Analytical model for ion angular distribution functions at rf biased surfaces with collisionless plasma sheaths

2002 ◽  
Vol 92 (12) ◽  
pp. 7032-7040 ◽  
Author(s):  
Laxminarayan L. Raja ◽  
Mark Linne
Keyword(s):  
Angular Distribution ◽  
Analytical Model ◽  
Collisionless Plasma ◽  
Distribution Functions ◽  
Plasma Sheaths

Analytical model of a magnetopause with countercurrents: multicomponent plasma with arbitrary particle energy distributions

2021 ◽  
Author(s):  
Anton Nechaev ◽  
Vitaly Kocharovsky ◽  
Vladimir Kocharovsky
Keyword(s):  
Energy Distribution ◽  
Analytical Model ◽  
Energy Content ◽  
Magnetic Transition ◽  
Collisionless Plasma ◽  
Distribution Functions ◽  
Magnetic Clouds ◽  
Energy Distributions ◽  
Current Sheets ◽  
Effective Temperatures

<p><span>We propose a</span>n analytical model <span>f</span>or a distributed current sheet separating two regions of anisotropic collisionless plasma with different values of <span>magnetization</span> and different effective temperatures of the energy distributions of electrons and ions <span>[1, 2]</span>. <span>Namely, we find a solution to the Vlasov–Maxwell equations in the form of </span>a superposition of arbitrary isotropic <span>distribution functions</span> of particle <span>energy</span>, <span>each </span>multiplied by a Heaviside step function <span>of</span> one of the projections of the generalized momentum. This solution admits the shear of magnetic <span>field</span> lines and the presence of several ion components with different effective temperatures and localized countercurrents <span>with arbitrary densities and spatial shifts</span>.</p><p>It is shown that <span>a</span> <span>certain</span> <span>choice </span>of the energy distribution of particles (Maxwellian, kappa, and others) <span>determine only the </span>quantitative, not qualitative, properties of the constructed models. <span>Sheets</span> containing several fractions of particles with countercurrents, shifted relative to each other in space and having different scales, allow multiple non-monotonic changes in the magnetic field value and direction. The total <span>thickness of the current </span><span>sheet</span> is determined by the values <span>o</span>f <span>s</span>hifts between <span>the </span>currents of <span>the </span><span>plasma</span> fractions with the highest energy content and <span>by </span>the typical gyroradii of the<span>ir</span> particles.</p><p><span>We carried out p</span><span>article-in-cell </span><span>simulati</span>ons of <span>the </span>analytically constructed magnetic transition layers in one-dimensional and two-dimensional geometries. The stability of the simplest models of the considered class is demonstrated, which is consistent with qualitative estimates of stability against Weibel-type perturbations.</p><p>The proposed models make it possible to interpret<span> modern </span>data of satellite observations of multicomponent current sheets in the regions of <span>the </span>magnetopause <span>and </span>the bow shock, solar wind magnetic clouds and high coronal magnetic structures, and to analyze the<span>ir</span> fine structure taking into account the observed suprathermal, nonequilibrium particle fractions.</p><p>The investigation of stability of current sheets was supported by the Russian Science Foundation under grant No. 20-12-00268.</p><p><span>1. K</span><span>ocharovsky V. V., Kocharovsky Vl. V., Martyanov V. Yu., Nechaev A. A. An analytical model for the current structure of the magnetosheath boundary in a collisionless plasma // Astron. Lett. 2019. V. 45, No. 8. P. 551–564. doi:10.1134/S1063773719080048 .</span></p><p><span>2. </span><span>Kocharovsky V. V., Kocharovsky Vl. V., Nechaev A. A.</span> <span>Analytical model of a magnetopause in a multicomponent collisionless plasma with a kappa energy distribution of particles </span><span>// </span><span>Doklady Physics</span><span>. 2021. </span><span>V</span><span>. 496. </span><span>In press.</span></p>

Experimental investigation and modelling of light scattering in a-Si:H solar cells deposited on glass/ZnO:Al substrates

2002 ◽  
Vol 715 ◽  
Author(s):  
J. Krc ◽  
M. Zeman ◽  
O. Kluth ◽  
F. Smole ◽  
M. Topic
Keyword(s):  
Surface Roughness ◽  
Experimental Investigation ◽  
Solar Cells ◽  
Angular Distribution ◽  
Light Scattering ◽  
Optical Model ◽  
Distribution Functions ◽  
Interface Roughness ◽  
Scattering Parameters ◽  
Good Agreement

AbstractThe descriptive scattering parameters, haze and angular distribution functions of textured ZnO:Al transparent conductive oxides with different surface roughness are measured. An approach to determine the scattering parameters of all internal interfaces in p-i-n a-Si:H solar cells deposited on the glass/ZnO:Al substrates is presented. Using the determined scattering parameters as the input parameters of the optical model, a good agreement between the measured and simulated quantum efficiencies of the p-i-n a-Si:H solar cells with different interface roughness is achieved.

