On Electron Concentration Distribution along the Radius of the Positive Column of a Glow Discharge in Electronegative Gases

It is shown in this paper that the form of the electron concentration distribution along the radius of the positive column in an oxygen discharge depends on the relative concentration of negative ions α = n_-/n_e in the plasma. It is found that in discharges in electronegative gases everywhere along the radius of the positive column, where α > 10, the electron concentration is equal to its value on the tube axis (plane electron distribution along the radius of the positive column). It is shown that an increase of the discharge current leads to the decrease of α and to the change of the distribution of profile n_e from plane to parabolic. However, weak laminar oxygen pumping along the positive column leads to more plane an electron concentration distribution because an increase of the negative ions concentration takes place. It is induced by the decrease of oxygen atoms density on account of their carrying out by the flow.     

Zur Radialstruktur der diffusionsbestimmten positiven Säule der Sauerstoff-Entladung bei niederen Gasdrucken

The radial distribution of the electrons, negative and positive ions in the cylindrical positive column of the direct current discharge in 0₂ has been calculated. The negative ions are formed by dissociative attachment (0₂ + e →^? + 0), the destruction of negative ions is effected by the reverse process (0^? + 0 0₂ + e). The pressure is assumed to be low enough that the radial variation of 0-concentration can be neglected. By use of the condition of the quasineutrality and the ambipolarity for the radial current from the balance equations of the electrons and the negative ions two differential equations of second order are derived, which has been solved numerically for different values of the ratio z_j/z_a and β[0]. Numerical results show that the radial distributions of the charge carriers are not-proportional. If z_j ≈? z_a the radial distribution of the electron density is enlarged, compared to a Bessel distribution. The radial distribution of the negative ions is also enlarged in the centre of the column, but near the wall of the tube a lack in the density exists. The effective diffusion coefficient of the negative ions is negative, i.e., they are moving from the wall of the tube to the centre of the discharge. The enlargement of the radial distributions of the charge carriers, which results in an improvement of the economy of the balance of electrons, increases if z_j/z_a and β/[0] are decreased.     

Radiation losses of a theta pinch plasma in the wave-length range 10–200 Å

In order to measure the radiation losses of a theta pinch plasma (electron densityn _e=1?5×10¹⁶ cm^?3, electron temperatureT _e=150?350 eV), a grazing incidence spectrograph is absolutely calibrated in the range 10–200 Å. This is done in two steps: First the measured intensity ratios of lines emitted by hydrogen-like ions are compared with their calculated values thus yielding the relative sensitivity of the instrument. The result is confirmed by incorporating well known intensity ratios of lithium-like ions. Secondly absolute calibration is possible by hanging the spectrograph on an absolutely calibrated monochromator via the branching-ratios of lithium-like ions. Radiation losses from the plasma turn out to be negligible as compared with heat conduction losses and the total energy radiated is found to be small compared with the energy content of the electrons, if the impurity concentration does not exceed 0.5 percent. The radiation is found to be predominantly emitted by the resonance lines of the oxygen and carbon ions O VI, O VII, O VIII, CV, CVI whereas continuum radiation and the contribution from other ions are negligible small. However, in discharge where the oxygen concentration reaches 5 percent, radiation losses can exceed the losses by heat conduction during the early phase of the discharge. But still the final electron temperature is not significantly influenced by the impurities.     

Pressure Ionization in Nonideal Alkali Plasmas

A system of electrons (e) and ions (i) is considered in which beside the Coulomb interaction short range forces are taken into account, i.e. for the e-i interaction a pseudopotential is used, and for the (classical) ions crystallographic radii are used. For a Cesium plasma the thermodynamic properties are calculated quantumstatistically in a wide temperature-density region. Degeneration effects are taken into account approximately. In the region with bound states the ionization equilibrium is discussed, and the Mott-Transition is investigated critically. A phase transition occurs in the framework of the model chosen at T_c ≈ 4500 K and n^c ≈ 4.10²⁰ cm^?3.     

