Velocity Distribution Function Of Atoms Research Articles

Velocity distribution function of spontaneously evaporating atoms

Numerical solutions of the Enskog-Vlasov (EV) equation are used to determine the velocity distribution function of atoms spontaneously evaporating into near-vacuum conditions. It is found that an accurate approximation is provided by a half-Maxwellian including a drift velocity combined with different characteristic temperatures for the velocity components normal and parallel to the liquid-vapor interface. The drift velocity and the temperature anisotropy reduce as the liquid bulk temperature decreases but persist for relatively low temperatures corresponding to a vapor behaviour which is only slightly non-ideal. Deviations from the undrifted isotropic half-Maxwellian are shown to be consequences of collisions in the liquid-vapor interface which preferentially backscatter atoms with lower normal-velocity component.

Determination of divertor stray light in high-resolution main chamber Hα spectroscopy in JET-ILW

The theoretical model suggested for ITER main chamber Hα spectroscopy is applied to the high-resolution spectroscopy (HRS) data of recent JET ITER-like wall (ILW) experiments. The model is aimed at reconstructing the neutral hydrogen isotope density in the SOL, as well as the isotope ratio, by solving a multi-parametric inverse problem with allowance for (i) the strong divertor stray light (DSL) on the main-chamber lines of sight (LoS), (ii) substantial deviation of the neutral atom velocity distribution function (VDF) from a Maxwellian in the SOL, and (iii) data for the direct observation of the divertor. The JET-ILW HRS data on resolving the power at the deuterium and hydrogen spectral lines of the Balmer-alpha series is analysed, with direct observation of the divertor from the top and with observation of the inner wall along the tangential and radial LoS from the equatorial ports. This data allows the spectrum of the DSL and the signal-to-background ratio for the Balmer-alpha light emitted from the far SOL and divertor in the JET-ILW to be evaluated. The results support the expectation of the strong impact of the DSL upon the ITER main chamber Hα (and visible light) spectroscopy diagnostics.

Synthetic H-Alpha Diagnostics for ITER: Inverse Problems and Error Estimations for Strong Non-Maxwellian Effects and Intense Divertor Stray Light

The use of an all-metal first wall in future magnetic fusion reactors equipped with a divertor may impose severe limitations on the capabilities of optical diagnostics in the main chamber because of the divertor stray light (DSL) produced by reflections of the intense light emitted in the divertor. Here, we introduce a synthetic H-alpha diagnostics to estimate the errors of solutions of the inverse problems aimed at recovering the neutral hydrogen parameters (density and isotope ratio) in the scrape-off layer (SOL) with allowance for (a) strong DSL on the observation chords in the main chamber, (b) substantial deviation of the neutral atom velocity distribution function from a Maxwellian in the SOL, and (c) the data from the direct observation of the divertor. The results of recovering the relative contributions of all three sources to the signal along an observation chord in the main chamber (namely, from the high-field-side and low-field-side SOL sections of the observation chord, and the DSL), together with the isotope ratios in the SOL, are presented for the flattop stage of Q = 10 inductive operation of ITER.

Parameterization of Balmer-alpha asymmetric line shape in tokamak SOL plasmas

A parameterization of the Balmer-alpha spectral line shape asymmetry in the tokamak scrape-off layer (SOL) plasmas is suggested, which describes the contribution of nonMaxwellian components of the neutral atom velocity distribution function. Parameterization is needed for a fast-routine interpretation of high-resolution spectroscopy data and should be incorporated into the algorithms for the recovery of hydrogen neutral atom parameters in the SOL. We illustrate the efficiency of the parameterization on the example of spectral data calculated using the predictive modeling of the International Thermonuclear Experimental Reactor (ITER) tokamak operation.

