Sheath Oscillations Research Articles

Influence of discharge power and grid structure on an RF-biased ion thruster

The RF-biased ion thruster applies radio-frequency (RF) power on the grid system, which can extract both ions and electrons to achieve self-neutralization. The performance of the RF-biased ion thruster is significantly influenced by the structure of the grid system and the discharge power since these factors play a crucial role in determining the focusing condition of the grid system. In this paper, the influence of discharge power and grid structure on the RF-biased ion thruster’s voltage parameters is investigated. According to the screen grid voltage waveform results under different discharge power and grid structure, the relationship between self-bias voltage and RF voltage is acquired. In order to explain the different waveform variations, the impacts of the direct impingement current as well as the oscillation of the upstream sheath voltage are considered in the theoretical calculation for self-bias voltage. It has been found that the opposite oscillation of the upstream sheath voltage is the primary reason for the decline in self-bias voltage. Moreover, the mechanisms through which discharge power and grid structure influence the self-bias voltage are explained in terms of their impact on upstream sheath oscillation. Several methods for increasing the self-bias voltage in RF-biased ion thrusters are also proposed.

Numerical investigations of spatiotemporal dynamics of space-charge limited collisional sheaths

Electrostatic particle-in-cell (PIC) and direct simulation Monte Carlo (DSMC) methods are used to compare the plasma dynamics of collisionless with collisional emissive sheaths in partially ionized environments. Space-charge limited emissive sheaths submersed in a plasma with a density of ∼1017 m−3 are examined using a PIC-DSMC solver, CHAOS. Collisionless emissive sheaths with plasma domains sufficiently long (30 and 60 Debye lengths, λD) are subject to strong oscillations due to two-stream electron instability, whereas emissive sheaths in weakly collisional conditions with a short domain (15 λD) exhibit self-spike (sawtooth) oscillations in the plasma field due to the trapped charge-exchange (CEX) ion population within the virtual cathode (VC) region. The two-stream electron instability leads to strong temporal fluctuations in the total emission current, with maximum deviations of 60% and 100% from the time-averaged current for the long plasma domains, whereas CEX collisions cause strong spikes in the emission current if the domain size is short. Our PIC-DSMC simulations show for the first time that the interaction of the two types of instabilities causes the strength of the self-spike to be weakened due to the strong fluctuations caused by the two-stream instability when a sufficiently long computational domain with ion-neutral collisions is employed. By conducting a two-dimensional Fast Fourier Transform (FFT) on the collisional and collisionless sheaths with long domains, we show that the transient evolution of CEX entrapment in the VC increases frequency of sheath oscillations up to two times the ion-acoustic frequencies observed in the collisionless sheath. CEX collisions weaken the VC region and result in a total emission current more than that obtained from the collisionless case for the same domain length. With a more rarefied neutral environment of 1019 m−3 in the plasma sheath, the total emission current increases only 4% in comparison with 14% for one order of magnitude denser environment, within 20 μs. In addition, the spike period is tested with different neutral temperatures and densities. While we do not observe any self-spike in the more rarefied environment, the spike period increased from 5 to 7.5 μs when the neutral temperature is increased from 300 to 2000 K in the denser environment with the simulation time of 20 μs.

Dual-frequency sheath oscillations and consequences on the ion and electron transport in dielectric barrier discharges at atmospheric pressure

Current–voltage characteristics, space- and time-resolved optical emission spectroscopy, and 1D fluid modeling are used to examine the effect of dual-frequency sheath oscillations on the ion and electron transport in dielectric barrier discharges sustained by a combination of low frequency (LF, 50 kHz, 650 V) and radiofrequency (RF, 5.3 MHz, 195 V) voltages, exhibiting the α-to-γ mode transition. On one hand, when polarities of the LF and RF voltages are opposite, an electric field near the LF cathode (due to LF cathode sheath) drives the secondary electrons to the plasma bulk and an opposite electric field between the sheath edge and the LF anode attracts the electrons toward the LF cathode (to maintain quasi-neutrality in the plasma bulk). At the sheath edge, electrons become trapped and ions drift toward the cathode and the anode simultaneously according to their position in the gap. On the other hand, when the RF voltage has the same polarity as the LF voltage, the total applied voltage increases and this yields to enhanced production of electrons and ions in the sheath. To maintain quasi-neutrality in the bulk, the electric field along the gap exhibits the same polarity as the one in the sheath, allowing electrons created in the sheath to be evacuated toward the LF anode. The behavior of the LF cathode is, therefore, controlled by the LF sheath, and, thus, by the LF voltage amplitude, while the behavior in the bulk and at the anode alternates on the time scale of the RF voltage.

