V. S. Sukhomlinov

Experimental and theoretical determination of the strongly anisotropic velocity distribution functions of ions in the intrinsic gas plasma in strong fields

The first seven coefficient of expansion of the energy and angular distribution functions in the Legendre polynomials for Hg+ ions in the Hg vapor plasma with parameter E/P ≈ 400 V/(cm Torr) are measured for the first time using a planar one-sided probe. The analytic solution to the Boltzmann kinetic equation for ions in the plasma of their parent gas is obtained in the conditions when the resonant charge exchange is the predominant process, and an ion acquires on its mean free path a velocity much higher than the characteristic velocity of thermal motion of atoms. The presence of an ambipolar field of an arbitrary strength is taken into account. It is shown that the ion velocity distribution function is determined by two parameters and differs substantially from the Maxwellian distribution. Comparison of the results of calculation of the drift velocity of He+ ions in He, Ar+ in Ar, and Hg+ in Hg with the available experimental data shows their conformity. The results of calculation of the ion distribution function correctly describe the experimental data on its measurement. Analysis of the result shows that in spite of the presence of the strong field, the ion velocity distribution functions are isotropic for ion velocities lower than the average thermal velocity of atoms. With increasing ion velocity, the distribution becomes more and more extended in the direction of the electric field.

Simulations of ion velocity distribution functions taking into account both elastic and charge exchange collisions

Based on accurate representation of the He+-He angular differential scattering cross sections consisting of both elastic and charge exchange collisions, we performed detailed numerical simulations of the ion velocity distribution functions (IVDF) by Monte Carlo collision method (MCC). The results of simulations are validated by comparison with the experimental data of the ion mobility and the transverse diffusion. The IVDF simulation study shows that due to significant effect of scattering in elastic collisions IVDF cannot be separated into product of two independent IVDFs in the transverse and parallel to the electric field directions.

Ion velocity distribution functions in argon and helium discharges: detailed comparison of numerical simulation results and experimental data

Using Monte Carlo Collisions (MCC) method, we have performed simulations of ion velocity distribution functions (IVDF) taking into account both elastic collisions and charge exchange collisions of ions with atoms in uniform electric fields for argon and helium background gases. The simulation results are verified by comparison with the experiment data of the ion drift velocities and the ion transverse diffusion coefficients in argon and helium. The recently published experimental data for the first seven coefficients of the Legendre polynomial expansion of the ion energy and angular distribution functions are used to validate simulation results for IVDF. Good agreements between measured and simulated IVDFs show that the developed simulation model can be used for accurate calculations of IVDFs.

Comment on “Ion distribution function in a plasma with uniform electric field” [Phys. Plasmas 19, 113703 (2012)].

The comparison between experimental data of ion distribution function at the parent gas plasma obtained by the authors and results of calculations presented by Lampe et al. are considered. It is shown that the experimental and calculated angular distributions of ions in the case at least of argon differ considerably. The analysis of Lampe et al. assumptions showed that the main reasons of these discrepancies were the assumptions of ion distribution function independence on field orientation and independence of charge exchange cross-section on the relative velocity of ion and atom.

Ion energy distribution function in the wall layer at a negative wall potential with respect to the plasma

On the basis of the kinetic approach, the self-consistent problem of the gas discharge ion distribution function in the sheath near a surface at a negative potential with respect to the plasma is solved. For the first time, the solution takes into account the dependence of the ion charge exchange cross section from the atom on the ion energy, as well as the real ion distribution function in the unperturbed plasma. It is shown that the dependence of the charge exchange cross section on the ion energy significantly affects the shape of the ion distribution function. It is found that the mean energy of the ions near the wall depends on the electron mean energy in the unperturbed plasma. It was also found that, at the same electron mean energy, the form of the distribution function has practically no effect on the ion distribution function in the wall sheath. The calculations are in good agreement with the known mass spectrometric measurements of the ion distribution function. The obtained results give an opp...

