Inelastic Electron-atom Collisions Research Articles

From macro-measure of Franck–Hertz curves to micro-collisions between electrons and argon atoms

A Franck–Hertz experiment is adopted in our undergraduate laboratory by using a cylindrical tetrode tube filled with argon vapor. The Franck–Hertz curves, i.e. the variation of the anode current via the accelerating voltage, are experimentally measured, and the key roles of the filament voltage, the control voltage, and the retarding voltage played in the experiments are studied. Diagrams of the micro-elastic/inelastic collisions between the electrons and argon atoms, which are of significance for students to build a connection between the macroscopic measurements and microscopic collisions occurring inside the Franck–Hertz tube, are schematically presented based on the experimental results. The peak/valley interval in the experimental Franck–Hertz curves of argon vapor increases as the accelerating voltage increases. The results further suggest that the lowest excitation energy of an argon atom cannot be exactly derived from the experimental results since all the four sub energy levels within the first excitation energy state of the argon atom are involved in the inelastic electron–atom collisions.

Electron energy distribution in a dusty plasma: analytical approach.

Analytical expressions describing the electron energy distribution function (EEDF) in a dusty plasma are obtained from the homogeneous Boltzmann equation for electrons. The expressions are derived neglecting electron-electron collisions, as well as transformation of high-energy electrons into low-energy electrons at inelastic electron-atom collisions. At large electron energies, the quasiclassical approach for calculation of the EEDF is applied. For the moderate energies, we account for inelastic electron-atom collisions in the dust-free case and both inelastic electron-atom and electron-dust collisions in the dusty plasma case. Using these analytical expressions and the balance equation for dust charging, the electron energy distribution function, the effective electron temperature, the dust charge, and the dust surface potential are obtained for different dust radii and densities, as well as for different electron densities and radio-frequency (rf) field amplitudes and frequencies. The dusty plasma parameters are compared with those calculated numerically by a finite-difference method taking into account electron-electron collisions and the transformation of high-energy electrons at inelastic electron-neutral collisions. It is shown that the analytical expressions can be used for calculation of the EEDF and dusty plasma parameters at typical experimental conditions, in particular, in the positive column of a direct-current glow discharge and in the case of an rf plasma maintained by an electric field with frequency f=13.56MHz.

Coincidence investigation of inelastic electron–atom collisions with magnetic selection of scattering angle – feasibility study

New apparatus for electron–atom collision investigations incorporating the magnetic angle changing method into the coincidence technique has been set-up. Combination of the two enables measurements of Electron Impact Coherence Parameters in the full range of scattering angles. First energy loss and coincidence spectra are presented.

About the EDF formation in a capacitively coupled argon plasma

The formation of the electron distribution function (EDF) in the bulk plasma of a capacitively coupled radio-frequency (rf) discharge in argon generated in the plasma-chemical reactor PULVA-INP is investigated experimentally and theoretically. Measurements of the EDF and internal plasma parameters were performed by means of a Langmuir probe at pressures of 0.5–100 Pa and discharge powers of 5–100 W. The observed EDFs have revealed a two-temperature behaviour at low pressures and evolved into a Maxwellian distribution at high gas pressures and large discharge powers. Theoretical determination of the EDF is based on the numerical solution of the Boltzmann kinetic equation in the local and non-local approaches under experimental conditions. The model includes elastic and inelastic electron–atom collisions and electron–electron interactions. Low electron temperatures and relatively high ionization degrees are the features of the PULVA-INP rf discharge. This leads to significant influence of the electron–electron collisions on the EDF formation. The modelled and measured distributions show good agreement in a wide range of discharge parameters, except for a range of low gas pressures, where the stochastic electron heating is intense. Additionally, mechanisms of the EDF formation in the dc and rf discharge were compared under similar discharge conditions.

Relation between the UV luminescence yield and electron drift velocity in the gaseous xenon at high electric fields

The excitation of xenon atoms by electron impact in the gaseous xenon is studied in high electric fields in which the inelastic electron–atom collisions become the main channel of the electron energy losses. A simple diffusion model is used to determine the electron momentum distribution and the excitation rate of xenon atoms as a function of the electric field strength, E, normalised to the number density, N, of xenon atoms. The generation rate of the electron excited xenon atoms and electron drift velocity are found at the electric fields near the threshold field of the xenon atom excitation. The model agrees well with experimental data on the UV luminescence of xenon due to electron excitation and with measurements of the electron drift velocity in the range of E=N up to 10 � 15 Vc m 2 . 2003 Elsevier Science B.V. All rights reserved.

