Exact damped sinusoidal electric field of nonlinear one-dimensional Vlasov-Maxwell equations

1984 ◽  
Vol 32 (2) ◽  
pp. 197-205 ◽  
Author(s):  
B. Abraham-Shrauner
Keyword(s):  
Distribution Function ◽  
Electric Field ◽  
Maxwell Equations ◽  
Angular Frequency ◽  
Wave Number ◽  
One Dimensional ◽  
Damping Decrement ◽  
Sinusoidal Electric Field ◽  
The One ◽  
Special Case

An exact solution for a temporally damped sinusoidal electric field which obeys the nonlinear, one-dimensional Vlasov-Maxwell equations is given. The electric field is a generalization of the O'Neil model electric field for Landau damping of plasma oscillations. The electric field is a special case of the form found from the invariance of the one-dimensional Vlasov equation under infinitesimal Lie group transformations. The time dependences of the damping decrement, of the wave-number and of the angular frequency are derived. Use of a time-dependent BGK one-particle distribution function is justified for weak damping where, in general, it is necessary to carry out a numerical calculation of the invariant of which the distribution function is a functional.

The general Lie group and similarity solutions for the one-dimensional Vlasov–Maxwell equations

1985 ◽  
Vol 33 (2) ◽  
pp. 219-236 ◽  
Author(s):  
Dana Roberts
Keyword(s):  
Lie Group ◽  
Maxwell Equations ◽  
Transformation Group ◽  
Spatial Dimension ◽  
Similarity Solutions ◽  
One Dimensional ◽  
Special Cases ◽  
General Similarity ◽  
The One ◽  
The Individual

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov–Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multi-species case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution (t→∞) for a one-species, one-dimensional plasma is one of the general similarity solutions.

A perturbation solution to the full Poisson–Nernst–Planck equations yields an asymmetric rectified electric field

Soft Matter ◽  
2020 ◽  
Vol 16 (30) ◽  
pp. 7052-7062
Author(s):  
S. M. H. Hashemi Amrei ◽  
Gregory H. Miller ◽  
Kyle J. M. Bishop ◽  
William D. Ristenpart
Keyword(s):  
Electric Field ◽  
Perturbation Solution ◽  
One Dimensional ◽  
Ionic Mobilities ◽  
The One

We derive a perturbation solution to the one-dimensional Poisson–Nernst–Planck (PNP) equations between parallel electrodes under oscillatory polarization for arbitrary ionic mobilities and valences.

Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

1999 ◽  
Vol 51 (5) ◽  
pp. 915-935 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Christoph Leuenberger
Keyword(s):  
Unit Circle ◽  
Complex Flow ◽  
One Dimensional ◽  
Holomorphic Motions ◽  
Strictly Convex ◽  
Fixed Domain ◽  
Polynomial Hulls ◽  
Polynomial Hull ◽  
The One ◽  
Special Case

AbstractConsider the polynomial hull of a smoothly varying family of strictly convex smooth domains fibered over the unit circle. It is well-known that the boundary of the hull is foliated by graphs of analytic discs. We prove that this foliation is smooth, and we show that it induces a complex flow of contactomorphisms. These mappings are quasiconformal in the sense of Korányi and Reimann. A similar bound on their quasiconformal distortion holds as in the one-dimensional case of holomorphic motions. The special case when the fibers are rotations of a fixed domain in C2 is studied in details.

Dielectric conductivity of a bounded plasma and its rate of convergence towards its infinite-geometry value

2003 ◽  
Vol 69 (5) ◽  
pp. 449-463
Author(s):  
PASCAL OMNES
Keyword(s):  
Distribution Function ◽  
Electric Field ◽  
Rate Of Convergence ◽  
Dielectric Function ◽  
Bounded Geometry ◽  
First Order ◽  
First Order Correction ◽  
Time Periodic ◽  
Special Case ◽  
Distance To The Boundary

This paper deals with the linear response of a plasma in a one-dimensional bounded geometry under the action of a time-periodic electric field. The nonlinear Vlasov equation is solved by following the characteristic curves until they reach the boundary of the domain, where the distribution function of the incoming particles is supposed to be known and independent of time. Then, a first-order Taylor expansion in the velocity variable is performed, thanks to an approximation of the exact characteristics by the unperturbed ones. The resulting first-order correction to the distribution function is finally integrated over velocities to yield the dielectric function. The special case of a plane wave for the electric field is examined and the results are compared with the more usual unbounded case: the integral does not present any singularity in the vicinity of resonant particles and the dielectric function depends on the distance to the boundary and tends to the usual infinite-geometry value when this distance tends to infinity, with a rate of convergence proportional to its inverse square root. Numerical examples are provided for illustration.

