THE STATIC POTENTIAL ATTAINED BY AN INFINITE CYLINDER IMMERSED IN A MOVING AND LOW DENSITY PLASMA OF INFINITE EXTENT

1963 ◽  
Vol 41 (1) ◽  
pp. 132-142
Author(s):  
Dipak L. Sengupta

The static potential acquired by an infinite cylinder immersed in a low density collisionless plasma is discussed in detail. It is assumed that the plasma is uniform at large distances from the cylinder and of infinite extent and has a constant drift velocity in one specific direction. Approximate expressions for the distribution functions of the electrons and ions in the presence of the conducting cylinder are derived from the collisionless Boltzmann equation. Expression for the static potential of the cylinder is derived from the condition that the electrical neutrality of the plasma is maintained at large distances from the cylinder. Simplified expressions for the static potential are given for various physical situations. The case of stationary plasma is obtained as a special case of the former when the drift velocity equals zero. Numerical values are given for some cases.

1973 ◽  
Vol 51 (24) ◽  
pp. 2604-2611 ◽  
Author(s):  
H. E. Wilhelm

Based on the Lenard–Balescu equation, the interaction integral for the intercomponent momentum transfer in a two-component, collisionless plasma is evaluated in closed form. The distribution functions of the electrons and ions are represented in the form of nonisothermal, displaced Max wellians corresponding to the 5-moment approximation. As an application, the transport of electrical current in an electric field is discussed for infrasonic up to sonic electron–ion drift velocities.


2004 ◽  
Vol 11 (2) ◽  
pp. 153-163 ◽  
Author(s):  
N. Singh

Abstract. Using a fully 3-D particle in-cell simulation, we studied the electrodynamics of a thin current sheet (CS). Starting with a uniform plasma and anti-parallel magnetic field, Harris equilibrium is achieved during the early stage of the simulation. In the processes of reaching the equilibrium, both electrons and ions in the newly formed CS are energized and develop pitch-angle anisotropies. We find two distinct stages of primarily electrostatic instabilities; in the first stage the relative drift between electrons and ions drives the instability in the central regions of the CS. The electrostatic fluctuations scatter electrons causing current disruption in the central region. The associated reduction in the average drift velocity of the current-carrying electrons generates sheared flow. The second stage of the instability begins when the drift velocity develops a minimum in the central plane. Then the shear and the growing electrostatic fluctuations under the condition of the maintained anti-parallel driving magnetic field configuration feed each other making the instability explosive. The growing fluctuations create plasma clumps as the electrons and ions are progressively trapped in the large-amplitude waves. The density clumping also generates clumps in the current. The non-uniform current distribution causes magnetic reconnection, accompanied by heating of electrons and ion at a fast rate and nearly complete bifurcation of the current sheet. Anomalous resistivity during different stages of the evolution of the CS is calculated and compared against theory.


1968 ◽  
Vol 2 (2) ◽  
pp. 257-281 ◽  
Author(s):  
D. S. Butler ◽  
R. J. Gribben

The mathematical formulation for the problem of non-linear oscillations in a self-consistent, non-uniform, collisionless plasma is considered. The fully nonlinear treatment illuminates the effect of the wave on the background distribution of the plasma through which it is passing. It is assumed that, although the overall non-uniformity may be large, significant changes occur only over time or length scales which are large compared with the plasma period or Debye length respectively. Exclusion of secular terms from the solution leads to a Liouvile type equation, which must be satisfied by the background distribution, and to propagation laws for the waves.The theory is restricted to almost one-dimensional electrostatic waves and a general presentation is given from a relativistically-invariant point of view. Then the equations are derived in terms of physical variables for the special case in which: (i) the distribution functions and electrostatic potential depend on one space co-ordinate (that of propagation of the wave) and the former on the corresponding particle velocity component only, (ii) the wave is slowly-varying only with respect to this co-ordinate and time, and (iii) the magnetic field is zero. Finally, the non-relativistic limit of this case is considered in more detail. The boundary conditions satisfied by the distribution functions are discussed and this leads to the conclusion that in some circumstances thin sheets of probability fluid are formed in phase space and the background distribution cannot be strictly defined. This motivates a reformulation and subsequent re-solution of the problem (for this non-relativistic special case) in terms of weak functions, corresponding to the physical assumption of the presence of a small-scale mixing mechanism, which is excited by and smears the sheeted distribution but is otherwise dormant.The results of the investigation are given as a system of differentio-integral equations which must be solved if necessary conditions for the absence of nonsecular solutions (of the Vlasov and Maxwell equations) are to be satisfied. No solution of this system is attempted here.


2017 ◽  
Vol 817 ◽  
pp. 374-387 ◽  
Author(s):  
Arzhang Khalili ◽  
Bo Liu

Finite container sizes in experiments and computer simulations impose artificial boundaries which do not exist when they are meant to mimic ambient fluid of infinite extent. We show here that this is the case with flows past an infinite cylinder placed in an infinite ambient fluid (Stokes’ paradox). Using a highly efficient and stable numerical method that is capable of handling computational domains several orders of magnitude larger than in previous studies, we provide a criterion for the minimum necessary extent around an object in order to provide accurate velocity and pressure fields, which are prerequisites for correct calculation of secondary quantities such as drag coefficient. The careful and extensive simulations performed suggest an improved relation for the drag coefficient as a function of Reynolds number, and identify the most suitable experimental data available in the literature.