Energy spectra of electrons in a dc glow discharge with a semitransparent anode

A numerical model for a planar dc discharge with a semitransparent anode positioned between two symmetrical cathodes is developed. The kinetic equation is solved iteratively by means of the direct Monte Carlo method. This approach makes it possible to find stationary particle fluxes and space-charge distributions with controlled precision. The numerical calculations are carried out for hydrogen, in which case the model can be well tested. The role of the semitransparency of the anode is investigated with respect to the formation of a space-charge layer and electron energy spectra. The conditions for a stable self-sustained discharged with a semitransparent anode are discussed. The energy spectra for electrons are found to be very far from equilibrium and to have peaks linked with the peculiarities of the inelastic electron–atom collisions at low energies. The possibility of controlling the electron energy spectra using the transparency of the anode is considered.

Correlations in Electron - Atom Collisions involving Polarised Electrons and Photons

More sophisticated experimental methods to study inelastic electron–atom collisions include polarisation-correlation measurements such as electron–photon (e, eγ) and electron–electron (e, 2e) coincidence studies or stepwise electron–photon (eγ, γ) correlations. Electron correlations and spin effects can be explored on the most fundamental level in such experiments. In this paper recent (e, eγ) studies with Hg and Xe, (eγ, γ) studies with Ne and (e, 2e) studies with Xe using polarised electrons and/or polarised photons are reviewed.

Accurate models of collisions in glow discharge simulations

Very detailed, self-consistent kinetic glow discharge simulations are used to examine the effect of various models of collisional processes. The effects of allowing anisotropy in elastic electron collisions with neutral atoms instead of using the momentum transfer cross-section, the effects of using an isotropic distribution in inelastic electron-atom collisions, and the effects of including a Coulomb electron-electron collision operator are all described. It is shown that changes in any of the collisional models, especially the second and third described above, can make a profound difference in the simulation results. This confirms that many discharge simulations have great sensitivity to the physical and numerical approximations used. Our results reinforce the importance of using a kinetic theory approach with highly realistic models of various collisional processes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Connection between superelastic and inelastic electron-atom collisions involving polarized collision partners.

It is shown how the results of a recent experiment by Jiang, Zuo, Vu\ifmmode \check{s}\else \v{s}\fi{}kovi\ifmmode \acute{c}\else \'{c}\fi{}, and Bederson [Phys. Rev. Lett. 68, 915 (1992)], who investigated low-energy electron scattering from laser-excited polarized sodium atoms in the initial (3p) $^{2}$P${\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}_{3/2}$ (F=3, ${\mathit{M}}_{\mathit{F}}$=3) state, can be related to the inelastic 3S\ensuremath{\rightarrow}3P transition involving initially unpolarized electron and atom beams. Hence, this method can provide an independent check of the traditional electron-scattering experiment with unpolarized beams.

An accelerator based electron-photon coincidence spectrometer for the study of inelastic electron-atom collisions

Inelastic electron-photon collisions can be studied with our two-photon coincidence spectrometer by replacing one of the Ge detectors with a Si(Li) detector with a 0.4 μm polymer window coupled to the target vacuum chamber. The present geometry has the detectors at ± 45° to the incident electron beam. The counting rate in the Si(Li) detector is dominated by the elastic scattered electrons and the backscattering tail of the elastic peak and is several orders of magnitude larger than the photon rate. Nevertheless, the coincidence electronics is able to separate real coincidences as a function of both photon and electron energy from the large accidental coincidence background. This permits the study of such processes as the doubly differential cross section for inner-shell ionisation and the triply differential cross section for single bremsstrahlung. This setup has a much more rapid data collection rate and yields a statistical error comparable to or better than has been previously achieved in the few experiments that have been done using a magnetic spectrometer on the electron. Preliminary examples of two dimensional energy spectra with 70 kev electrons on targets of Al, Cu, Ag, Tb and Au are discussed.

Program to calculate observable quantities from scattering amplitudes for inelastic electron-atom collisions

Programme OBSERVABLES pour calculer la section efficace, la polarisation de spin, l'asymetrie de diffusion, les parametres d'alignement et d'orientation, la distribution angulaire et la polarisation du rayonnement emis lors d'experiences de coincidence electron-photon en diffusion inelastique electron-atome

Program to calculate observable quantities from scattering amplitudes for inelastic electron-atom collisions

We describe a code which utilizes partial-wave amplitudes to calculate a variety of physical quantities studied in electron–atom scattering. For elastic scattering and excitation of atoms with arbitrary angular momenta in collisions with spin-polarized and unpolarized electrons, the program can calculate angle-integrated and angle-differential cross sections, the spin polarization of scattered electrons, the spin left–right (up–down) asymmetry, generalized STU parameters, and the statistical tensors of the final atomic state, which determine polarization and correlation parameters in radiative and nonradiative decays of these states. In addition, the program transforms partial-wave scattering amplitudes into a representation of projections of the angular momenta in the natural and collision coordinate frames, thereby providing the possibility for a user to conveniently calculate any observable not explicitly included in the code. The program can be used directly as a final module after running the Belfast R-matrix codes in the Breit–Pauli mode.