Hollow cathode effect in radio frequency hollow electrode discharge in argon

Radio frequency capacitively coupled plasma source (RF-CCP) with a hollow electrode can increase the electron density through the hollow cathode effect (HCE), which offers a method to modify the spatial profiles of the plasma density. In this work, the variations of the HCE in one RF period are investigated by using a two-dimensional particle-in-cell/Monte-Carlo collision (PIC/MCC) model. The results show that the sheath electric field, the sheath potential drop, the sheath thickness, the radial plasma bulk width, the electron energy distribution function (EEDF), and the average electron energy in the cavity vary in one RF period. During the hollow electrode sheath’s expansion phase, the secondary electron heating and sheath oscillation heating in the cavity are gradually enhanced, and the frequency of the electron pendular motion in the cavity gradually increases, hence the HCE is gradually enhanced. However, during the hollow electrode sheath’s collapse phase, the secondary electron heating is gradually attenuated. In addition, when interacting with the gradually collapsed hollow electrode sheaths, high-energy plasma bulk electrons in the cavity will lose some energy. Furthermore, the frequency of the electron pendular motion in the cavity gradually decreases. Therefore, during the hollow electrode sheath’s collapse phase, the HCE is gradually attenuated.

Resonant electron confinement and sheath expansion heating in magnetized capacitive oxygen discharges

In weakly magnetized capacitive radio frequency (RF) plasmas electrons accelerated into the plasma bulk by the expanding RF boundary sheath at one electrode can be returned to this electrode due to their gyromotion around an externally applied magnetic field oriented parallel to the electrodes. If the driving frequency and magnetic field are chosen so that the electron cyclotron frequency, ω ce, equals half of the driving RF, ω rf, such energetic beam electrons will be returned to the sheath during its expansion phase and, thus, will be confined and heated resonantly. This magnetized RF sheath resonance (MRSR) effect is studied based on kinetic particle-in-cell simulations in weakly magnetized capacitively coupled oxygen plasmas. In comparison with electropositive argon plasmas, this resonance mechanism is found to be affected strongly by the electronegativity of oxygen discharges. In the unmagnetized case, low-pressure capacitive oxygen discharges operate in an electropositive mode, where nonlinear high-frequency sheath oscillations play an important role similar to previous observations in electropositive discharges with low electron densities. If the resonance condition is fulfilled (), the discharge efficiency is enhanced due to the MRSR effects, resulting in an increase in plasma density. Our numerical results demonstrate that this resonance effect is particularly efficient at low pressure and low electronegativity. However, in strongly electronegative discharges, the time it takes a typical resonant electron to return to the expanding sheath edge is found to be affected by drift and ambipolar electric fields in the plasma bulk, which cause a deviation from the resonance condition, resulting in a reduction of this type of resonance effect.

High energy electrons induced by nonlinear effect in synchronized dual-level radio frequency pulsing capacitively coupled plasmas

The surface charging effect of positive ions at the trench bottom during the etching of dielectric materials has become a severe problem with the shrinkage of electronic feature dimensions. Pulsed plasmas have been widely used to overcome surface charging issues during plasma etching in industry. In this work, synchronized dual-level radio frequency pulsed modulation on capacitively coupled plasmas is investigated based on 1D3V particle-in-cell/Monte Carlo collision simulations. It is found that the plasma always remains a certain initial density during the dual-level pulse modulation, as the high frequency (HF) source still presents during pulse off time (with a reduced voltage amplitude), which may facilitate high processing efficiency. Meanwhile, many HF sheath oscillations are simulated at the initial stage of a pulse period, which induces vast high energy electrons to strike the electrode. When the HF voltage is maintained at a very low value during the pulse off (i.e. 0.1), more electrons with higher energy bombard the bottom of the trench, effectively alleviating the charging effect. Furthermore, the nonlinear behavior of sheath oscillations is proved to be very sensitive to dual-frequency voltage amplitudes and pulse ramp-up times.

