Collisions Of Charged Particles Research Articles

Measurements of electron temperature, electron density, and neutral density in a radio-frequency inductively coupled plasma

Electron temperature, electron density, and neutral atom density were measured in a radio-frequency (rf) inductively coupled plasma using Thomson and Rayleigh scattering of laser radiation. Measurements were made in an argon discharge for pressures from 1 to 20 mTorr and input rf powers from 100 to 500 W. Spatial distribution profiles were measured for discharges with different aspect ratios. Electron temperature was found to depend on pressure but only weakly on power. Electron density depended strongly on both pressure and power. The neutral density was found to be significantly depleted in the plasma center and this depletion was attributed to heating of the neutrals by charged particle collisions. These results were compared to a simple model of inductively coupled plasmas.

Symmetrisation procedures for detailed balancing of classical energy transfer probabilities

In a few previous papers, we introduced a so-called fluctuation model accounting for inelastic effects in molecular energy transfers induced by collisions. This model resulted in «symmetrisation rules» to be applied to the classical expressions for energy transfer probabilities, in order to insure detailed balancing. In this paper, we show that the symmetrisation procedures can also be applied successfully to the classical equations for energy loss and radiative transitions induced by Coulomb collisions of charged particles in stopping media. The resulting expressions display correct threshold behaviours and are worthwhile to be compared with the exact QM results. The comparison demonstrates interesting conceptual improvement of the classical equations and confirms that the symmetrisation procedures—as well as the underlying fluctuation model—are of a somewhat general applicability to inelastic processes in physics.

Classical description of state-selective transitions in collisions of charged particles with atoms

A classical description of state selective excitation processes in atom-charged particle collisions is provided for arbitrary values of the collision energy. Closed-form expressions for the cross sections of nl to n', nl to l' and nl to n'l' transitions are obtained in the high energy limit. The scaling properties of sigma (nl to n'l') cross sections are briefly discussed.

Plasma permittivity of weakly ionized inhomogeneous magnetized plasmas

The longitudinal permittivity of weakly ionized low-temperature inhomogeneous magnetized plasmas is derived on the basis of the kinetic plasma model. Oblique propagation (with respect to the external, comparatively weak, magnetic field) of potential perturbations in d.c. discharge plasmas sustained under conditions of a diffusion-controlled regime is modelled. The equilibrium plasma state accounts for (i) collisions of charged particles with neutrals; (ii) plasma inhomogeneity in a direction perpendicular to the external magnetic field; (iii) crossed electric and magnetic fields; and (iv) electric field parallel to the external magnetic field. The solution of the Boltzmann equation obtained in the framework of successive approximations approaches the case of a non-complete ion magnetization and comparatively strong E*B drift of the ions due to an enhanced ambipolar electric field. The methods of integration over the unperturbed trajectories and over the angle of the gyromotion are applied.

Dipole-allowed transitions in collisions of charged particles and Rydberg atoms: method of virtual quanta in low velocity collisions

Experiments involving collisions between charged particles and Na Rydberg atoms have been undertaken to study the projectile-velocity dependence of collisionally induced dipole-allowed transitions. Measurements being carried out in this laboratory, involving H +, H 2 +, He +, Ne +, and e − projectiles incident on Na(30s) and Na(29d), cover the reduced projectile velocity range from 1.7 to 200 times the mean orbital velocity of the excited electron. Absolute cross sections for the dipole-allowed transitions, 30s to 30p and 29d to 30p, have been measured and exhibit pronounced and unique projectile-velocity dependent thresholds. The Weizsäcker-Williams method of virtual quanta has been extended to include low projectile velocities and is found to be in good agreement with the observed projectile-velocity dependent dipole-allowed thresholds.

Screening effects for transition probabilities in collisions of charged particles with an atom or stripped ion.

Screening effects for transition probabilities in collisions of charged particles with an atom or stripped ion are investigated using the modified hyperbolic-orbit path in the semiclassical approximation. Effective nuclear charges for bound electrons in many-electron atoms are determined by new screening constants [Y.-D. Jung and R. J. Gould, Phys. Rev. A 44, 111 (1991)]. Applications were made to O, ${\mathrm{O}}^{4+}$, and ${\mathrm{O}}^{7+}$. For these targets, the transition probabilities are calculated for 1s\ensuremath{\rightarrow}2p transitions. The results show that the maximum point of the transition probability is shifted to the nucleus with an increase of the screening effect. Moreover, the maximum amplitude of the transition probability is appreciably reduced as the screening effect increases.