Atomic excitations in sputtering studied with group two element targets

Solid targets of Be, Mg, Zn, and Cd have been bombarded with 50 keV Ar + ions. The relative excitation of lowest-lying excited levels in sputtered neutrals and singly-charged ions have been measured using optical spectrometry. It is found that singly charged ions are excited much more efficiently than neutral atoms. This is discussed, and it is concluded that atomic excitation in sputtering results from electron pick-up to excited states in initially ionized atoms rather than from inelastic atom-atom or electron-atom collisions.

Atomic excitations in sputtering studied with group two element targets

Solid targets of Be, Mg, Zn, and Cd have been bombarded with 50 keV Ar + ions. The relative excitation of the lowest-lying excited levels in sputtered neutrals and singly-charged ions have been measured using optical spectrometry. It is found that singly-charged ions are excited much more efficiently than neutral atoms. This is discussed, and it is concluded that atomic excitation in sputtering results from electron pick-up to excited states in initially ionized atoms rather than from inelastic atom-atom or electron-atom collisions.

Line width and displacement with temperature of the electron-exciton-collision line in highly excited semiconductors

The solution of Boltzmann equation taking account the elastic and inelastic electron-atom collisions and in the absence of the external electric field has been obtained as function of the temperature. This solution that corresponds to the energy distribution function f has been applied for the similar case of electron-exciton collisions in highly excited semiconductor CdS. Knowing the values of f at a particular temperature T, the line width and the strong shift of the electron-exciton collision line to lower quantum energy as T increases have been calculated for this semiconductor. The results which are independent of any parameter are in good agreement with experiment. In these calculations the elastic collision which has been neglected previously by the different authors plays an important role.

Electron distribution function in electron-beam-excited plasmas

In monatomic plasmas excited by high-intensity relativistic electron beams, the electron secondary distribution function is dominated by elastic electron-electron collisions at low electron energies and by inelastic electron-atom collisions at high electron energies (above the excitation threshold). Under these conditions, the total rate of excitation by inelastic collisions is limited by the rate at which electron-electron collisions relax the distribution function in the neighborhood of the excitation threshold. To describe this effect quantitatively, an approximate analytic solution of the electron Boltzmann equation is obtained, including both electron-electron and inelastic collisions. The result provides a simple formula for the total rate of excitation.

Simulation of the Electron Energy Relaxation in a Weakly Ionized Plasma

Abstract The motion of electrons in a weakly ionized plasma under the influence of an electric field is simulated by a Monte Carlo method. Elastic and inelastic electron-atom collisions are taken into account using the experimental cross sections. In an application to a low pressure argon positive column the temporal and spatial relaxation of the electron energy distribution is calculated for high electric fields (30 ≦ E/p0 ≦ V/cm Torr). The influence of the wall recombination and the anisotropy due to the high field can be shown.

A Useful Simple Recursion Formula to Account for Inelastic Collision Effects on the Electron Distribution in a Plasma

The competitive effects of inelastic electron-atom collisions and electron-electron interactions on a sufficiently isotropic electron distribution is considered for a low temperature monatomic plasma. It is presupposed that unbalanced collisional transitions between ground state and resonance level of the plasma atoms are the dominant disturbance effect on the electron distribution. The unbalance is assumed to be due to resonance radiation escape and excitation diffusion. An analytical solution, which permits the calculation of the electron distribution even well above the ionization energy of the atomic ground state, is presented. In particular, it is demonstrated that due to the rapid decrease of the Coulomb cross section with increasing electron energy, the solution for the high energy tail of the electron distribution can be related to its form at lower energies by a simple recursion formula. The latter enables an easy computation of the ionization coefficients even for the lowest atomic energy levels. The analytical solution and its high energy approximation are numerically evaluated for the example of a low temperature -low pressure cesium plasma.

Eikonal Theory of Inelastic Electron-Atom Scattering at Intermediate Energies

An eikonal distorted-wave theory is proposed for inelastic electron-atom collisions at intermediate energies. The primary interaction, responsible for the transition, is treated to first order, while the initial- and final-state interactions are taken into account by using the eikonal approximation. Direct and exchange collisions are both considered. Detailed numerical calculations are performed for the excitation of the n=2 levels of atomic hydrogen by electron impact. The results for the differential excitation cross sections are compared with those obtained in the Glauber eikonal approximation at small scattering angles. © 1972 The American Physical Society.

Distribution function of electrons and kinetic coefficients in cesium-argon mixture discharge

The distribution function of electrons in a cesium-argon mixture discharge is found in the present paper by solving Boltzmann's equation. The elastic and inelastic electron-atom collisions and electron-electron collisions are taken into consideration.