Hydrogen Spectral Line Shape Formation in the SOL of Fusion Reactor Plasmas

The problems related to the spectral line-shape formation in the scrape of layer (SOL) in fusion reactor plasma for typical observation chords are considered. The SOL plasma is characterized by the relatively low electron density (1012–1013 cm−3) and high temperature (from 10 eV up to 1 keV). The main effects responsible for the line-shape formation in the SOL are Doppler and Zeeman effects. The main problem is a correct modeling of the neutral atom velocity distribution function (VDF). The VDF is determined by a number of atomic processes, namely: molecular dissociation, ionization and charge exchange of neutral atoms on plasma ions, electron excitation accompanied by the charge exchange from atomic excited states, and atom reflection from the wall. All the processes take place step by step during atom motion from the wall to the plasma core. In practice, the largest contribution to the neutral atom radiation emission comes from a thin layer near the wall with typical size 10–20 cm, which is small as compared with the minor radius of modern devices including international test experimental reactor ITER (radius 2 m). The important problem is a strongly non-uniform distribution of plasma parameters (electron and ion densities and temperatures). The distributions vary for different observation chords and ITER operation regimes. In the present report, most attention is paid to the problem of the VDF calculations. The most correct method for solving the problem is an application of the Monte Carlo method for atom motion near the wall. However, the method is sometimes too complicated to be combined with other numerical codes for plasma modeling for various regimes of fusion reactor operation. Thus, it is important to develop simpler methods for neutral atom VDF in space coordinates and velocities. The efficiency of such methods has to be tested via a comparison with the Monte Carlo codes for particular plasma conditions. Here a new simplified method for description of neutral atoms penetration into plasma is suggested. The method is based on the ballistic motion of neutrals along the line-of-sight (LoS) in the forward–back approximation. As a result, two-dimensional distribution functions, dependent on the LoS coordinate and the velocity projection on the LoS, and responsible for the Doppler broadening of the line shape, are calculated. A comparison of the method with Monte Carlo calculations allows the evaluation of the accuracy of the ballistic model. The Balmer spectral line shapes are calculated for specific LoS typical for ITER diagnostics.

The atom velocity distribution function in the process of liquid evaporation

Analytical expressions determining the velocity distribution function of evaporating particles were obtained for evaporation into vacuum. The formulas are compared with numerical simulation results; the coincidence can be treated as sufficiently good.

Effect of atoms evaporated from the anode on the structure of the vacuum arc space charge sheath

The structure of the anode space charge sheath of a vacuum arc is studied with allowance for the dependence of the negative anode fall on the ratio of the directed electron velocity v 0 to the electron thermal velocity v T for different values of the flux density of atoms evaporated from the anode. Poisson’s equation for the sheath potential is solved taking into account the electron space charge, fast cathode ions, and slow ions produced due to the ionization of atoms evaporated from the anode. The kinetic equation for atoms and slow anode ions is solved with allowance for ionization in the collision integral. Analytic solutions for the velocity distribution functions of atoms and slow ions and the density of slow ions are obtained. It is shown that the flux of slow ions substantially affects the spatial distribution of the electric field E(z) in the sheath. As the flux density increases, the nonmonotonic dependence E(z) transforms into a monotonic one and the sheath narrows. For a given flux of evaporated atoms Πa, the increase in the ratio of the directed electron velocity to the electron thermal velocity leads again to a nonmonotonic dependence E(z). As z increases, the electric field first increases, passes through the maximum, decreases, passes through the minimum E min, and then again increases toward the anode. There is a limiting value of the ratio (v 0/v T )* at which E min(z) vanishes. At v 0/v T > (v 0/V T )*, the condition for the existence of a steady-state sheath is violated and the profiles of the field and potential in the sheath become oscillating. The dependence of (v 0/v T )* on the flux density of evaporated atoms Π a is obtained. It is shown that the domain of existence of steady-state solutions in the sheath broadens with increasing Π a .

Examination of argon metastable atom velocity distribution function close to a conducting wall

The spatial evolution of the 1s5 metastable argon atom velocity distribution function is recorded in the sheath and pre-sheath regions of a metallic wall using laser induced fluorescence (LIF) spectroscopy. Metastable argon atom temperature and fluid velocity are computed from measured data. Owing to the loss of metastable argon atom after a collision with the surface, the atom temperature seemingly decreases and the velocity increases when approaching the wall. These artifacts are carefully examined and explained in terms of changes in the metastable argon atom distribution function. In addition, the atom nonelastic reflection coefficient is computed from the ratio of outward to inward atom flux to the surface. This study indicates less than 1% of metastable atoms survive a collision with the metallic wall.

Spectral properties of backscattered solar Ly- α radiation in the heliosphere: A search for heliospheric boundary effects

We explore the imprints of the solar wind interaction with the local interstellar medium on spectral properties of backscattered solar Ly- α radiation. We employ a newly developed effective model for the interstellar H atom velocity distribution function in the heliosphere ( Katushkina and Izmodenov, 2011). The model takes into account both global effects of H atom perturbations at the heliospheric boundaries and local (i.e. within 10–20 AU from the Sun) effects of the solar ionization, charge exchange, solar gravitation and radiation pressure. Backscattered solar Ly- α profiles, intensities, line-shifts and line-widths were computed at 1 AU for the anti-solar lines-of-sight. Then the intensities, line-shifts and line-widths are compared with those calculated by using more simplified one-component and two-component hot models. The largest differences between the new model and hot models are seen in the line-width of the backscattered Ly- α profiles. The line-width is very sensitive to the kinetic properties of the H atom distribution function after passing the interaction region between the solar wind and the interstellar medium.

