scholarly journals Кинетическая теория пристеночного слоя при произвольных условиях в газоразрядной плазме

2019 ◽  
Vol 89 (9) ◽  
pp. 1384
Author(s):  
O. Мурильо ◽  
А.С. Мустафаев ◽  
В.С. Сухомлинов
Keyword(s):  
Distribution Function ◽  
Electron Energy ◽  
Electron Distribution Function ◽  
Debye Length ◽  
Ion Distribution ◽  
Ion Energy ◽  
Charge Exchange Cross Section ◽  
The Mean ◽  
Exchange Cross Section ◽  
The One

For an arbitrary relation of the Debye length to the ion free path, based on the kinetic approach, it was solved the self consistent problem of the structure of the perturbed wall sheath in a DC plasma gas discharge, near a flat surface at a negative potential in relation to the plasma. The solution was obtained without an artificial separation of the perturbed wall sheath into a quasineutral "presheath" and a wall sheath where quasineutrality is substantially violated. They were taken into account the real ion distribution function in the unperturbed plasma, the dependence of the charge exchange cross section on the ion energy, and the nonzero electric field in the unperturbed plasma. It was found that, if the mean electron energy is preserved, the structure of the perturbed wall sheath weakly depends on the form of the electron distribution function. It was shown that, even under the assumption that the mean electron energy is much higher than the mean ion energy, is the mean ion energy in the unperturbed plasma the one that has a significant effect both on the structure of the quasineutral "presheath" and on the structure of a part of the wall sheath, where there is no quasineutrality. The calculations of the parameters of the ion flux and the structure of the perturbed wall sheath are in agreement with other authors’ experimental results that didn’t have previously an adequate interpretation.

scholarly journals Inelastic Collisions in the Townsend?Huxley Diffusion Experiment

1971 ◽  
Vol 24 (4) ◽  
pp. 841 ◽  
Author(s):  
JLA Francey ◽  
PK Stewart
Keyword(s):  
Distribution Function ◽  
Energy Loss ◽  
Cross Sections ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Inelastic Collisions ◽  
Diffusion Experiment ◽  
Inelastic Energy Loss ◽  
The Mean ◽  
Range Of Values

The Boltzmann equation, including density gradients, is solved for the electron distribution function in the Townsend-Huxley experiment. Elastic and inelastic collisions with constant cross sections are assumed to occur, the inelastic energy loss per collision being small compared with the mean energy. The inelastic energy loss and the electron mean energy are calculated and tabulated over a range of values of EIP.

Solution with Third-order Accuracy for the Electron Distribution Function in Weakly Ionized Gases (or in Intrinsic Semiconductors): Application to the Drift Velocity

1981 ◽  
Vol 34 (4) ◽  
pp. 361 ◽  
Author(s):  
G Cavalleri
Keyword(s):  
Distribution Function ◽  
Legendre Polynomials ◽  
Taylor Expansion ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Mean Free Path ◽  
Third Order ◽  
Order Accuracy ◽  
Weakly Ionized ◽  
The Mean

The first four components 10, I" 12 and 13 of the expansion in Legendre polynomials of the electron distribution function I are shown to be of order t:D, et, e2 and e3 respectively, with e = (m/M)'/2 where m and M are the masses of the electron and molecule respectively. This allows the solution of the so-called P3 approximation to the Boltzmann equation applied to a weakly ionized gas (or to an intrinsic semiconductor) in steady-state and uniform conditions and for dominant elastic collisions. However, nonphysical divergences appear in 10 and in the drift velocity W. This can be understood by the equivalence of the Boltzmann-Legendre formulation and the mean free path formulation in which a Taylor expansion is performed around the 'origin', i.e. for a -+ 0, where a = eE/m is the acceleration due to an external electric field E. Indeed, one sees that the expansion under the integral sign (integrals appear in the evaluation of transport quantities) leads to divergent integrals if the expansion is around a = O. Fortunately, it is easy to perform a Taylor expansion around a oft 0 in the mean free path formulation and then to find the corresponding expansion in Legendre polynomials outside the origin. In this way, explicit convergent expressions are found for 10, I" 12, 13 and W, with third-order accuracy in e = (m/M)'/2. This is better than the best preceding expression, that by Davydov-Chapman-Cowling, which has first-order accuracy only (it is the solution of the P, approximation to the Boltzmann equation).