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)     

Floating double probe in non‐Maxwellian plasmas: Determination of the electron density and mean electron energy

A theoretical study of the floating double probe based on the Druyvesteyn theory is developed in the case of non‐Maxwellian electron energy distribution functions (EEDFs). It is used to calculate the EEDF in the electron energy range larger than –e(V_f ? V_p) from the I–V double probe characteristics. V_f and V_p are the floating and plasma potential, respectively. The analytical distribution function corresponding to the best fit of EEDF in the energy range larger than e(V_f ? V_p) allows the determination of the total electron density (n_e) and the mean electron energy (<?_e>). The method is detailed and tested in the case of a theoretical Maxwell–Boltzmann distribution function. It is applied for experiments that are performed in expanding microwave plasmas sustained in argon. Analytical EEDFs determined by this method are compared with those measured by means of single probes under the same experimental conditions. A good agreement is observed between single and double probe measurements. Results obtained under different experimental conditions are used to define the best conditions to obtain reliable results by means of the double probe technique.     

Branching of electron current and quantum effects in two-dimensional dislocation barrier of n-type semiconductor

The current flow through the dislocation wall of the bicrystal (or intergrain) boundary in semiconductor is considered. It is known that the broken bonds along the dislocations make up the acceptor levels (being offset by energy ?_d from the bottom of the conductance band) whose population by electrons is defined by the bulk donor concentration n_D, the ?_d-value and the dislocation spacing D_y. At low enough n_D-value (n_D<e²/?_dD_y⁴), electrons captured at the dislocation acceptors produce the periodic 2D-lattice with two comparable periods of the order of n_s^−1/2 where n_s∼(?_dN_D/e²)^1/2 is 2D-density of captured electrons. Charges of those electrons result in the formation of the dislocation potential barrier whose height (with mean value in order of ?_d) is periodically modulated in the wall plane. Naturally, the electron current prefers to flow along the paths with the lowest barrier height, i.e. through the saddle points of the 3D-potential relief positioned in the dislocation wall plane. At low enough temperatures that leads to separation of the electron current into numerous branches. Provided both 2D-lattice periods of the captured charges are smaller as compared with the electron mean free path, all those narrow and short branches make up a filamentary 1D-conductors with the ballistic transport. As this takes place, effects associated with the 1D-conductance quantization define the whole system resistance and could be observed experimentally. In particular, exponentially strong temperature dependence of the whole system resistance vanishes.     

On the energy dependence of the yield of doubly charged negative ions during the capture of free electrons by C60(CF3)12 trifluoromethylfullerene molecules

Peaks of C₆₀(CF₃) _n ^2? doubly charged negative ions (n = 6–12) have been observed in the mass spectra of the resonance electron capture by trifluoromethylfullerene C₆₀(CF₃)₁₂ molecules. It has been established that these ions are formed owing to the attachment of two free isoenergetic electrons. The autodetachment of an extra electron has been detected for the doubly charged molecular ions (n = 12). It has been established from the observation of the delayed fragmentation of the most abundant ions with n = 8 and 10 that the doubly charged negative ions, like their singly charged analogs, are metastable with respect to the separation of the CF₃ fragment(s). The yield of doubly charged negative ions has been obtained as a function of the electron energy. By comparing them with the analogous dependences for the singly charged ions, the specific features have been revealed which were associated with the presence of the repulsive Coulomb barrier and the regular effect of the doubled energy of two additional electrons on the energy dependence of the dissociative decay of the doubly charged negative ions. The absolute cross section for the formation of the C₆₀(CF₃) ₁₀ ^2? ions has been measured. At the energy of their yield maximum near the 5 eV, it is ～1 × 10^?19 cm².     

Velocity distribution of plasma electrons in the negative H2- and He-glow with superimposed longitudinal magnetic field

The negative glow plasma has been found nearly field free in axial direction. Therefore plasma electrons in the stationary glow can thermalize down to the temperature of the neutral gas, whenever their diffusion—and recombination—lifetime is high enough. Applying Boltzmann's equation to this problem, the conditions of thermalization of plasma electrons are derived as a function of the outer parameters of the plasma: vessel diameter 2R, neutral gas pressurep and longitudinal magnetic fieldB. — If plasma electrons have a too short diffusion—and recombination—lifetime to be in thermal equilibrium with the neutral gas, the electron energy increases. For this case the distribution function of plasma electrons is derived using Boltzmann's equation. Approximating the calculated energy distribution by a Maxwellian distribution function, the electron temperature in the glow is obtained as a function of the parameters:R, p, B. OurT _e -measurements carried out in the H₂- and He-glows of different tube diameters, neutral gas pressures and magnetic fields agree closely with the theoretical results. TheT _e -measurements have been performed with Langmuir probes and by the method of reversal of the radial ambipolar electric field in a longitudinal magnetic field.     

