Electron-neutral Elastic Collisions Research Articles

Density profile transition and high-energy electron transport in a magnetically expanding radio frequency plasma

The density profile transition and high-energy electron transport in a magnetically expanding radio frequency (RF) plasma were investigated using particle-in-cell and Monte Carlo collision techniques, where both the plasma source and the diffusion region were simulated self-consistently. The simulation results show that the density profile changes from center-peaked to bimodal plasma with increasing magnetic field strength, where bimodal plasma was observed in previous experiments. Then, the density profile transition is discussed with respect to ionization, electron temperature, and high-energy electron density. This indicates that electrons were heated by the RF field and transported radially inward across magnetic field lines. The moving distance of high-energy electrons is explained by an electron-neutral elastic collision. Therefore, the density formation depends on where the electrons are heated and how far the high-energy electrons are transported by an elastic collision, implying the longer existing time of high-energy electrons that move radially inward away from the RF antenna.

Kinetic investigation of the planar multipole resonance probe under arbitrary pressure

A new plasma diagnostic tool called planar multipole resonance probe (pMRP) has been proposed in the past decade. It has a minimally invasive structure and allows simultaneous measurement of electron density, temperature, and collision frequency. Previous work has investigated the behavior of the pRMP by the Drude model, which misses kinetic effects, and the collisionless kinetic model, which misses collisional damping. To further study the pMRP at arbitrary pressure, a collisional kinetic model is proposed in this paper. The electron dynamics is described by the kinetic equation, which considers the electron-neutral elastic collision. Under the electrostatic approximation, the kinetic equation is coupled to the Poisson equation. The real part of the general complex admittance is calculated to describe the spectral response of the probe–plasma system. The calculated spectra of the idealized pMRP demonstrate that this collisional kinetic model can capture both collisionless kinetic damping and collisional damping. This model overcomes the limitations of the Drude model and the collisionless kinetic model and allows discussion of the validity of simpler models.

Nonlinear transmission line (NTL) model study of electromagnetic effects in high-frequency asymmetrically driven capacitive discharges

In this work, we generalize a nonlinear transmission line (NTL) model introduced in a previous work [Liu et al. Plasma Sources Sci. Technol. 30, 045017 (2021)] to achieve more comprehensive simulations. The improved NTL model allows a variable-sized (instead of a one grid cell) vacuum spacer between the powered and grounded electrodes and takes into account the (previously neglected) electron-neutral elastic collision frequency term in the plasma dielectric constant, and the radial variation of the plasma density. Using this model, we study the effects of the spatial and series resonances, associated with the (axially) z-antisymmetric and z-symmetric radially propagating surface wave modes, and the nonlinear harmonic excitations on the plasma uniformity. We conduct simulations in which we increase the driving frequency f from 30 to 120 MHz for an asymmetric capacitive argon discharge at a fixed pressure and electron power of pg=20 mTorr and Pe=40 W, respectively. The first antisymmetric mode resonance frequency fa1 occurs between 80 and 90 MHz, and the first symmetric mode resonance frequency fs1 occurs at about 100 MHz. The powered electrode sheath becomes smaller than the grounded electrode sheath for f≈fa1, and the source voltage reaches a minimum for f≈fs1. The radially varying electron power density shows a narrow center peak due to the finite mode wavelengths and the nonlinearly excited harmonics, which can be further enhanced by spatial or series resonances. A second peak appears above the vacuum spacer edge as f exceeds fs1 at 120 MHz because the shorter wavelengths at higher f allow secondary maxima of the surface waves to form within the reactor.

Computing the Paschen curve for argon with speed-limited particle-in-cell simulation

Upon inclusion of collisions, the speed-limited particle-in-cell (SLPIC) simulation method successfully computed the Paschen curve for argon. The 1D3V simulations modeled an electron cascade across an argon-filled capacitor, including electron-neutral ionization, electron-neutral elastic collisions, electron-neutral excitation, and ion-induced secondary electron emission. In electrical breakdown, the timescale difference between ion and electron motion makes traditional PIC methods computationally slow. To decrease this timescale difference and speed up computation, we used SLPIC, a time-domain algorithm that limits the speed of the fastest electrons in the simulation. The SLPIC algorithm facilitates a straightforward, fully kinetic treatment of dynamics and collisions. SLPIC was as accurate as PIC, but ran up to 200 times faster. SLPIC accurately computed the Paschen curve for argon over three orders of magnitude in pressure.

