Langmuir Probe in Non‐Maxwellian Plasma: Correlation Between the Electron Energy Distribution Function,the Ion Energy at the Sheath Edge and the Floating Voltage

This work is devoted to the study of the Langmuir probe in non‐Maxwellian plasma, assuming mono‐energetic singly charged ions and a collisionless sheath. Using a general analytical equation for the Electron Energy Distribution Function (EEDF), we study the effect of the EEDF profile on: a) The ion energy at the sheath edge of a negatively biased collector, b) the I‐V probe characteristic and c) the floating voltage (V_p‐Vf). Different methods are used and compared to determine these parameters or characteristics. A correlation is given between the floating voltage, the ion energy at the sheath edge and the EEDF profile. The study is also extended to distribution functions with several components. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probe measurements in a plasma having an anisotropic electron velocity distribution function

In this paper a number of questions connected with the diagnostics of anisotropic electron velocity distribution functions possessing a drift velocity were examined. In an example involving a model distribution function, the possible errors in measurements of the electron energy distribution function (EEDF) using a cylindrical probe oriented parallel to the particle flow are estimated. It is shown that application of a standard method for treating probe volt-ampere characteristics leads to over- and underestimates relative to the true values of the measured temperatures T _e ⁺ and T _e ^– , found respectively according to the currents i⁺(V) and i^–(V) on a flat probe, oriented along and against a specific direction. A comparison of calculated T _e ⁺ +/T _e ^– ratios is made with experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 9–13, September, 1990.     

Effect of molecular nitrogen on the electron mobility in a mixture of argon and optically excited sodium vapor

A parametric study of the electron energy distribution function (EEDF) and the electron mobility in the mixture Na + Ar + N₂ is carried out. An analysis is made of the conditions that obtain in a photoplasma when the detachment of the mean electron energy from the neutral gas temperature is due to superelastic collisions (collisions of the second kind) with excited sodium atoms. The case of low ionization of the medium at low vibrational temperatures of the ground state of the nitrogen molecules is considered. To find the EEDF a numerical solution of the Boltzmann transport equation is carried out. It is found that in the indicated mixture the presence of nitrogen leads to a depletion of the EEDF in the region of efficient vibrational excitation of the molecules and promotes the formation of inversion in the EEDF ∂f(ɛ)/∂ɛ>0 in the energy range corresponding to the Ramsauer minimum in the cross section of elastic collisions of electrons with the argon atoms. It is shown that the nonequilibrium character of the EEDF leads to a complicated dependence of the electron mobility on the partial ratios of the components of the mixture, the degree of ionization of the medium, and the population of the resonantly excited sodium atoms. Zh. Tekh. Fiz. 69, 14–19 (April 1999)     

射频感应耦合Ar-N2等离子体物理特性的Langmuir探针测量及理论研究

分别通过Langmuir探针测量和动力学模型模拟方法研究了射频感应耦合Ar-N₂等离子体中电子能量分布、电子温度、电子密度等物理量随N₂含量的变化规律.实验研究结果表明：电子能量分布呈现出非Maxwell型分布,并由双温分布向三温分布过渡;电子温度在不同的气压下随N₂含量的增加呈现出不同的变化规律.在放电气压小于1.3 Pa时,电子温度随N₂含量的增加而下降;当气压大于1.3 Pa时,电子温度随N₂关键词： 感应耦合等离子体 2混合气体放电')" href="#">Ar-N₂混合气体放电 电子能量分布 Langmuir探针     

An approach for unipolar corona discharge in N2/O2 gas mixture by considering townsend conditions

In this study (α/p) = f(E/p) functional relation is derived for the gas mixture of N₂/O₂ by considering Townsend approach, and formation mechanism of corona discharge is investigated for the coaxial electrode system located in this gas medium. The electron energy distribution function (EEDF) which is required for estimation of ionization coefficient, is determined by considering probability distribution function of inelastic electron collisions versus energy. An algorithm for determining ionization coefficient for binary gas mixture is presented. The development and motion of the electron avalanche in inter-electrode gap are studied by considering the effect of positive space charges. It is determined by considering the derived mathematical expressions that the formation of corona discharge is related with the variation of the current characteristics in inter-electrode gaps depending on the change of potential of central electrode.     

