Kinetic analysis of the ionization ratio effects on a three‐species plasma

In partially ionized plasmas, the energy transferred to electrically charged species by the electromagnetic field can be partly channelized to the population of neutrals, due to interspecies collisional processes. Depending on the relative density of neutrals, these effects may govern the collective plasma dynamics by drastically modifying particle dynamics and energy‐transport processes with respect to the fully ionized plasma‐approximation models. In this work, the influence of the ionization ratio r_i on a partially ionized plasma is analysed by means of a three‐species one‐dimensional kinetic model to compute transient and steady state velocity‐dependent distribution functions. The conservative collision operators accounting for charge–charge and charge–neutral interactions allow studying several plasma scenarios with the same entire number of particles per unit of volume but for an increasing r_i parameter, in the presence of a modulated signal‐like electric field. For a sequence of plasma scenarios of fixed r_i, ranging from typical weakly ionized to highly ionized plasma values r_i ～ 10^?7–10^?4, the mass species flows are examined. These flows behave linearly with respect to r_i up to a value r_i ? 10^?5 from which the quasi‐linear dependence is critically altered. The convection–diffusion equations are solved with the semianalytical Propagator Integral Method, which behaves well to deal with conservative operators, density, and field discontinuities, allowing for the use of collision terms of disparate time and spatial characteristic scales. The results can be relevant to a wide class of plasma systems and to analyse the ionization ratio effects on transport coefficients.     

Electrostatic Probe Measurements in the Glow Discharge Plasma of a D. C. Magnetron Sputtering System

The characteristics of the plasma surrounding the substrates in a planar magnetron sputtering system with a graphite target have been investigated by electrostatic probe measurements. The behaviour of the ion density n_i and the electron temperature T_e, determining the ion flux that can be extracted by the substrate, with the variation of the basic system parameters, has been studied.     

Atomic Model Calculations of Gain Saturation in the 46.9 nm Line of Ne‐like Ar

The gain saturation in the 46.9 nm line of the Ar⁺⁸ laser is analyzed using an atomic kinetics code. The dependence of the gain (G) on the electron kinetic temperature (T_e) in the region (50 ‐150 eV) is calculated in the quasi steady‐state approximation for the different values of the electron density (N_e) and the plasma radius (r_pl). The influence of radiat on trapping, ion random and mean velocities, Stark line broadening and refraction losses on the gain saturation is taken into consideration. For r_pl = 150‐600 μm, the amplplication (G > 0 cm^‐1) exists in the large temperature/density domain (T_e = 60‐150 eV, N_e = 0.5‐10 × 10¹⁸ cm^‐3). However, the value G_s ∼ 1.4 cm^‐1 required for the gain saturation at the typical plasma length L_pl ∼ 15 cm is reached in the extremely narrow density regions at the high temperatures. The saturation is reached for r_pl = 600 μm at T^s_e = 150 eV in the region N^s_e = 1.8‐2 × 10¹⁸ cm ^‐3, for r_pl = 300 μm at T^s_e = 125 eV and N^s_e = 2.5‐3 × 10¹⁸ cm^‐3, and for r_pl = 150 μm at T^s_e = 110 eV and N^s_e = 3‐4 × 10¹⁸ cm^‐3. The broadest density region (N^s_e = 2 ‐8 × 10¹⁸ cm^‐3) is predicted for the narrowest column (r_pl = 150 μm) at the highest temperature (T^s_e = 150 eV). The operation in the broadest density region N^s_e, should make easier achievement of the gain saturation in the experiments.     

Kinetic Current-Convective Instability in Hot Electron Plasma

The kinetic current-convective instability excited in a hot electron plasma, i.e. for T_e ? T_i, is investigated in the linear stage. Density and temperature of plasma components have gradients along the x-direction. In the absence of longitudinal current (u = 0) and homogeneous temperature the instability is also excited with maximum growth rate much exceeding that obtained in the case of u ≠ 0. Gradual increasing of the ion temperature over that of the electrons and a large density gradient leads to reduce the instability in the linear stage.     

Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strongly Non-Linear Ion-Acoustic Solitons

Solitary wave solutions of the coupled equations for the ion dynamics and the Poisson equation are investigated in a plasma with T_e ? T_i.     