Influence of electron-neutral elastic collisions on the instability of an ion-contaminated cylindrical electron cloud: 2D3V PIC-with-MCC simulations

This paper is a simulation based investigation of the effect of elastic collisions and effectively elastic-like excitation collisions between electrons and background neutrals on the dynamics of a cylindrically trapped electron cloud that also has an ion contaminant mixed in it. A cross section of the trapped non neutral cloud composed of electrons mixed uniformly with a fractional population of ions is loaded on a 2D PIC grid with the plasma in a state of unstable equilibrium due to differential rotation between the electron and the ion component. The electrons are also loaded with an axial velocity component, vz, that mimics their bouncing motion between the electrostatic end plugs of a Penning-Malmberg trap. This vz loading facilitates 3D elastic and excitation collisions of the electrons with background neutrals under a MCC scheme. In the present set of numerical experiments, the electrons do not ionize the neutrals. This helps in separating out only the effect of non-ionizing collisions of electrons on the dynamics of the cloud. Simulations reveal that these non-ionizing collisions indirectly influence the ensuing collisionless ion resonance instability of the contaminated electron cloud by a feedback process. The collisional relaxation reduces the average density of the electron cloud and thereby increases the fractional density of the ions mixed in it. The dynamically changing electron density and fractional density of ions feed back on the ongoing ion-resonance (two-stream) instability between the two components of the nonneutral cloud and produce deviations in the paths of progression of the instability that are uncorrelated at different background gas pressures. Effects of the collisions on the instability are evident from alteration in the growth rate and energetics of the instability caused by the presence of background neutrals as compared to a vacuum background. Further in order to understand if the non-ionizing collisions can independently be a cause of destabilization of an electron cloud, a second set of numerical experiments were performed with pure electron plasmas making non-ionizing collisions with different densities of background neutrals. These experiments reveal that the nature of potential energy extraction from the electron cloud by the non-ionizing collisions is not similar to the potential energy extraction of other destabilizing processes, e.g., a resistive wall instability. This difference in the energy extraction process renders these non-ionizing collisions incapable of independently triggering an instability of the cloud.

Differential cross section in PIC-MCC simulation of plasma-solid interaction

This paper focuses on the particle modelling of the interaction of low-temperature plasma with immersed cylindrical Langmuir probe. Particle modelling gives comprehensive information about the system, which is being analyzed, but the simulations are highly time-consuming. Especially in the high-pressure plasma the interactions between charged and neutral particles play an important role and they are often simulated by the Monte Carlo method. For this paper we prepared a simulation, which contains these interactions in as accurate way as possible, including the angular dependence of the electron-neutral elastic collision. We showed the effect of neglecting this angular dependence as well as the energy dependences of the cross sections of all included interactions.

Theoretical study of plasma effect on a conical shock wave

Experiments conducted previously in a Mach 2.5 wind tunnel showed that localized plasma generated by an on-board 60Hz electric discharge in front of a 60° cone-shaped model considerably increases the shock angle of the attached shock generated by the cone model. Based on the measured power and cycle energy of the electric discharge, the estimated peak and average temperature enhancements were too low to justify the heating effect as a possible cause of the observed shock wave modification. In this work, a theory also using a cone model as the shock wave generator is presented to explain the observed plasma effect on the shock wave. Through electron-neutral elastic collisions and ion-neutral charge transfer collisions, plasma generated in front of the baseline shock front can deflect the incoming flow before it reaches the cone model; such a flow deflection modifies the structure of the shock wave generated by the cone model from a conic shape to a slightly curved one. The shock remains to be attached to the tip of the cone; however, the shock front moves upstream to increase the shock angle, consistent with the experimental results.

ホールスラスタ流れ場の一次元計算

One-dimensional Hall thruster flowfield calculation, in which axial motion of ions; axial and azimuthal motions of electrons perpendicular to magnetic field were considered, was carried out to understand the plasma features and the plasma acceleration processes. The model included first ionization by direct electron-neutral collisions, electron-neutral elastic collisions, electron-ion Coulomb collisions, Bohm diffusion (anomalous diffusion); channel wall losses of ion flux and electron energy with secondary electron emission effect. The flowfield in an acceleration channel was divided into diffusion, ionization and ion acceleration regions. Both ionization and ion acceleration were found to, intensively and efficiently, occur in their thin regions with a few millimeter thick near the acceleration channel exit. The calculated thruster performance roughly agreed with an experimental one.

Diffusion-controlled regime of surface-wave-produced plasmas in helium gas

The study presents a numerical fluid-plasma model of diffusion-controlled surface-wave-sustained discharges in helium gas. The self-consistent behaviour of the discharge based on the interrelation between plasma density and Θ, the power absorbed on average by one electron, is described. The nonlinear process of step ionization in the charged particle balance equation is the main factor, which ensures the self-consistency. However, it is shown that in helium discharges, the ionization frequencies enter the dependence of Θ on the plasma density also through the ambipolar-diffusion coefficient. Results at two different values of the gas pressure and of the wave frequency are discussed. The lower value of the gas pressure is chosen according to the condition to have a pure diffusion-controlled regime without interference with a transition to the free-fall regime. The boundary condition for the ion flux at the wall sheath is used for determination of the value of µ, the quantity denoting the degree of the radial plasma-density inhomogeneity which, together with the electron-neutral elastic collision frequency, influences the wave propagation characteristics. The two values of the wave frequency chosen provide descriptions of high-frequency and microwave discharges. The model results in the self-consistent structure of the discharge: interrelated variations along the discharge length of wavenumber, space damping rate, Θ, plasma density and electron temperature. The power necessary for sustaining discharges of a given length is also calculated. Comparisons with argon discharges are shown.