Kinetic electron reflection coefficient in a low-voltage Knudsen arc

The influence of the escape of fast plasma electrons on the electron distribution function (EDF) in a low-voltage cesium Knudsen arc is discussed. It is shown that even with a large Knudsen parameter l _e /h∼5–10 (where h is the gap and l _e is the mean free path of electrons with energy of the order of the anode barrier) the electron flux from the plasma to the anode is virtually identical to that calculated with a Maxwellian EDF. Zh. Tekh. Fiz. 68, 61–64 (May 1998)     

Formation of doubly charged negative ions under the conditions of the resonant electron capture by fluorofullerenes

Doubly charged negative ions formed when electrons with controlled energies interact with isolated fluorinated fullerene molecules C₆₀F _n (n = 36, 48) have been detected and investigated by resonant electron capture mass spectrometry. The dependence of the intensity of the formation of doubly charged negative ions of fluorofullerenes on the energy of attached electrons has been measured. An original method, which is based on the experimental data and does not require additional calibration quantities, has been developed for estimating the absolute cross section for the formation of doubly charged negative ions. The absolute cross sections for the formation of the most intensely formed ions C₆₀F ₃₆ ^2? and C₆₀F ₄₈ ^2? are estimated to be about 1.1 × 10^?24 and 1.5 × 10^?24 m² at their maximum-yield energies of 2.0 and 1.6 eV, respectively.     

The fragmentation of negative ions of fullerene C60 trifluoromethyl derivatives

The formation and decay of gas-phase negative ions of trifluoromethylated fullerenes C₆₀(CF₃) _n (n = 2–10) were studied. The resonance electron capture mass spectra were measured to find that the main fragmentation channel of negative ions was the detachment of trifluoromethyl groups. The degree of fragmentation directly depended on the energy of electrons and reached the complete splitting off of all the CF₃ addends with the formation of C₆₀⁻ ions. The observed metastable ion signals were analyzed to determine the scheme of sequential fragmentation of negative ions.     

Non-Maxwellian Electron Velocity Distribution Resulting from Electron-SF6 Attachment Collisions

A model reaction system is considered consisting of a heat bath of argon atoms (c) and small concentrations of SF₆-molecules (m) and electrons (e) (number densities: n_e ? n_m ? n_c). Within the model the time behaviour of the electron velocity distribution function is studied under the influence of elastic electron-argon collisions and electron SF₆ attachment collisions. On the basis of the distribution function time-dependent macroscopic quantities (kinetic electron temperature. nonequilibrium rate constant of the attachment reaction) are calculated.     

Ionization Dynamics in a Pulse Disturbed Magnetically Confined Helium Plasma

The equilibrium of a magnetized Helium plasma is disturbed by a pulsed Trivelpiece-Gouldwave. The electrons obtain the energy by linear collisionless wave absorption. The relaxation phenomena of density and energy are explained in terms of two relaxation times τ_E, τ₁ and a quantity giving the additional ionization. These quantities are derived from a small signal fluid model based upon energy and particle balance equations. In the experiment they are taken from the transient curves of Langmuir-probe current, optical line radiation and the noise power at the electron cyclotron frequency. The experimental conditions are: Helium-gas, p = 1 …? 5 Pa, T_e = 4 eV, n = 1 …? 5 · 10¹⁰ cm^?3, B = 6,5 · 10^?2 T, 27 MHz rf plasma source, low frequency fluctuation level < 1%, classical losses. The energy relaxation time …?_E = 10 …? 15 μs is given by inelastic collision losses. The ionization time constant τ₁ is related to the instantaneous ionization frequency during the transient state. It shows a high value at the very beginning of the pulse which must be explained by a tail formation in the distribution function and enhanced radial losses becoming Bohm-like in the transition phase.     