Comments on the Bohm Criterion and on the Determination of the Ion Velocity at the Sheath Edge in Non‐Maxwellian Plasma

This work is devoted to the study of the Bohm criterion in the general case of the electron energy distribution function (EEDF). Investigations are performed by means of a Monte Carlo integration method. We resolve the cold fluid equation system describing the ion motion within the sheath, assuming collisionless conditions, singly charged and mono kinetic incoming ions (BOHM model). Results confirm that the limit ion velocity at the sheath edge to assure a monotone electric field with a positive charge over the entire sheath is v_i ≥ (kT_e/M_i) or ε_i ≥ 1/3 <ε_e> in the case of Maxwellian electrons. We show that in the case of a Druyvesteyn electron energy distribution, this limit is larger, it is ε_i ≥ 0.6 <ε_e>. The study is also extended to other distributions functions. Because of the large controversy in recent publications, concerning the boundary conditions at the sheath entrance, we discuss the collisionless conditions at the sheath edge according to the plasma parameters. It is shown that in a collisionless sheath, the condition n_i(χ) ≥ n_e(χ) can be used to determine the limit ion velocity at the sheath edge of the negatively biased collector (Langmuir probe for instance) (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of parameters of krypton plasma excited by electron beam with additional heating by high-frequency electric field

The electron energy-distribution functions, the rates of plasmochemical reactions, and the densities of various plasma components have been calculated for a microwave discharge (f = 1000 MHz, P = 100–700 mW) in krypton plasma (p = 0.5 atm) excited by an electron beam with an energy of 12 keV. It has been found that the heating by a microwave field shifts the peak of the electron energy-distribution function (EEDF) from 0.5 to 2 eV, which leads to higher rates of reactions with excitation thresholds lying near the EEDF peak. As a result, the population of excited levels increases by two to three times.     

Langmuir probe and optical emission spectroscopy studies for RF magnetron sputtering during TiON thin film deposition

Low-pressure plasma of gas mixture of Ar, O₂ and N₂ generated by RF magnetron sputtering was characterized by Langmuir probe and optical emission spectroscopy (OES). The electron temperature (T_e), ion density (n_i) and electron energy distribution function (EEDF) in Ar-O₂-N₂ plasma atmosphere were calculated from I-V characteristic of Langmuir probe. Boltzmann plot method was applied for calculating the vibrational temperature (T_vib) of the second positive system of N₂ (N₂SPS) in Ar-O₂-N₂ plasma. The T_e, n_i, EEDF and T_vib in Ar-O₂-N₂ plasma were studied as a function of O₂ percentages. It was found, the T_vib increased from 0.47 eV to 0.55 eV as the oxygen percentage in Ar-N₂-O₂ plasma increased from 10% to 40%. Further, the T_e increased from 1.6 eV to 3 eV as the O₂ concentration increased from 10% to 40%.     

弱电离大气等离子体电子能量分布函数的理论研究

使用球谐展开的方法求解玻尔兹曼方程,得到了弱电离大气等离子体(79％氮气和21％的氧气)的电子能量分布函数(EEDF).发现当约化电场较小时(E/N＜100 Td),EEDF在2-3 eV急剧下降,在此情况下,高能尾部比麦氏分布要小;当约化电场增加,E/N＞ 400 Td,分布函数趋近于麦氏分布;当约化电场进一步增加,E/N＞ 2000 Td,EEDF的高能尾部(超过200 eV)相对于麦氏分布增加,在高频场作用下,EEDF更倾向于麦氏分布.当ω》vm时,有效电子温度只依赖于E/ω,而与碰撞频率无关;当ω《vm时,有效电子温度只依赖于E/N,与微波频率无关.与一些单原子分子等离子体中电子-电子碰撞在电离度大于10-6时就会影响EEDF不同,空气等离子体中,只有当电离度大于0.1％时,电子-电子碰撞才会对EEDF有明显影响.     

Non-Maxwellian electron energy distribution function in He,He/Ar,He/Xe/H<Subscript>2</Subscript> and He/Xe/D<Subscript>2</Subscript> low temperature afterglow plasma

Experimental studies of the electron energy distribution function “EEDF” under well defined conditions in flowing afterglow plasma, using a Langmuir probe are reported. The EEDF is measured in He₂ ⁺ and Ar⁺ dominated plasmas and in XeH⁺ and XeD⁺ dominated recombining plasmas. He is used as a buffer gas at medium pressures in all experiments (1600 Pa, 250 K). The deviation of the measured EEDF from Maxwellian distribution is shown to depend on plasma composition and on the processes governing the plasma decay. The influence of energetic electrons produced during the plasma decay on the body and tail of the EEDF is observed. The mechanism of energy balance in afterglow plasma is discussed.     