Specific Features of Stark Broadening of Helium-Like Multi-Charged Ion Spectral Lines

1988 ◽  
Vol 102 ◽  
pp. 83-86
Author(s):  
V.P. Gavrilenko ◽  
I.M. Gaisinsky ◽  
Y.O. Ispolatov ◽  
E.A. Oks
Keyword(s):  
Dense Plasma ◽  
Energy Levels ◽  
Spectral Lines ◽  
Stark Broadening ◽  
Ion Energy ◽  
Fine Structures ◽  
The Mean ◽  
Active Research ◽  
The One ◽  
Charged Ions

Recently as a result of more active research on dense high temperature plasmas prominent importance has been acquired by the development of the theory of Stark broadening of multi-charged ions’Spectral lines (SL). This theory must take into account, on the one hand, the presence of fine structures in ion energy levels, and on the other hand, the effects appearing in the dense plasma:(1) dipole as well as quadrupole interaction with plasma ion microfield; (2) plasma polarization shift (PPS) of SL due to the mean electric field where the ion emitter is situated. Over the recent years a number of papers has appeared [1-4] which consider different aspects of the theory for ions with one and with two electrons.

scholarly journals Enhanced ion acoustic lines due to strong ion cyclotron wave fields

2008 ◽  
Vol 26 (8) ◽  
pp. 2081-2095 ◽  
Author(s):  
H. Bahcivan ◽  
R. Cosgrove
Keyword(s):  
Distribution Function ◽  
Electric Fields ◽  
Near Field ◽  
Electron Distribution Function ◽  
Ion Distribution ◽  
Incoherent Scatter Radars ◽  
Ion Acoustic ◽  
Ion Cyclotron ◽  
Observational Fact ◽  
Step Mechanism

Abstract. The Fast Auroral Snapshot Explorer (FAST) satellite detected intense and coherent 5–20 m electric field structures in the high-latitude topside auroral ionosphere between the altitudes of 350 km and 650 km. These electric fields appear to belong to electrostatic ion cyclotron (EIC) waves in terms of their frequency and wavelengths. Numerical simulations of the response of an electron plasma to the parallel components of these fields show that the waves are likely to excite a wave-driven parallel ion acoustic (IA) instability, through the creation of a highly non-Maxwellian electron distribution function, which when combined with the (assumed) Maxwellian ion distribution function provides inverse Landau damping. Because the counter-streaming threshold for excitation of EIC waves is well below that for excitation of IA waves (assuming Maxwellian statistics) our results suggest a possible two step mechanism for destabilization of IA waves. Combining this simulation result with the observational fact that these EIC waves share a common phenomenology with the naturally enhanced IA lines (NEIALS) observed by incoherent scatter radars, especially that they both occur near field-aligned currents, leads to the proposition that this two-step mechanism is an alternative path to NEIALS.

scholarly journals On the Brownian displacements and thermal diffusion of grains suspended in a non-uniform fluid

1928 ◽  
Vol 119 (781) ◽  
pp. 34-54 ◽  
Keyword(s):  
Distribution Function ◽  
Equilibrium Distribution ◽  
Mean Free Path ◽  
Physical Analysis ◽  
Brownian Particles ◽  
Uniform Case ◽  
The Mean ◽  
The One ◽  
Coefficient Of Diffusion ◽  
Uniform Fluid

1. In two famous papers on the Brownian motion of grains suspended in a stationary uniform fluid (liquid or gaseous) Einstein obtained, inter alia , the distribution function for the displacements of the grains during any interval t = 0 to t = τ from their positions at time t = 0. The object of this paper is to determine the distribution function for the more general case of a non-uniform fluid. The non-uniformity may refer to temperature, composition, or any other property which affects the coefficient of diffusion (D) of the grains in the fluid. The distribution function is given in 8, where it is shown how its accuracy might be experimentally tested. It contains terms additional to the one given by Einstein for the uniform case; certain of these are definitely determined, but another important term contains a coefficient that cannot be evaluated by considerations of the kind used in this paper (which depend purely on the conservation of the number of grains), but requires more detailed physical analysis; it is surmised that this coefficient vanishes in the case of Brownian particles which are large compared with the mean free path of the surrounding molecules. The main results of the paper refer to the rate of diffusion of the grains due to the non-uniformity of the fluid (9), and to the equilibrium distribution of the grains (10, 11). It is found that if their density is the same as that of the fluid, so that there is no tendency for them to settle in the lower strata, their steady distribution when the fluid is non-uniform is such that the concentration n (or number per unit volume of the fluid) is inversely proportional to D; a solution is also given for the case when the densities are not equal.