Electron heat transport with non-Maxwellian distributions

Measurements are presented of electron heat transport with non-Maxwellian (flattopped) distributions due to inverse bremsstrahlung absorption of intense microwaves in the University of California at Davis Aurora II device [Rogers et al., Phys. Fluids B 1, 741 (1989)]. The plasma is created by pulsed discharge in a cylindrical vacuum chamber with surface magnets arranged to create a density gradient. The ionization fraction (∼1%) is high enough that charged particle collisions are strongly dominant in the afterglow plasma. A short microwave pulse (∼2 μs) heats a region of the afterglow plasma (ne/ncr≤0.5) creating a steep axial (LT∼1–10λei) temperature gradient. Langmuir probes are used to measure the relaxation of the heat front after the microwave pulse. Time and space resolved measurements show that the isotropic component of the electron velocity distribution is flat topped (∼exp[−(v/vm)m], m≳2) in agreement with Fokker–Planck calculations using the measured density profile. Classical heat transport theory is not valid both because the isotropic component of the electron velocity distribution is flattopped and the temperature gradients are very steep.

Influence of relaxation phenomena in the unified description of resonant and nonresonant radiative transitions.

A comprehensive quantum-mechanical description of resonant and nonresonant radiative transitions in complex electronic systems is developed, using a density-matrix approach. Specific applications are made to the unified treatment of radiative and dielectronic recombination of electrons with many-electron ions in high-temperature plasmas and to the unified treatment of transverse bound-bound and free-bound radiative transitions of energetic electrons channeled in crystal lattices. Both time-independent (resolvent-operator) and time-dependent (equation-of-motion) formulations of the density-matrix approach are presented. Liouville-space projection-operator techniques, which have been developed in the nonequilibrium quantum-statistical-mechanics description of relaxation phenomena, are employed. Self-consistent treatments are achieved for the excited-level populations and the spectral-line shapes. Applications are discussed for the broadening of atomic spectral lines by autoionization processes, radiative transitions, charged-particle collisions, and the action of the plasma electric microfields, and also for electron-channeling-radiation broadening by electron-electron, electron-photon, and electron-phonon interactions in a crystal lattice. The unified treatment of resonant and nonresonant radiative transitions is accomplished by means of a partition of the ``relevant'' Liouville space into separate subspaces corresponding to discrete resonance and nonresonant continuum states of the electronic system of interest. Although only single-photon processes are considered and only lowest-order quantum-electrodynamical perturbation theory is explicitly evaluated for the electron interaction with the radiation field, the general resolvent-operator and propagator formulations that are presented in this investigation can be applied to the description of multiphoton processes and, with the adoption of a suitable renormalization program, to the incorporation of radiative corrections to the transition probabilities.

Generalized Chapman–Enskog method in the kinetic theory of reacting ionized gases

In this paper the problem of kinetic coefficient calculations for a nonequilibrium mixture of chemically reacting ionized gases is investigated. The study is based on the generalized Chapman–Enskog method (GCEM) proposed by Alexeev [Theor. Exp. Chem. 5, 541 (1969)]. This work should be considered as a direct continuation of the paper [Phys. Rev. E 49, 2809 (1994)]. An effective method for the solution of the basic equation with non-self-adjoint operator (A equation) of the GCEM is developed for the case of reacting ionized gases and the calculation of the bracket expressions for elastic collisions of charged particles is given. Several concrete results of the kinetic coefficient calculations are discussed.

Onset of dipole-allowed transitions in inelastic collisions of charged particles with Na(30s) Rydberg atoms

An experimental study of the depopulation of Na(30s) Rydberg atoms under He+ ion bombardment has been undertaken to identify the range of collision velocities at which strongly coupled behaviour of the 30s and nearby levels at low velocity changes to predominantly dipole-allowed coupled at high velocity. Ion energies ranged from 700 to 3900 eV corresponding to collision velocities of 2.4 to 5.6 times the mean orbital speed of the excited 30s electron. The ratio of the cross section for the dipole-allowed transitions (30s to 30p and 30s to 29p) to the total depopulation cross section was determined for each collision velocity. (Other dipole-allowed transitions were observed to be negligible.) This ratio was found to increase from only 20% at a reduced velocity of 2.4 to 65% at a reduced velocity of 5.6. The ratio of the two dipole cross sections, sigma (30s-30p)/ sigma (30s-29p), was also determined and compared to calculations based on the dipole approximation with first-order perturbation theory.

Stochastic Theory of Motion and Collision of Charged Particle in a Uniform Electric Field

Relaxation of ions in a uniform electric field is analyzed by using the theory of stochastic process. Ion-neutral interaction is assumed to be Maxwellian. The drift velocity, the mean energy, and the longitudinal and transverse diffusion coefficients thus obtained agree with the exact solution of the moment equations of the Boltzmann equation.