Intercomponent Momentum Transport and Electrical Conductivity of Collisionless Plasma

1973 ◽  
Vol 51 (24) ◽  
pp. 2604-2611 ◽  
Author(s):  
H. E. Wilhelm
Keyword(s):  
Electrical Conductivity ◽  
Electric Field ◽  
Collisionless Plasma ◽  
Electrical Current ◽  
Distribution Functions ◽  
Momentum Transport ◽  
Ion Drift ◽  
Moment Approximation ◽  
Electrons And Ions ◽  
Two Component

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.

An Analytical Model for the Current Structure of the Magnetosheath Boundary in a Collisionless Plasma

2019 ◽  
Vol 45 (8) ◽  
pp. 551-564
Author(s):  
V. V. Kocharovsky ◽  
Vl. V. Kocharovsky ◽  
V. Yu. Martyanov ◽  
A. A. Nechaev
Keyword(s):  
Analytical Model ◽  
Collisionless Plasma ◽  
Current Structure

Stability of different plasma sheaths near a dielectric wall with secondary electron emission

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
Shaowei Qing ◽  
Jianguo Wei ◽  
Wen Chen ◽  
Shengli Tang ◽  
Xiaogang Wang
Keyword(s):  
Electron Emission ◽  
Secondary Electron ◽  
Collisionless Plasma ◽  
Secondary Electron Emission ◽  
Plasma Sheath ◽  
Dielectric Wall ◽  
Maxwellian Plasma ◽  
Wide Range ◽  
Plasma Sheaths ◽  
Sheath Structure

The linear theory stability of different collisionless plasma sheath structures, including the classic sheath, inverse sheath and space-charge limited (SCL) sheath, is investigated as a typical eigenvalue problem. The three background plasma sheaths formed between a Maxwellian plasma source and a dielectric wall with a fully self-consistent secondary electron emission condition are solved by recent developed 1D3V (one-dimensional space and three-dimensional velocities), steady-state, collisionless kinetic sheath model, within a wide range of Maxwellian plasma electron temperature $T_{e}$ . Then, the eigenvalue equations of sheath plasma fluctuations through the three sheaths are numerically solved, and the corresponding damping and growth rates $\unicode[STIX]{x1D6FE}$ are found: (i) under the classic sheath structure (i.e. $T_{e}<T_{ec}$ (the first threshold)), there are three damping solutions (i.e. $\unicode[STIX]{x1D6FE}_{1}$ , $\unicode[STIX]{x1D6FE}_{2}$ and $\unicode[STIX]{x1D6FE}_{3}$ , $0>\unicode[STIX]{x1D6FE}_{1}>\unicode[STIX]{x1D6FE}_{2}>\unicode[STIX]{x1D6FE}_{3}$ ) for most cases, but there is only one growth-rate solution $\unicode[STIX]{x1D6FE}$ when $T_{e}\rightarrow T_{ec}$ due to the inhomogeneity of sheath being very weak; (ii) under the inverse sheath structure, which arises when $T_{e}>T_{ec}$ , there are no background ions in the sheath so that the fluctuations are stable; (iii) under the SCL sheath conditions (i.e. $T_{e}\geqslant T_{e\text{SCL}}$ , the second threshold), the obvious ion streaming through the sheath region again emerges and the three damping solutions are again found.

A New Central Angle Estimation Method of Bistatic MIMO Radar

2013 ◽  
Vol 846-847 ◽  
pp. 1197-1200
Author(s):  
Jian Gong ◽  
Yi Duo Guo ◽  
Hui Xie ◽  
Zhi Long Li
Keyword(s):  
Angular Distribution ◽  
Hadamard Product ◽  
Estimation Method ◽  
Estimation Algorithm ◽  
Mimo Radar ◽  
Distribution Functions ◽  
Central Angle ◽  
Angle Estimation ◽  
Bistatic Mimo Radar ◽  
Simulation Results

Based on the theory that the steering vectors of coherently distributed targets for bistatic MIMO radar possess a property called Hadamard product rotational invariance (HPRI), a novel central angle estimation algorithm is derived. The proposed algorithm has the advantage of no searching and easily pair the estimated angles. Furthermore, it can deal with different coherently distributed targets with different angular distribution functions or unknown angular distribution functions. Simulation results show the proposed method is effective.

Relativistic formulation for non-linear waves in a non-uniform plasma

1968 ◽  
Vol 2 (2) ◽  
pp. 257-281 ◽  
Author(s):  
D. S. Butler ◽  
R. J. Gribben
Keyword(s):  
Mathematical Formulation ◽  
Collisionless Plasma ◽  
Debye Length ◽  
Type Equation ◽  
Distribution Functions ◽  
Small Scale ◽  
Relativistic Limit ◽  
Background Distribution ◽  
Non Linear ◽  
Special Case

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.

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