Triple differential cross section of electron impact ionisation of Na(3s, 3p, 3d)

The fivefold differential cross section (5DCS) of the ionisation by electron impact of atomic sodium is determined theoretically for its fundamental 3s(² S) state and the excited 3p(² P) and 3d(² D) states by a procedure which employs in the transition matrix element of the first order Born approximation, the correlated double continuum (3C) wave function. This permits us to determine the statistical M-state population and the orientation and alignment tensors in (e,2e) detection. It is also shown that, the use of Gamow correlation term, in the independent particle (2C) model, reproduces, only in some situations, the shape of the angular distribution of the 5DCS obtained by the (3C) wave function. Received: 17 November 1997 / Received in final form: 16 March 1998 / Accepted: 21 March 1998     

Nuclear mean fields through self-consistent semiclassical calculations

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V _n( r) and V _p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields. Received: 12 February 2000 / Accepted: 14 March 2002     

Comment on Vub from exclusive semileptonic B and D decays

The prospects for determining |V_ub| from exclusive B semileptonic decay are discussed. The double ratio of form factors (f^(B→ρ)/f^(B→K*))/(f^(D→ρ)/f^(D→K*)) is calculated using chiral perturbation theory. Its deviation from unity due to contributions that are non-analytic in the symmetry breaking parameters is very small. Combining experimental data obtainable from , and can lead to a model independent determination of |V_ub| with an uncertainty from theory of about 10%.     

Double‐probe measurement in recombining plasma using NAGDIS‐II

We have studied the validity of the double‐probe method in recombining plasmas. Electron temperature (T_e) measured with a double probe was quantitatively evaluated by taking into account the influences of plasma potential fluctuation, plasma resistivity, and electron density fluctuation on the current–voltage characteristics. Differential potential fluctuation and plasma resistivity between two electrodes have a minor effect on T_e especially when the inter‐distance is small (typically 1 mm). Scattering of measured T_e due to the density fluctuation was sufficiently suppressed by making the data acquisition time long (typically 4 s) and taking the average. There is a good agreement between T_e measured with the optimized double‐probe method and that with laser Thomson scattering diagnostics.     

Diffusionstheoretische Beschreibung der Dissoziation und des Ionenhaushaltes im schwachionisierten Säulenplasma der Wasserstoffentladung. II. Makroskopische Kenngrößen der Elektronen im H/H2-Mischplasma

The results of the calculation of the energy distribution function f(U), of the transport coefficients ū, b_e, D_e, of the collision frequencies for dissociation and direct ionization and of the main energy loss rates due to elastic and inelastic collisions of the electrons with the components of the mixture are presented for a stationary and homogeneous hydrogen plasma. These calculations, based upon the Boltzmann equation for the electrons, are performed in dependence of the normalized electric field strength E/p₀ and the mixture ratio x_D in the range of 7.5 to 100 V/cm Torr for E/p₀ and for any mixture ratio.     

Modelling of electron stream discharge

Particle-in-cell Monte Carlo code is used to simulate gas discharge initiated by a high current (I _e10kA) middle energy ( _e10keV) hot ( _e1 keV) electron stream. The generation of such an overthermal electron stream has been clearly demonstrated at the experimental REBEX facility during the relativistic electron beam-plasma interaction. When the electron beam (represented by1000 macroparticles) is injected into the drift tube filled by neutral gas (hydrogen,p=13.3–133 Pa) two different stages are observed. During the initial stage the arising Virtual Cathode (VC) is filled by hydrogen ions. The VC disappears when the quasineutrality of ionized gas is achieved. Then the severe exponential growth of electron and ion component of ionized gas is observed.List of symbols x distance from the left electrode [m] - t time [s] - v _x ,v _y velocity components [m/s] - g4(x) potential [Volt] - g4 _1/2(t) middle potential [Volt] - E(x) electric field [Volt/m] - Q _wall wall charge [C/m.m] - I current [C/s] - _tot total energy [J] - N number of macroparticles - f() energy distribution of electron macroparticles at the left electrode, is kinetic energy of macroparticle [eV]. Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.     

Reconstruction of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity according to holographic dark energy

We develop the reconstruction of the f(T) gravity model according to the holographic dark energy. T is the torsion scalar and its initial value from the teleparallel gravity is imposed for fitting the initial value of the function f(T). The evolutionary nature of the holographic dark energy is essentially based on two important parameters, Ω _V  and ω _V , respectively, the dimensionless dark energy and the parameter of the equation of state, related to the holographic dark energy. The result shows a polynomial function for f(T), and we also observe that, when Ω _V →1 at the future time, ω _V may cross −1 for some values of the input parameter b. Another interesting aspect of the obtained model is that it provides a unification scenario of dark matter with dark energy.     

Excitation cross sections of thulium atom transitions terminating at 4f13(2Fo)6s6p(3Po (7/2, J2) levels with J2 = 0, 1

The excitation of odd levels of the thulium atom, spontaneous transitions from which terminate at the 4f ¹³(² F ^o)6s6p(³ P ^o) (7/2, J ₂) levels with J ₂ = 0, 1, is studied by the method of extended crossing beams. Fifty four excitation cross sections are measured at an excitation electron energy of 50 eV. Seven optical excitation functions are recorded in the electron energy range of 0–200 eV.