电子回旋共振等离子体特性及其对生长氮化镓晶膜的影响

为了解并优化在电子回旋共振等离子体辅助化学汽相沉积GaN晶膜的工艺研究中的等离子体特性,利用朗缪尔探针及法拉第筒系统地测量了离子密度(N_i)、等离子体势(V_p)、电子温度(T_e)及离子流强(J_i)等多个等离子体参量随微波功率(P_w)及沉膜室气压(p)变化的关系.给出了在P_w＝850W,p＝0.22Pa时,上述等离子体参量的轴向及径向分布.GaN晶膜的生长速率、电学及晶体学性能 关键词：     

"荧光-1"实验装置物理设计

本文主要介绍"荧光-1"实验装置物理参数设计, 并依据半经验公式预估在实验装置上可能达到的磁化等离子体状态参数. 理论设计结果表明: "荧光-1"实验装置最大放电电流1.5 MA, 四分之一周期3 μs, 最大反向磁场4 T; 以此为实验平台, 当θ箍缩线圈内充气压力50 mTorr(D₂气体)时, 形成的等离子体靶直径约为2 cm, 长度17 cm; 等离子体靶密度6.6×10¹⁶ cm^-3, 温度 (T_i+T_e) 约300 eV; 等离子体平均β值为0.95. 该状态参数接近磁化靶聚变所要求的等离子体靶初始状态参数. 关键词： 脉冲功率技术 反场构形 磁化等离子体 磁化靶聚变     

Stationary Propagation of Coupled Nonlinear High Frequency Waves and Ion-Acoustic Waves in a Plasma

Stationary solutions of the coupled equations for high frequency transverse waves in a plasma and for the low frequency ion motion (T_e?T_i) are investigated numerically. The use of the nonlinear hydrodynamic equations instead of the linear wave equation for ion acoustic waves allows to look for solutions without restrictions of the Mach number M = V/c_s (V group velocity, c_s ion acoustic velocity) and the ratio ω/ω_pe (ω frequency of the HF-field, ω_pe electron plasma frequency at the undisturbed region). In particular, supersonic soliton-like solutions with n/n_o > 1 were found. Dispersion effects due to charge separation are not included.     

Stimulated brillouin scattering of electromagnetic ion cyclotron waves in a plasma

Using the fluid model for the nonlinear response of ions, we have studied the nonlinear scattering of an electromagnetic ion cyclotron wave off the ion acoustic wave in a plasma. The low frequency nonlinearity arises through the parallel ponderomotive force on ions and the high frequency nonlinearity arises through the nonlinear current density of ions. For a typical nonisothermal plasma (T _e/T _i∼10) the threshold for this instability in a uniform plasma is ∼1mW/cm². At power densities ≳10² W/cm², the growth rate for backscatter turns out to be ∼10⁴s⁻¹.     

Plasma parameters in the upgraded Trimyx-M Galathea

Results are presented from measurements of the plasma parameters in the upgraded Trimyx-M Galathea. After the barrier magnetic field and the energy of the injected hydrogen plasma bunch were increased to B _bar ∼ 0.1 T and W ₀ ≈ 200 J, respectively, the following plasma parameters were achieved: the density n ∼ 5 × 10¹³ cm⁻³, the plasma confinement time τ* = 800–900 μs, the elergy of the confined plasma W ₁ ∼ 100 J, the ratio of the plasma pressure to the barrier magnetic pressure β ₀ ∼ 0.2, the electron temperature T _e ∼ 20 eV, and the ion temperature T _i ∼ 2T _e . The maximum time during which the plasma density decreased e-fold, τ _p , was found to be 300 μs at B _bar = 0.1 T, which agrees with the classical transport model.     

Cover Picture: Contrib. Plasma Phys. 10/2011

The spatial distribution of plasma parameters such as equipotential line, ion density n_i, and radial ion velocity V_ir for the low‐emissive segmented dielectric wall case, L = 3 mm. (Figure 5 of the paper by D. R. Yu, et al.)     

Excited-state populations of hydrogenlike and heliumlike ions and diagnostics of dense transient plasmas from the relative intensities of spectral lines

A collisional-radiative model of H- and He-like ions is constructed. The model allows a determination of excited-state population densities for arbitraryN _e ,T _e , and ion composition. The coefficientsr ₀ andr ₁, the collisional-radiative ionization and recombination coefficients for H-like ions and for the He-like ions F VIII and Mg XI are calculated. The methods of plasma diagnostics from the relative intensities of spectral lines are substantiated. It is indicated that the possibility of measuringN _e from the resonance-to-intercombination line intensity ratio of a [He] ion is determined by the knowledge of the ion composition andT _e . Translated from Trudy Fizicheskogo Instituta im. P. N. Lebedeva, Lebedev Physics Institute, Russian Academy of Sciences, Moscow, Vol. 195, pp. 158–178, 1989.     