Probe measurements of the electron velocity distribution function in beams: Low-voltage beam discharge in helium

Previously developed methods based on the single-sided probe technique are altered and applied to measure the anisotropic angular spread and narrow energy distribution functions of charged particle (electron and ion) beams. The conventional method is not suitable for some configurations, such as low-voltage beam discharges, electron beams accelerated in near-wall and near-electrode layers, and vacuum electron beam sources. To determine the range of applicability of the proposed method, simple algebraic relationships between the charged particle energies and their angular distribution are obtained. The method is verified for the case of the collisionless mode of a low-voltage He beam discharge, where the traditional method for finding the electron distribution function with the help of a Legendre polynomial expansion is not applicable. This leads to the development of a physical model of the formation of the electron distribution function in a collisionless low-voltage He beam discharge. The results of a n...

Analytical Theory of Energy Relaxation Upon Propagation of a High-Energy Electron Beam in Gas

This study is devoted to the development of an analytical theory for calculating the spatial distribution of the energy release upon propagation of a high-energy (1–100 keV) electron beam in a gas (based on the example of air). Based on the analysis of data on the cross sections of elastic and inelastic interactions between electrons and molecules of gases that are in the air composition, it was suggested that inelastic interaction causes energy relaxation, whereas elastic interaction leads to momentum relaxation. The model cross section of inelastic collisions of electrons with molecules is used for solving the Boltzmann kinetic equation for electrons; this cross section provides adequate description of the experimentally found energy dependence of the mass stopping power of electrons. The results for the dependence of the mean electron energy on the number of inelastic collisions are in good agreement with the results of calculation based on expansion of the distribution function in the number of collisions and solution by the Monte Carlo method. The calculations we performed show that the consideration of elastic collisions increases the spatial density of the energy release due to narrowing of the region where the main part of the energy of fast electrons is released, in comparison with calculations where only inelastic deceleration is taken into account.

Effect of Elastic Collisions on the Ion Distribution Function in Parent Gas Discharge Plasma

An analytical solution is obtained for the Boltzmann kinetic equation for ions in the plasma of its gas with allowance for the processes of resonant charge exchange and elastic ion scattering on the atom. The cross section of differential elastic scattering was assumed to be isotropic in the system of the mass center, and the resonant charge exchange process is independent of the elastic scattering. It is shown that the ion velocity distribution function is determined by two parameters and differs significantly from the Maxwellian one. The allowance for elastic scattering with these assumptions leads to a change in the ion angular distribution and also to a decrease in the average ion energy due to the transfer of part of the ion energy to atoms upon elastic collisions. The calculated values of the drift velocity, the average energy, and the coefficient of transverse diffusion of He+ ions in He, Ar+ ions in Ar are compared with the known experimental data and the results of Monte Carlo calculations; they show good agreement.

New Possibilities of Probe Detection of Anisotropic Charged-Particle Distribution Functions in an Arbitrary-Symmetry Plasma

We have analyzed the precision and systematic errors of the familiar method of a plane single-ended probe for measuring the anisotropic distribution functions for electrons and ions in plasma. Analytic relations that connect the plasma parameters and the required number of terms in a series are obtained under the conditions when anisotropy is due to the presence of an electric field in the plasma. It has been shown that ten terms of the series are usually sufficient to adequately describe the ion distribution function, except for the case of strong fields. For strongly anisotropic charged particle distribution functions, the spline interpolation technique for experimental data is proposed and tested, which substantially reduces the systematic error for a preset number of terms in the series. It has been shown for abundant actual plasma objects with the mirror symmetry that the number of required orientations of a plane probe for the experimental distribution function can be reduced by half compared to the most general case of the absence of any symmetry for a fixed number of terms in the Legendre series, while for the same number of orientations, the number of terms in the series, which are determined from these measurements, doubled accordingly.

Ion velocity distribution function in intrinsic gas at cryogenic gas temperatures

The influence of elastic scattering on the ion distribution function in the plasma of an intrinsic gas in weak fields has been considered. An analytical expression valid for cryogenic temperatures of atoms has been obtained. The reduced He+–He, Ar+–Ar mobilities as functions of the temperature of atoms in a range of 4–1000 K have been calculated in the approximation of the zero field taking into account elastic collisions; the calculated dependences well agree with the available experimental data. It has been demonstrated that elastic collisions play an important role in the formation of the ion distribution function at low temperatures. The results of measurement of the ion mobility in the limit of the zero field at low temperatures can be used to obtain data on the ratio of elastic scattering and resonance charge exchange cross sections.