Semiclassical model for δ-electron emission from multielectronic atoms

A new semiclassical simple model is presented to study electron emission by atoms during heavy charged particle collisions. This model is based on the use of the plane wave Born theory and the semiclassical WKB approximation for atoms.

Charged Plasma Particle Collision in the Presence of a Strong Laser Field

Starting from a quantum mechanical approach the transition probability between charged particles is transformed to inelastic cross-section. From this a simple and useful approximation is obtained for the multiphoton energy transfer processes which accompany the scattering of a charged particle. Due to the plasma potential in the presence of a strong laser field, an effective collision frequency is found. The amplitude of the electron oscillatory velocity v 0 in the radiation field is assumed to exceed the electron thermal velocity v t e . Under these conditions, the absorption rate is independent of the initial distribution function and depends only on the photon flux intensity. The calculated effective collision frequency can be scaled as I p , where the p -parameter is in the range of -0.5< p ≤0.5. Our results are compared with those of other formalisms and experimental results.

Interference effects in the double ionization of helium by charged particles

The interference between different double-ionization mechanisms by collisions of charged particles with helium is studied in the second order of perturbation theory series in terms of the interaction potential of the projectile with the helium electrons and the correlation potential of atomic electrons. It is shown that the contribution to the interference term in the integrated double-ionization cross section of helium comes only from the interference between the process of independent electron removal and the process in which an ejected electron, as a result of the interaction with the projectile electron, scatters on another helium electron, resulting in double ionization.

Bremsstrahlung of fast charged particles moving in an external magnetic field

Using the method of small perturbations a theory of bremsstrahlung is developed. The bremsstrahlung is caused by radiational collisions of fast relativistic charged particles moving in opposite directions along a constant non-quantizing magnetic field.

Secondary electrons from charged particle collisions with atoms and molecules

Since a large fraction of the energy transfer in energetic atomic collisions is in the production of secondary electrons, most of the radiation effects are a result of this process. Therefore, a knowledge of the energy spectrum (and for some purposes the angular distribution) of secondaries is crucial in understanding the interaction of charged particles with matter. Semi-empirical models for the differential cross sections for secondary electron production by proton and electron impact on atoms and molecules have been developed which summarize a large amount of information in the form of analytical equations with a few parameters for each target species.

Inelastic electronic collision cross sections for Monte Carlo calculations

For very thin absorbers, the energy losses of fast charged particles vary widely because of the stochastic nature of the interactions. In order to visualize and understand this process, a simulation with Monte Carlo calculations can be used. The distribution functions needed in these calculations, describing the electronic energy losses in single collisions of fast charged particles traversing silicon, have been found to depend only slightly on particle speed. This simplifies such calculations. A similar behaviour is expected to exist for other materials.

Erratum: Spin-dependent phenomena induced by electromagnetic-hadronic interference at high energies

Interference phenomena should be seen in many spin-dependent observables for the collision of spin-half hadrons. The phenomena occur both in the collision of charged particles and in the collision of neutral particles with charged particles. Of most direct interest are the reactions pp ..-->.. pp, np ..-->.. np, and Lp ..-->.. Lp. Much information about the phases of the helicity-flip amplitudes near the forward direction can be obtained from the measurement of the interference. Detailed expressions are given for many experimental observables in the interference region, and the extraction of the hadronic amplitudes is discussed in depth. The existence of a new type of enhanced order alpha correction to the hadronic amplitudes is exhibited and its consequences are explored. In particular the role of electromagnetically induced helicity-flip outside the interference regions is stressed and shown to complicate the interpretation of the small measured values of the polarization at Fermilab energies.

Semiclassical impact-parameter expansion of delta-electron spectrum

The impact-parameter dependence of the secondary electron production in collisions of heavy charged particles with atoms and the energy distribution of delta-electrons are studied using a statistical model of an atom and the binary encounter approximation. As a result of this model the analytical expressions, describing inelastic scattering of heavy charged particles by a statistical atom have been derived.

Collision of fast charged particles in solids

This book contains the following chapters: The transport equation of charged particles in matter; Elastic scattering of fast charged particles; Solution of transport equations for inelastic collisions; Angular and energy distributions of charged particles; Backscattering of charged particles from a continuous medium; Orientation effects in the coherent scattering of charged particles in single crystals; Channeling of charged particles in single crystals; Orientational phenomena in radiation of charged particles in single crystals; and Changes in the properties of matter in the particle track.