Collective Dust‐Dust Attraction in Strong Magnetic Field

It is shown that the collective dust‐dust attraction is enhanced by strong magnetic fields larger then the critical magnetic field determined be the condition that the Lorentz force acting on ions is larger than the friction of ions on dust grains related with the dust drag. It is demonstrated that with an increase of the magnetic field the deepness of the attraction potential well is increased in all directions to the magnetic field, that the distance of the minimum of the potential well along the magnetic filed (in both directions) is changed only slightly while the distance of the minimum of the attraction potential well is substantially decreased for directions perpendicular to the magnetic field. This means that the structures formed by attraction forces such as plasma crystals will be compressed perpendicular to the magnetic field (inter‐dust distance becomes smaller) and that the melting transition temperature should increased with an increase of the strength of the magnetic field. Numerical results are presented for dependence of the attraction potential well on the ratio of the strength of the magnetic field to the critical magnetic field strength, on the parameter P = n_dZ_d/n_i (n_d and n_i being the dust and ion densities respectively) and on the temperature ratio τ = T_i/T_e (T_e and T_i being the electron and ion temperatures respectively). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lokale Messung von Driftgeschwindigkeit und Temperatur der Ionen einer Argon-Niederdruckentladung mit resonanter Laserstreuung

The radial ion drift velocity and temperature in an argon low-pressure discharge have been measured by a resonant laser scattering method with high spatial resolution. The detection limit for the drift velocities was 2 · 10⁴ cm · s^?1. In the vicinity of the discharge axis the drift velocity grows linear with the distance from the axis. The measurements have shown the existence of a radial dependence of the ion temperature T¹(r). Comparisons of axial ion temperature T_? with T_‖(r = 0) are an experimental demonstration of the anisotropy of the ion velocity distribution in this kind of discharges.     

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)     

Measurements of Flow Velocity in the Plasma Generator PSI‐2

The plasma flow velocity in the Plasma Generator PSI‐2 has been investigated by using of Mach probe. PSI‐2 is a stationary high‐current arc discharge in which the quasi‐neutral plasma expands along the magnetic field lines. The low‐temperature (T_e < 20 eV), medium density (n_e ∼ 10¹⁸— 10¹⁹ m^—3 ) plasma in the discharge is similar to the plasma in the divertor region of tokamaks. From the ratio of ion saturation currents collected from opposite sides of the probe the flow velocities (Mach numbers) in argon and hydrogen discharges are obtained.     

Längsfeldstärke,Elektronentemperatur, mittlere Neutralgasdichte,Ionenstromdichte auf die Wand und mittlere Entladungsstromdichte in der Freifallsäule bei hohem Ionisationsgrad

On the basis of a foregoing paper new theoretical results for the positive column at low pressure and strong ionization, especially for discharges in noble gas ion lasers, are given. The mean velocity v_n0 of the neutral atoms reemitted from the wall is taken into account. The electric conductivity is calculated for an argon plasma. The formulas connecting the electron temperature, the mean neutral gas density, and the electric field strength are derived. The electron temperature, the axial electric field intensity, the degree of ionization, the axial electron drift velocity, the ion flux to the wall, and the force density causing the main part of gas pumping along the column are calculated as functions of the product of the mean current density and the tube radius, and of v_n0 for argon. The axial drift velocity of the electrons is still smaller than the mean thermal electron velocity for high discharge currents, except at very low gas pressures. In general, the ion flux to the wall is not directly proportional to the discharge current. The factor for the determination of the charged particle density by means of probe measurements at the wall is discussed. The self-magnetic field affects the discharge only at high electron temperature, high degree of ionization, and relatively large tube radius, i.e. at high current density and low gas pressure in not too narrow discharge channels.     

Electron Temperature Measurement in a Premixed Flat Flame Using the Double Probe Method

The electron temperatures T_e were measured using a double probe in a premixed methane flame produced by a calibration burner according to Hartung et al. The experiment was performed at atmospheric pressure. In contrast to other authors, we have managed to find typical nonlinearities corresponding to the retarding electron current region and to calculate electron temperatures using a suitable fit on the basis of the measured characteristics. A Pt‐Rh thermocouple was used to measure temperatures T_h corresponding to “heavy” species. Our results indicate that the flame plasma can be considered to be weakly non‐isothermic — T_e = (2400–4000) K, T_h = (1400–1600) K. On the basis of measurement of the saturated ion current, the number density of the charged particles was estimated at (0.3–3.8) · 10¹⁷ m^‐3. The trends in T_e and T_h in dependence on the positions of the probes and thermocouple in the flame differ substantially; this fact has not yet been explained (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optical Emission Diagnostics of an U-Shaped Argon Stabilized d.c. Arc

The radial distribution of parameters has been measured by using the optical emission spectroscopy of an U-shaped argon stabilized low current arc at atmospheric pressure. All the measurements reported here were performed from a side-on observation direction by applying the Abel inversion routine. Radial distributions of apparent temperatures (T_exc., T_e, T_i, T_g) and of electron number density (n_e) for the plasma were measured, with and without presence of KCl (spectrochemical buffer). The measured data of n_e are compared to the theoretically calculated values of the equilibrium plasma composition. On the basis of the measured data, the validity of LTE concept is considered. It was found that deviation from LTE increases to the plasma periphery.