scholarly journals Full particle-in-cell simulations of kinetic equilibria and the role of the initial current sheet on steady asymmetric magnetic reconnection

2016 ◽  
Vol 82 (3) ◽  
Author(s):  
J. Dargent ◽  
N. Aunai ◽  
G. Belmont ◽  
N. Dorville ◽  
B. Lavraud ◽  
...  
Keyword(s):  
Distribution Function ◽  
Magnetic Reconnection ◽  
Current Sheet ◽  
Initial Conditions ◽  
Electron Flow ◽  
Electron Distribution Function ◽  
Ion Distribution ◽  
Initial Current ◽  
Particle In Cell ◽  
Kinetic Equilibrium

Tangential current sheets are ubiquitous in space plasmas and yet hard to describe with a kinetic equilibrium. In this paper, we use a semi-analytical model, the BAS model, which provides a steady ion distribution function for a tangential asymmetric current sheet and we prove that an ion kinetic equilibrium produced by this model remains steady in a fully kinetic particle-in-cell simulation even if the electron distribution function does not satisfy the time independent Vlasov equation. We then apply this equilibrium to look at the dependence of magnetic reconnection simulations on their initial conditions. We show that, as the current sheet evolves from a symmetric to an asymmetric upstream plasma, the reconnection rate is impacted and the X line and the electron flow stagnation point separate from one another and start to drift. For the simulated systems, we investigate the overall evolution of the reconnection process via the classical signatures discussed in the literature and searched in the Magnetospheric MultiScale data. We show that they seem robust and do not depend on the specific details of the internal structure of the initial current sheet.

scholarly journals Solutions of Sodium in Liquid Ammonia as Described by a Hard Sphere Charge-Dipole Model in the Neutralizing Background

1991 ◽  
Vol 46 (1-2) ◽  
pp. 19-26
Author(s):  
M. F. Golovko ◽  
L A. Protsykevych
Keyword(s):  
Distribution Function ◽  
Hard Sphere ◽  
Liquid Ammonia ◽  
Analytic Solution ◽  
Ion Concentration ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Ion Distribution ◽  
Dipole System ◽  
The Mean

AbstractThe analytic solution of the mean spherical approximation obtained by us previously for the ion-dipole system in a neutralizing background is applied to study the structural, thermodynamic and dielectric properties of sodium-ammonia solutions. It is shown that the structure of ammonia is closepacked and changes little with ion concentration. The shape of the ion-ion distribution function changes from solvation behaviour with Debye-like asymptotics at low ion concentration to density ordering in the metalic region.

scholarly journals Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Alessandro Geraldini
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Electrostatic Potential ◽  
Grazing Angle ◽  
Debye Length ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Ion Temperature ◽  
Ion Distribution ◽  
Orbit Model

A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field $\boldsymbol {B}$ inclined at a small angle, $\alpha \ll 1$ (in radians), to the target. Adiabatic electrons are assumed, requiring $\alpha \gg \sqrt {Zm_{e}/m_{i}}$ , where $m_{e}$ and $m_{i}$ are the electron and ion mass, respectively, and $Z$ is the charge state of the ion. An electric field $\boldsymbol {E}$ is present to repel electrons, and so the characteristic size of the electrostatic potential $\phi$ is set by the electron temperature $T_{e}$ , $e\phi \sim T_{e}$ , where $e$ is the proton charge. An asymptotic scale separation between the Debye length $\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$ , the ion sound gyro-radius $\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$ and the size of the collisional region $d_{c} = \alpha \lambda _{\textrm {mfp}}$ is assumed, $\lambda _{D} \ll \rho _{s} \ll d_{c}$ . Here $\epsilon _0$ is the permittivity of free space, $n_{e}$ is the electron density, $T_{i}$ is the ion temperature, $B= |\boldsymbol {B}|$ and $\lambda _{\textrm {mfp}}$ is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances $x$ from the wall such that $\rho _{s} \ll x \ll d_{c}$ , that is, collisions are not treated. A self-consistent solution of the electrostatic potential for $x \sim \rho _{s}$ is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of $\phi (x)$ and results in an analytical expression for the ion distribution function at the target. It assumes that $\tau =T_{i}/(ZT_{e})\gg 1$ , and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For $\tau \gtrsim 1$ , the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.

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