1996 ◽  
Vol 55 (1) ◽  
pp. 87-94 ◽  
Author(s):  
Yu. I. Chutov ◽  
A. Yu. Kravchenko ◽  
P. P. J. M. Schram

The expansion of a bounded plasma with dust particles is investigated by means of computer modelling, taking into account the dynamics of the dust particle charge as well as the Coulomb collisions of electrons and ions with dust particles. The PIC method is used for the computer modelling. The collection of electrons and ions by dust particles is described in a way similar to orbit-limited probe theory. Coulomb interactions are described in the framework of stochastic differential equations. It is shown that the mean distribution functions of electrons and ions are influenced by the dust particles during plasma expansion. The evolution of the ion distribution function leads to a strong deviation from equilibrium. Dust particles also influence the temporal behaviour of the plasma parameters.


2014 ◽  
Vol 80 (3) ◽  
pp. 517-528 ◽  
Author(s):  
S. K. Zaghbeer ◽  
H. H. Salah ◽  
N. H. Sheta ◽  
E. K. El-Shewy ◽  
A. Elgarayhi

A theoretical investigation has been made of obliquely propagating nonlinear electrostatic shock structures. The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger (KdV-Burger) equation for dust acoustic shock waves in a homogeneous system of a magnetized collisionless plasma comprising a four-component dusty plasma with massive, micron-sized, positively, negatively dust grains and non-extensive electrons and ions. The effect of dust viscosity coefficients of charged dusty plasma of opposite polarity and the non-extensive parameters of electrons and ions have been studied. The behavior of the oscillatory and monotonic shock waves in dusty plasma has been investigated. It has been found that the presence of non-extensive parameters significantly modified the basic properties of shock structures in space environments.


1990 ◽  
Vol 45 (8) ◽  
pp. 979-985 ◽  
Author(s):  
Martin Kretzschmar

Abstract Assuming a sufficiently low density of the trapped particles the methods of equilibrium statistical mechanics for non-interacting particles are used to find expectation values and distribution functions for the most interesting 1-particle observables. The results are applied in a perturbation calculation to estimate space charge effects at low particle densities


1995 ◽  
Vol 310 (2) ◽  
pp. 417-426 ◽  
Author(s):  
D F Meyer ◽  
M O Mayans ◽  
P H E Groot ◽  
K E Suckling ◽  
K R Bruckdorfer ◽  
...  

The oxidative modification of low-density lipoproteins (LDL) is recognized to be a key event in the development of atherosclerotic plaques on artery walls. The characteristics of LDL oxidized by cells of the artery wall can be imitated by the addition of Cu2+ ions to initiate lipid peroxidation in LDL. Neutron scattering of LDL in 2H2O buffers enables the time course of changes in the gross structure of LDL during oxidation to be continuously monitored under conditions close to physiological. Oxidation of LDL [2 mg of apolipoprotein B (apoB) protein/ml] was studied in the presence of 6.4, 25.6 and 51.2 mumol of Cu2+/g of apoB by incubation at 37 degrees C for up to 70 h. Neutron Guinier analyses showed that the radius of gyration RG (indicative of size) and the forward-scattered intensity at zero angle I(0) (indicative of M(r)) continuously increased during oxidation, indicating that LDL had aggregated. Both the rate of aggregation and the change in RG and I(0) values after 10 and 50 h increased with Cu2+ concentration. Distance-distribution functions P(r) showed that, within 4 h, the maximum dimension of LDL increased from 23 to 55 nm. The P(r) curves of oxidatively modified LDL exhibited two peaks at 10-12 nm and 26 nm. The 10-12 nm peak corresponds to native LDL, and the 26 nm peak is assigned to the initial formation of LDL dimers and trimers and their progression to form higher oligomers. The growth of the 26 nm peak depended on Cu2+ concentration. Particle-size-distribution functions Dv(r) suggested that the polydisperse spherical structure of LDL ceased to exist after 30 h, at which point the LDL samples underwent a phase separation. Related, but not identical, changes in the I(Q) and P(r) curves were observed when native LDL was self-aggregated by brief vortexing. Parallel assessment of LDL protein modification by SDS/PAGE showed increased aggregation and degradation of apoB with increased Cu2+ concentrations, and that the main apoB protein band had diminished after 2-8 h, depending on the amount of Cu2+ added. The uptake and degradation of oxidized 125I-labelled LDL by mouse peritoneal macrophages occurred maximally within the first 10 h, and increased in proportion to the Cu2+ concentration. ApoB protein broke down within the first 10 h of oxidation, and this is the period when scavenger receptors on macrophages can recognize and internalize oxidized LDL. Within 10 h, the protein-lipid interactions responsible for the spherical LDL structure became destabilized by protein fragmentation.(ABSTRACT TRUNCATED AT 400 WORDS)


1982 ◽  
Vol 27 (1) ◽  
pp. 191-191
Author(s):  
R. Balescu

I cannot agree with the reasoning of Vekstein, Ryutov & Sagdeev (1982) (VRS), the more so as I see no basic contradiction between their results and mine.The basic equations of the quasi-linear theory are the kinetic equations determining the time evolution of the distribution functions of the electrons and ions, ∂tfe,i and of the spectral densities ∂tψσ(κ) (plus the definition of the diffusion coefficient and the dispersion relations). It is agreed that these equations must be satisfied in any event. The marginal stability is an added approximation (as VRS, of course, admit), and can only be accepted if it is compatible with the basic equations.


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