Variations of interstellar H atom parameters in the outer heliosphere: solar cycle effects

In this paper, we study response of the heliospheric plasma interface, the region of the solar wind interaction with the local interstellar medium, to 11-year solar cycle variations of the solar wind. We explore how the solar wind variations influence interstellar H atoms in the heliospheric interface, which are coupled to plasma by charge exchange. We develop the self-consistent model, where the kinetic equation for interstellar H atom velocity distribution function is solved self-consistently with the gas dynamic equations for the charged (electrons and protons) component. It is shown that the termination shock location varies within ±7 AU, the heliopause variation is ∼2 AU, and the bow shock variation is negligible. The important new result is that at large heliocentric distances the density of the interstellar H atoms varies within ∼10% with solar cycle. The variation of density increases closer to the Sun up to 30% at 5 AU.

Behavior of the H atom velocity distribution function within the shock wave of a hydrogen plasma jet.

The evolution of the ground-state hydrogen atom velocity distribution function throughout the stationary shock wave of a supersonic hydrogen plasma jet (3<Mach number<4) is studied using laser-induced fluorescence spectroscopy. The H atom velocity distribution function may be decomposed into two Maxwellian distributions. The fast component of the distribution corresponds to the unhampered supersonic conditions. The slow component corresponds to the conditions in the shock region, i.e., within the shock front, the mean velocity and the temperature of this atom group vary. Across the shock wave, the H atom population is gradually transferred from the fast to the slow component by means of collisions. The development of the mean axial velocity is modeled using the Mott-Smith approach. Departure from the theoretical shock profile is interpreted in terms of the nonconservation of both the H atom forward flux and momentum across the shock wave.

Semiclassical representation method in statistical physics of interacting molecules: II. Theory of open systems. Application to the theory of a single-mode laser taking into account the recoil effect

The generalization of the earlier reported semiclassical representation method for open systems is given. The quantum theory of a single-mode laser based on two-level atoms having translational degrees of freedom is considered as an example of using the developed approach. Correlation of the field and the atomic motion due to the recoil effect is taken into account in the system under consideration. The self-consistent theory describing dynamic and statistical properties of the system is performed. It is shown that, due to a friction of resonant atoms in a buffer gas, their translational motion is coupled with the radiation field. This coupling can lead to a nonequilibrium form of the atom velocity distribution function which results in essential changes of the field parameters, such as radiation intensity, frequency shift, line width, etc.

Geschwindigkeitsverteilungsfunktionen von Atomen und Ionen in verschiedenen Anregungs‐ und Ionisationsstufen in Niederdruck‐Entladungen bei hohem Ionisationsgrad

AbstractSupposing free‐fall conditions the velocity distribution functions of atoms and ions in various levels in gas discharges at low pressures are calculated. In particular, plasmas at high degrees of ionization are considered. Solving the Boltzmann equation for the motions transverse to the wall of the discharge tube it is shown that the velocity distribution functions can considerably deviate from the Maxwellian and become non‐isotropic. Inelastic collisions with electrons and the ionization by electron impacts considerably determine the velocity distribution function of the neutral atoms. The velocity distribution function of the ions is also essentially determined by the electric field within the plasma. For the motions transverse to the wall the half widths of the velocity distribution functions do not only depend on the temperature of the wall, but on the electron density and on the electron temperature as well. At small electron densities the half widths for excited atoms and for ions can be narrower than the one for the ground state atoms. The charge exchange between atoms and ions is shortly taken into consideration.

Nonequilibrium time dependent theory of hot atom reactions. I. Model calculations

The chemical kinetics of hot atoms is studied with a two temperature moment method of solution of the Boltzmann equation. Nonequilibrium time dependent results obtained from the numerical integration of the moment equations are compared with the results obtained with the assumption that the hot atoms are distributed in accordance with a Maxwell–Boltzmann velocity distribution function. The range of validity of the steady state temperature theory is investigated in detail. Extensive calculations of the time evolution of the hot atom velocity distribution function, number density and temperature are presented. These calculations involve the variation of several system variables such as cross sections and mass ratios.

Shock propagation in the one-dimensional lattice at a nonzero initial temperature

Recent studies of shock propagation in a one-dimensional discrete crystal lattice are extended to include the case for which the lattice is at a nonzero intitial temperature. The lattice is assumed to be monatomic, and its atoms are assumed to interact via a Morse-type interatomic potential. Behind the shock front, a spectrum of well-defined stable pulses (solitons) is observed to propagate amid the thermal background of the lattice. The solitons have varying amplitude and propagation velocities, and the different velocities introduce a spreading effect which prevents the shock profile from approaching a steady state. The velocity distribution function of atoms well behind the front is calculated and indicates an approach to thermal equilibrium at an elevated temperature in this region of the crystal. The implications of the nonsteady behavior and the slow approach to thermal equilibrium for currently used theories of detonation are noted and discussed.