Plasma parameters of diffusion-controlled microwave discharges in surface-wave fields

Results from diagnostics of diffusion-controlled stationary gas discharges maintained in the field of propagating surface waves are presented in this study. The set of the plasma parameters obtained includes: 1) the plasma density n~, averaged over the discharge cross section; and its axial profile n~(z);. 2) the electron-neutral elastic collision frequency /spl nu/; 3) the parameter /spl mu/, which describes the radial profile of the plasma density; 4) the parameter /spl Theta/, the power absorbed on average by an electron, and its axial variation /spl Theta/ (z); 5) the electron temperature T/sub e/ (z); and 6) the gas temperature T/sub g/. The mechanisms of electron heating and discharge self-consistency are discussed.

Diagnostics of microwave discharges sustained by propagating surface waves

A procedure for radiophysics diagnostics of stationary discharges sustained in the field of propagating surface waves is developed in this study. The capability of the interferogram method, well known as a method for obtaining the axial profile of the plasma density n( z), is extended to the determination of the electron-neutral elastic collision frequency ν and the parameter μ, which characterizes the transverse plasma inhomogeneity. The procedure involves: (i) measurements of the axial profile of the electric field power, (ii) numerical results for the surface-wave dispersion behaviour in inhomogeneous collisional plasma waveguides and, (iii) experimental results for the space-damping rate α of the wave, besides the data for the wavenumber β.

Global model and scaling laws for inductively coupled oxygen discharge plasmas

For inductively coupled oxygen rf discharge plasmas, a global model which consists of the energy and particle balance equations is formulated. The energy balance equation includes energy losses for electron-neutral elastic collision, excitation, ionization, dissociation, pair production, and charged particle wall loss. Particle balance equations are written for all species of interest. For a specified discharge length and diameter, absorbed power, pressure, electron temperature-dependent reaction rate coefficients and surface recombination constants, we solve these equations to determine the densities of all species and the electron temperature. We measure these parameters by the Langmuir probe method. According to the prevailing particle loss mechanism, the parameter space can be divided into a volume recombination-loss-dominated region and an ion-flux-loss-dominated region. Based on the global model equations, the scaling laws of plasma variables with the control parameters for the ion-flux-loss-dominated region are estimated and compared with the experimental results.

Low-pressure RF discharge in the free-flight regime

The self-consistent equations system for low-pressure RF discharge in the free-flight regime is formulated. The expressions for the electron energy diffusion coefficient due to electron-neutral collisions and to the electron collisions with the plasma-space charge moving boundary (stochastic heating) are derived. If the electron-neutral elastic collisions frequency exceeds the inelastic one, the conventional two-term approximation for the electron distribution function (EDF) can be generalized, and the space-time-averaged electron kinetic equation can be reduced to the one-dimensional energy diffusion one. The fast electrons attached to the electrode surface can also be accounted for in this equation. It is shown that in the cases of (a) spatially uniform ion profile, (b) for frequencies that are small compared with the electron bounce frequency, and (c) for frequencies exceeding the electron plasma one in the sheath, the stochastic heating vanishes. >

Energy transfer in positive streamers

A Schlieren optical system has been used to measure changes in neutral density in a point-plane gap, during and following positive streamers in air. The results show that energy is transferred to the air molecules by two processes. Electron-neutral elastic collisions during the streamer generate a shock-front which moves radially outwards at around 350 m s-1. Following the streamer current pulse,which lasts for around 0.1 mu s, positive ions drifting towards the negative plane transfer their energy to the neutrals over a period of tens of mu s. This positive ion transfer generates the corona wind and the schlieren technique allows the wind speed to be measured close to the point. Corona wind speeds were found to be in the range 8 to 12 m s-1.

The Thermic Excitation of Parametric Instability in a Plasma

The new possibility of controlled excitation of parametric instability in a partially ionized collisional plasma is suggested. This possibility is based on a special type of the interaction two radiowaves in a plasma, when the threshold amplitude value of parametric instability of plasma-wave resonant interaction, connected with one radiowave, is governed by electron heating, produced by another radiowave. The possibilities of utilization of such effects are connected with temperature excitation or attenuation of parametrical instabilities and separate determination of frequencies of electron-ion and electron-neutral elastic collisions in a local plasma region.