Cadmium Sulfide and Zinc Sulfide Nanostructures Formed by Electrophoretic Deposition

2012 ◽  
Vol 507 ◽  
pp. 101-105 ◽  
Author(s):  
Alejandro Vázquez ◽  
Israel López ◽  
Idalia Gómez
Keyword(s):  
Thin Films ◽  
Electric Field ◽  
Cadmium Sulfide ◽  
Zinc Sulfide ◽  
Electrophoretic Deposition ◽  
Cds Nanoparticles ◽  
One Dimensional ◽  
Cds Thin Films ◽  
The One ◽  
One Dimensional Nanostructures

Cadmium sulfide (CdS) and zinc sulfide (ZnS) nanostructures were formed by means of electrophoretic deposition of nanoparticles with mean diameter of 6 nm and 20 nm, respectively. Nanoparticles were prepared by a microwave assisted synthesis in aqueous dispersion and electrophoretically deposited on aluminum plates. CdS thin films and ZnS one-dimensional nanostructures were grown on the negative electrodes after 24 hours of electrophoretic deposition at direct current voltage. CdS and ZnS nanostructures were characterized by means of scanning electron (SEM) and atomic force (AFM) microscopies analysis. CdS thin films homogeneity can be tunable varying the strength of the applied electric field. Deposition at low electric field produces thin films with particles aggregates, whereas deposition at relative high electric field produces smoothed thin films. The one-dimensional nanostructure size can be also controlled by the electric field strength. Two different mechanisms are considered in order to describe the formation of the nanostructures: lyosphere distortion and thinning and subsequent dipole-dipole interactions phenomena are proposed as a possible mechanism of the one-dimensional nanostructures, and a mechanism considering pre-deposition interactions of the CdS nanoparticles is proposed for the CdS thin films formation.

Unified geometric and analytical treatment of magneto– gasdynamic shocks. Part 2. The shock polars

1973 ◽  
Vol 10 (3) ◽  
pp. 397-423 ◽  
Author(s):  
Lee A. Bertram
Keyword(s):  
Particle Velocity ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Analytical Treatment ◽  
Classification Schemes ◽  
One Dimensional ◽  
The One ◽  
Shock Solution ◽  
Special Case ◽  
Alfven Velocity

Previously derived shock solutions for a perfectly conducting perfect gas are used to compute shock polars for the one-dimensional unsteady and two- dimensional non-aligned shock representations. A new special-case shock solution, having a downstream particle velocity relative to the shock equal to upstream Alfvén velocity, is obtained, in addition to exhaustive analytical classification schemes for the shock polars. Eight classes of one-dimensional polars and twelve classes of two-dimensional polars are identified.

Proposed Use of the One-Dimensional Two-Fluid Model With Momentum Flux Parameters

2000 ◽  
Author(s):  
Jin Ho Song ◽  
H. D. Kim
Keyword(s):  
Differential Equations ◽  
Void Fraction ◽  
Momentum Flux ◽  
Fluid Model ◽  
Sufficient Conditions ◽  
Wave Number ◽  
One Dimensional ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

Abstract The dynamic character of a system of the governing differential equations for the one-dimensional two-fluid model, where the appropriate momentum flux parameters are employed to consider the velocity and void fraction distribution in a flow channel, is analyzed. In response to a perturbation in the form of a traveling wave, a linear stability analysis is performed for the governing differential equations. The analytical expression for the growth factor as a function of wave number, void fraction, drag coefficient, and relative velocity is derived. It provides the necessary and sufficient conditions for the stability of the one-dimensional two-fluid model in terms of momentum flux parameters. It is analytically shown that the one-dimensional two-fluid model is mathematically well posed by use of appropriate momentum flux parameters, while the conventional two-fluid model makes the system unconditionally unstable. It is suggested that the velocity and void distributions should be properly accounted for in the one-dimensional two-fluid model by use of momentum flux parameters.

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