Study of self‐organised criticality in a coaxial plasma source with gridded cathode

AbstractMultiple luminous sheath structures develop in the localised plasma formation inside a cylindrical gridded cathode plasma source. These structures gradually expand into the whole vessel and undergo a critical state through self‐organised criticality (SOC) along with pronounced sheath oscillations during the variation of anode potential. The present investigation emphasises the stability properties associated with the oscillations of the sheath potential structures in the cylindrical‐gridded cathode in glow discharge regime through SOC phenomena through non‐linear time series analysis. The non‐linear temporal and spatial analysis of potential structure and dynamics of charged particles are correlated with SOC in cylindrical‐gridded cathode in glow discharge regime through the dynamics of multiple sheath structure formations. The existence of flicker noise and long‐range correlation in the time series suggests the existence of SOC behaviour in the system, the multiple sheath structures evolve through reduction and addition of layers. Cylindrical‐gridded cathode discharge initiation during formations of multiple sheath structures, switching of discharge regimes with anode potential, layer reduction and addition inside the sheath structures through SOC behaviour, renders uniqueness to the present regime of investigation. Self‐organised pattern formations and self‐organised criticality behaviour investigated in the present glow discharge regime using the cylindrical‐gridded cathode source are of prime importance to understand the complex behaviour of plasmas in the field of hollow cathode discharges.

Resonant sheath heating in weakly magnetized capacitively coupled plasmas due to electron-cyclotron motion.

An electron heating mechanism based on a resonance between the cyclotron motion of electrons and the radio frequency sheath oscillations is reported in weakly magnetized capacitively coupled plasmas at low pressure. If half of the electron cyclotron period coincides with the radio frequency period, then electrons will coherently collide with the expanding sheath and gain substantial energy, which enhances the plasma density. A relation between the magnetic field and the driving frequency is found to characterize this resonance effect and the kinetics of electrons are revealed at resonance conditions for various driving frequencies.

Observation of nonlinear sheath oscillations in symmetric capacitive discharges at low pressures

The mechanism of nonlinear oscillations in symmetric capacitively coupled plasmas is studied by the particle-in-cell/Monte Carlo collisions approach. A physical origin of this nonlinear phenomenon is identified by spatiotemporal kinetic analysis of electron dynamics. It is found that multi-beams of high-energy electrons are stimulated at the sheath expansion phase, following with reversed electric field filaments. The instantaneous absence of the quasi-neutrality in the vicinity of the sheaths is responsible for the observed phenomenon. In addition, a simple theoretical model is introduced to qualitatively illustrate the numerical findings. Our simulations demonstrate that the frequency and intensity of this nonlinearity are very sensitive to the plasma density, sheath velocity, and sheath thickness. More nonlinear oscillations could be stimulated at the condition of high density and high sheath velocity, while a large sheath thickness normally induces large-amplitude oscillations. A simple relation of pressure and gap distance for nonlinear sheath oscillations has been built.

Comment on “Sheath oscillations during directional motion of fire tube formation in expanding RF plasma” [Phys. Plasmas 26, 113502 (2019)

Measurements regarding the plasma-sheath instability have been described in a recent paper [Phys. Plasmas 26, 113502 (2019)] by the authors Paul and Chakraborty. They measured low frequency oscillations in a cylindrical, highly transparent grid electrode by using Langmuir probes and magnetic field sensors. This topic is very interesting for low temperature plasma physics, especially when it comes to the fundamental understanding of the stability of (multiple) double layers. However, it is questionable if the measured frequencies are originating from a plasma-sheath resonance instability as the observed oscillations are not consistent with the established theory of the plasma-sheath resonance instability.

Response to “Comment on ‘Sheath oscillations during directional motion of fire tube formation in expanding RF plasma’” [Phys. Plasmas 27, 014702 (2020)

Response to “Comment on ‘Sheath oscillations during directional motion of fire tube formation in expanding RF plasma’” [Phys. Plasmas 27, 014702 (2020)

Sheath oscillations during directional motion of fire tube formation in expanding RF plasma

Low-frequency sheath oscillations, initiated by the sheath-plasma instability, are observed in connection with the complex structure formations in expanding radio frequency (RF) plasma generation. The temporal variations of the floating potential during the double layer formations, measured using electric and magnetic probe diagnostics, suggest the significant role of sheath-plasma instability in charged particle dynamics in the present operational regime. The burst oscillations of the potential occur due to the oscillations of the electric field associated with the high-gradient plasma source geometry, the sheath field. The initially localized discharge evolves into multiple luminous annular plasma structures with the progressive RF power. Although plasma discharges using additional electrodes immersed in plasma have been investigated extensively in DC plasmas, present experiments are carried out in the absence of any additional plasma source as well as any externally applied magnetic field. In line with our earlier reports, [Chakraborty et al., Phys. Plasmas 25, 033518 (2018); Paul et al., Phys. Plasmas 26, 023516 (2019)], the present work emphasizes the complex sheath structure formations, discharge transition from unstable to stable state, followed by the sheath oscillations through sheath-plasma instability during the expanding radio frequency discharge features that differentiate it in many ways from the earlier experimental investigations.