The Influence of Collisions in the Space Charge Sheath on the Ion current Collected by a Langmuir Probe

The current/voltage characteristics of a cylindrical Langmuir probe have been studied in Ar⁺/electron afterglow plasmas in helium carrier gas under truly thermal conditions at 300 K using our flowing afterglow/Langmuir probe (FALP) apparatus. The orbital motion limited (oml) ion and electron current regions of the probe characteristics have been explored over a wide range of the reduced probe voltage (up to ～ 100) and over a wide range of electron (n_e) and ion (n₊) number densities (1.6 × 10⁷ to 1.5 × 10¹⁰ cm^?3) at a constant pressure of the He carrier gas of 1.2 Torr. The observed increase of the probe ion currents above those predicted by collisionless oml theory, resulting in an apparent increase of the measured ion number density above n_e in the plasma, is explained by the enhancement in the ion current collection efficiency due to collisions of ions with neutral gas atoms in the space charge sheath surrounding the probe. The continuous change in the exponent, χ, of the power-law dependence,i₊ ∞ V of the ion current, i₊, on the probe voltage, V_p from 0.5 at the highest n₊ (smallest sheath) towards 1.0 at the lowest n₊ (large sheath) indicates that the ion current collection from the plasma changes from the oml current regime at the high n₊ to the continuum regime at the low n₊ when the ions undergo multiple collisions with the helium atoms in the space charge sheath and thus “drift” towards the probe.     

The energy of thermal electrons in electron beam created helium discharges

We have measured the electron energy of the thermal group of electrons in both longitudinal and transverse electron beam created helium glow discharges. The measurement technique employs the ratio of intensities of spectral lines in the 2s³S?np³P He I series. Values of kT_e between 0.07 and 0.11 eV were obtained. These energies are typical of the beam-generated electric field free plasmas. The competitive loss of helium ions by recombination and by charge transfer in a He?Hg electron beam created plasma is calculated. The results are applied to the Hg⁺ laser pumping scheme using a electron beam created He?Hg plasma.     

Ultrahigh charging of dust particles in a nonequilibrium plasma

Charging of dust particles in a plasma with the two-temperature energy distribution of electrons has been studied. It has been shown that the dust-particle potential divided by the electron temperature decreases with increasing electron temperature in the plasma with cold ions. Owing to this behavior, the potential of the dustparticle surface increases with the electron temperature more slowly than the linear function and is lower than the electron temperature (divided by the elementary charge) for T _e > 5.5 eV in hydrogen and for T _e > 240 eV in argon. The fraction of fast electrons at which these electrons begin to contribute to the charge of dust particles has been determined. It has been shown that the charge of micron particles can reach 10⁶ elementary charges. The effect of the cold and thermal field emission on the charge of dust particles has been analyzed. The possibility of obtaining ultrahigh charges (to 10⁷ elementary charges on dust particles with a radius of 50–100 μm irradiated by a 25-keV 1-mA electron beam has been demonstrated.     

Spectral Line HeII 6560 Å as a Sensor of the Electron Concentration in a Dense Plasma of a Current Sheet

Stark broadening of the spectral line HeII 6560 Å by plasma was studied. The profiles of the line HeII 6560 Å were calculated for different values of the electron concentration N_e. We used the quasi‐static approximation to account for the perturbing ions and the impact approximation to describe the perturbing electrons. The electron concentration N_e in the central region of a current sheet plasma was deduced by comparing the experimentally obtained profiles of the line HeII 6560 Å with the set of the theoretically calculated profiles of this line.     

Attenuation length and escape depth of excited electrons in solids

Escape probability and mean escape depth λ_e of emitted electrons are determined as a function of attenuation length λ_a of excited electrons, their initial energy E_n, and the height of the surface barrier χ. A variable energy loss parameter permits to apply the proposed model to different kinds of electron emission, including the energy loss free Auger and ESCA electrons. An analytical expression was found correlating the internal energy distribution of excited electrons and the external energy distribution of emitted electrons. By means of this excitation energies of secondary electrons and exoelectrons were determined.