽  
Cylindrical Layer ◽  
The Mean

The diochotron instability of a thin, tenuous, cylindrical layer of charged particles, whose gyro-radius is of the order of the mean radius of the cylindrical layer, is investigated using the Vlasov equation. Two distribution functions are considered which give practically the same density in the physical space, but are quite different in the velocity space: in the first the velocity spread is practically zero; in the second the particles oscillate around the mean radius of the cylindrical layer. It is shown that the first distribution exhibits the usual diochotron instability, while the second one does not. It is also shown that, however small the velocity spread, the thickness of the cylindrical layer cannot go to zero. Its minimum value is roughly determined by equating the plasma frequency to the cyclotron frequency.

The theory of the cosmic background radio signal received within the ionosphere

1964 ◽  
Vol 277 (1370) ◽  
pp. 365-384 ◽  
Keyword(s):  
Magnetic Field ◽  
Refractive Index ◽  
Magnetic Fields ◽  
Electric Field ◽  
Free Space ◽  
Wave Theory ◽  
Ordinary Wave ◽  
Mean Square ◽  
Ray Theory ◽  
The Mean

The electric and magnetic fields to be expected within the ionosphere from a background source uniformly distributed across the sky are studied. The ray theory for an isotropic, horizontally stratified loss-free slowly varying ionosphere is first given, and it is shown that the mean-square moduli of the electric field components have n times their free-space value, and the mean-square moduli of the magnetic field components have n 3 times their free-space value where n is the local refractive index. The corrections to be expected when a full-wave theory is used are discussed. The ray theory for an anisotropic, loss-free ionosphere is then given and it is shown that the energy flux in a given direction is proportional to the Gaussian curvature at the associated point on the refractive index surface. For the ordinary wave, near the level of reflexion, the electric field is predominantly parallel to the earth’s magnetic field, and the small perpendicular component is nearly 100% circularly polarized. Results for the magnetic fields and for the fields of the extraordinary wave are also given and discussed.

Properties of a bidisperse particle–gas suspension Part 2. Viscous relaxation time small compared with collision time

1993 ◽  
Vol 247 ◽  
pp. 643-660 ◽  
Author(s):  
V. Kumaran ◽  
Donald L. Koch
Keyword(s):  
Relaxation Time ◽  
Vertical Direction ◽  
Stokes Number ◽  
Terminal Velocity ◽  
Distribution Functions ◽  
Mean Square ◽  
Collision Time ◽  
Gas Suspension ◽  
The Mean ◽  
Viscous Relaxation

The properties of a dilute bidisperse particle–gas suspension under low Reynolds number, high Stokes number conditions are studied in the limit τv [Lt ] τc, where τc is the time between successive collisions of a particle, and τv is the viscous relaxation time. In this limit, the particles relax close to their terminal velocity between successive collisions, and we use a perturbation analysis in the small parameter ε, which is proportional to τv/τc, about a base state in which all the particles settle at their terminal velocities. The mean velocities of the two species are O(ε) different from their terminal velocities, and the mean-square velocities are O(ε) smaller than the square of the terminal velocity. The distribution functions for the two species, which incorporate the first effects of collisions between particles settling at their terminal velocities, are derived. The velocity distribution is highly anisotropic in this limit, and the mean-square velocity in the vertical direction is twice that in the horizontal plane. The distribution function for each species is singular at its terminal velocity, and the distributions are non-zero in a finite region in velocity space between the two terminal velocities.

Simulations of O2 adsorbed on graphite at 45 K: the monolayer to bilayer transition

1988 ◽  
Vol 66 (4) ◽  
pp. 866-874 ◽  
Author(s):  
Venkat Bhethanabotla ◽  
William Steele
Keyword(s):  
Translational Motion ◽  
Experimental Studies ◽  
Distribution Functions ◽  
Time Dependent ◽  
Dimensional Structure ◽  
Mean Square ◽  
Structure Factors ◽  
Orientational Distribution ◽  
The Mean ◽  
Graphite Basal Plane

Molecular dynamics computer simulations are reported for O2 physisorbed on the graphite basal plane at 45 K. Surface coverages ranged from the low density monolayer through the compressed monolayer up to roughly two layers. Thermodynamic properties, orientational distribution functions, and two-dimensional structure factors are presented. The time-dependent translational motion is characterized both by computer-generated trajectory plots and by evaluation of the mean square in-plane displacements as a function of time. It is concluded that the O2 orientations shift from predominantly surface-parallel to surface-perpendicular as the first layer density increases, in agreement with deductions from experiment. The structure factors indicate that some translational ordering is present in the fluid phases and that the bilayer is a composite made up of a solid monolayer plus a fluid overlayer; these observations are in agreement with recent experimental studies of this system.

DIFFUSING WAVE SPECTROSCOPY STUDY OF TAILING PHENOMENON OF COLLOIDAL ELECTRORHEOLOGY FLUIDS

2005 ◽  
Vol 19 (07n09) ◽  
pp. 1243-1248
Author(s):  
Y. H. MA ◽  
L. M. GUO ◽  
L. ZHONG ◽  
L. W. ZHOU
Keyword(s):  
Electric Field ◽  
Colloidal Particles ◽  
Mean Square Displacement ◽  
Electrorheological Fluid ◽  
Mean Square ◽  
Diffusing Wave Spectroscopy ◽  
Fluid Systems ◽  
The Mean ◽  
Electric Filed ◽  
Er Fluid

Back scattering of diffusing wave spectroscopy (DWS) method is employed to measure the mean square displacements of the colloidal particles in electrorheological fluid systems right after an electric field is applied and removed. An electrorheological fluid consisting of colloidal particles 30-40 nm in size shows a tailing phenomenon, namely the clusters of the colloidal ER particles do not return to their original state of Brownian motion as soon as the electric filed is removed. The DWS results of above ER fluid shows that the mean square displacement remains small and changes slowly with time right after the electric field is removed. The Van der Waals attractive force between colloidal particles is used to explain this tailing phenomenon.

A POWER SERIES EXPANSION OF THE MASTER EQUATION

1961 ◽  
Vol 39 (4) ◽  
pp. 551-567 ◽  
Author(s):  
N. G. van Kampen
Keyword(s):  
Power Series ◽  
Spectral Density ◽  
Master Equation ◽  
Approximation Method ◽  
Power Series Expansion ◽  
Planck Equation ◽  
Density Fluctuations ◽  
Mean Square ◽  
Approach To Equilibrium ◽  
The Mean

In order to solve the master equation by a systematic approximation method, an expansion in powers of some parameter is needed. The appropriate parameter is the reciprocal size of the system, defined as the ratio of intensive and extensive variables. The lowest approximation yields the phenomenological law for the approach to equilibrium. The next approximation determines the mean square of the fluctuations about the phenomenological behavior. In equilibrium this approximation has the form of a linear Fokker–Planck equation. The higher approximations describe the effect of the non-linearity on the fluctuations, in particular on their spectral density. The method is applied to three examples: density fluctuations, Alkemade's diode, and Rayleigh's piston. The relation to the expansion recently given by Siegel is also discussed.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

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