Numerical study of azimuthal sheath structure and asymmetric anomalous erosion in a stationary plasma thruster

The influence of the azimuthal electron drift on anomalous erosion and the sheath profile in a stationary plasma thruster (SPT) is analysed in this article. It is found that the anomalous erosion has a self-organized structure, which is formed by the interaction between the plasma and the ceramic walls. In order to interpret the mechanism of the azimuthal erosion structure, a particle in cell (PIC) model is developed to simulate the azimuthal sheath. The results show that the electron azimuthal Hall drift due to crossed electric and magnetic field plays a key role in the azimuthal erosion evolution process. Electron Hall drift can generate an asymmetric sheath structure and induce azimuthal sheath oscillation. Furthermore, an asymmetric sheath caused by the integrated effect of the azimuthal irregular wall structure and azimuthal Hall drift will result in the azimuthal movement of ions. Based on the sheath simulated results, an erosion model is used to simulate the azimuthal erosion evolution. An asymmetric erosion profile caused by the azimuthal asymmetric ion sputtering is found.

Sheath Oscillations During Fire Tube Formation In Expanding Rf Plasma

This paper is devoted to the temporal study of the sheath dynamics during “Fire Tube” formations in expanding radio frequency plasma source, using electric and magnetic probe diagnostics. Although plasma discharges using additional electrodes immersed in plasma have been extensively investigated in DC plasmas, present work exhibits features that make it unique in terms of complex sheath structure formations, sheath oscillations and significant presence of non-thermal electrons during the expanding radio frequency (RF) discharge. The burst oscillations of the potential occur due to the oscillations of the electric field associated with the high-gradient plasma source geometry, the sheath field. The luminous discharge transforms into multiple coaxial “Fire Tube” structures with progressive RF power in plasma.

A kinetic study of electron heating and plasma dynamics in microwave microplasmas

Microwave microplasmas ignited in argon are studied using a one-dimensional particle-in-cell with Monte Carlo collision (PIC-MCC) approach. One-dimensional PIC-MCC simulations are performed at specified input power densities to determine the influence of the applied frequency (ranging from 1 to 320 GHz), pressure, and total deposited power on the plasma dynamics. The frequency response study performed at a fixed input power density shows the presence of off-axis peaks in the electron number density profile at intermediate frequencies. These peaks are attributed to the interplay between the production of hot electrons by the oscillating sheath and their inability to diffuse sufficiently at higher operating pressures, thereby resulting in enhanced ionization at off-axis locations. This is confirmed by the pressure dependence study which shows that the electron number density peaks at the mid-point when the microplasma is ignited at lower pressures. As the excitation frequency is increased further, the sheath oscillation heating decreases and eventually vanishes, thereby requiring the bulk plasma to couple power to the electrons which in turn leads to an increase in electron temperature in the plasma bulk and the electron number density peak appearing at the mid-point. When the power coupled to the microplasma is decreased, the sheath oscillation at a given frequency decreases, thereby leading to higher contribution from heating in the bulk plasma which leads to the disappearance of off-axis peaks even at intermediate frequencies. The microplasma dynamics at all conditions considered in this work demonstrate the interplay between the electron momentum transfer collision frequency, the angular excitation frequency, and the plasma frequency.

Compensation of the sheath effects in cylindrical floating probes

In cylindrical floating probe measurements, the plasma density and electron temperature are overestimated due to sheath expansion and oscillation. To reduce these sheath effects, a compensation method based on well-developed floating sheath theories is proposed and applied to the floating harmonic method. The iterative calculation of the Allen-Boyd-Reynolds equation can derive the floating sheath thickness, which can be used to calculate the effective ion collection area; in this way, an accurate ion density is obtained. The Child-Langmuir law is used to calculate the ion harmonic currents caused by sheath oscillation of the alternating-voltage-biased probe tip. Accurate plasma parameters can be obtained by subtracting these ion harmonic currents from the total measured harmonic currents. Herein, the measurement principles and compensation method are discussed in detail and an experimental demonstration is presented.

Effect of Parallel-Plate Geometry on Mode Transition Behavior in Argon Microplasmas: Two-Dimensional Simulation**Supported by the Fundamental Research Funds in Heilongjiang Provincial Universities of China under Grant No 135209312.

A two-dimensional self-consistent fluid model is employed to investigate radio-frequency process parameters on the plasma properties in Ar microdischarges. The neutral gas density and temperature balance equations are taken into account. We mainly investigate the effect of the electrode gap on the spatial distribution of the electron density and electron temperature profiles, due to a mode transition from the γ regime (secondary electrons emission is responsible for the significant ionization) to the α regime (sheath oscillations and bulk electrons are responsible for sustaining discharge) induced by a sudden decrease of electron density and electron temperature. The pressure, radio-frequency sources frequency and voltage effects on the electron density are also elaborately investigated.

Modelling of radio frequency sheath and fast wave coupling on the realistic ion cyclotron resonant antenna surroundings and the outer wall

In order to model the sheath rectification in a realistic geometry over the size of ion cyclotron resonant heating (ICRH) antennas, the self-consistent sheaths and waves for ICH (SSWICH) code couples self-consistently the RF wave propagation and the DC SOL biasing via nonlinear RF and DC sheath boundary conditions applied at plasma/wall interfaces. A first version of SSWICH had 2D (toroidal and radial) geometry, rectangular walls either normal or parallel to the confinement magnetic field B0 and only included the evanescent slow wave (SW) excited parasitically by the ICRH antenna. The main wave for plasma heating, the fast wave (FW) plays no role on the sheath excitation in this version. A new version of the code, 2D SSWICH-full wave, was developed based on the COMSOL software, to accommodate full RF field polarization and shaped walls tilted with respect to B0. SSWICH-full wave simulations have shown the mode conversion of FW into SW occurring at the sharp corners where the boundary shape varies rapidly. It has also evidenced ‘far-field’ sheath oscillations appearing at the shaped walls with a relatively long magnetic connection length to the antenna, that are only accessible to the propagating FW. Joint simulation, conducted by SSWICH-full wave within a multi-2D approach excited using the 3D wave coupling code (RAPLICASOL), has recovered the double-hump poloidal structure measured in the experimental temperature and potential maps when only the SW is modelled. The FW contribution on the potential poloidal structure seems to be affected by the 3D effects, which was ignored in the current stage. Finally, SSWICH-full wave simulation revealed the left–right asymmetry that has been observed extensively in the unbalanced strap feeding experiments, suggesting that the spatial proximity effects in RF sheath excitation, studied for SW only previously, is still important in the vicinity of the wave launcher under full wave polarizations.

Electron heating mechanism in radio-frequency microhollow cathode discharge in nitrogen

A two-dimensional particle-in-cell/Monte-Carlo code has been developed to study the electron heating mechanism in radio-frequency microhollow cathode discharge (rf-MHCD) operated in nitrogen at 100 Torr. The influence of secondary electron emission coefficient (γ) on the electron density and total ionization rate, the occurrence of α ionization rate and γ ionization rate, and the electron heating rate are calculated. The results show that compared with the condition of γ = 0, the maximum electron density at γ = 0.1 shows an increase of 60% and the maximum total ionization rate increases by nearly one order of magnitude, which indicates secondary electron heating in rf-MHCD plays an important role. Through the detailed distribution of γ ionization rate and α ionization rate by two-electron model, it is found that γ ionization rate is about 90% of the total ionization rate and the spatial distribution of γ ionization rate presents the same characteristics of the total ionization rate. Therefore, we can further confirm secondary electron heating is the main heating mechanism in rf-MHCD. From the distribution of electron heating rate, it also shows the decisive role of secondary electron heating. With the increase of γ coefficient, α ionization rate increases. This means the electrons which are from fast electron group transferred into slow electron group in the plasma are heated again by sheath oscillation and do contribute to the occurrence of α ionization collision.

Mode transition in dusty micro-plasma driven by pulsed radio-frequency source in C2H2/Ar mixture**Project supported by the Natural Science Foundation of Heilongjiang Province, China (Grant Nos. A2015011 and A2015010), the Postdoctoral Scientific Research Developmental Fund of Heilongjiang Province, China (Grant No. LBH-Q14159), the National Natural Science Foundation of China (Grant Nos. 11404180 and 11405092), and the Program for Young Teachers Scientific

Physical qualities of dusty plasma in the pulsed radio-frequency C2H2/Ar microdischarges are carefully investigated by a one-dimensional hydrodynamic model and aerosol dynamics model. Since the thermophoretic force has a great effect on the nanoparticle density spatial distribution, the neutral gas energy equation is taken into accounted. The effects of pulse parameters (dust ratio, modulation frequency) on the nanoparticle formation and growth process are mainly discussed. The calculation results show that, as the duty ratio increases, the mode transition from the sheath oscillation (α regime) to the secondary electron heating (γ regime) occurred, which is quite different from the conventional pulsed discharge. Moreover, the effect of modulation frequency on the width of sheath and plasma density is analyzed. Compared with the H2CC ions, the modulation frequency effect on the nanoparticles density becomes more prominent.