Ionization Source Term Research Articles

Properties of collisional plasma sheath with ionization source term and two-temperature electrons in an oblique magnetic field

A collisional magnetized plasma sheath with two groups of electrons has been studied using a fluid model including the effects of the ionization source term and the collisional force between ions and neutral atoms. Two kinds of non-Maxwellian descriptions of electron velocity distribution, non-extensive distribution and truncated distribution, are applied in the model, and the ionization effects of both kinds are considered. By applying Sagdeev potential, the modified Bohm sheath criterion is derived. The effects of ionization, magnetic field, and high-temperature electron concentration ratio on plasma sheath density, potential, sheath thickness, and ion kinetic energy are studied. In cases with high background gas density, ion density accumulates at the sheath edge position, forming a peak and manifesting as a rapid drop in the potential profile. The distribution characteristics of electrons have a significant impact on the transport properties of ions. Oscillations and non-monotonic characteristics of net charge near the sheath edge occur as the magnetic field angle increases, leading to an increase in the sheath layer width. It can be seen that in the case of a collisional sheath structure with high-temperature electrons, it is essential to consider the sheath changes induced by the ionization and the collisional force. Compared to a symmetric electron velocity distribution, the actual thickness of the sheath layer in a truncated electron distribution assumption could be significantly reduced.

Modeling of magnetized collisional plasma sheath with nonextensive electron distribution and ionization source

The properties of an atmospheric-pressure collisional plasma sheath with nonextensively distributed electrons and hypothetical ionization source terms are studied in this work. The Bohm criterion for the magnetized plasma is extended in the presence of an ion–neutral collisional force and ionization source. The effects of electron nonextensive distribution, ionization frequency, ion–neutral collision, magnetic field angle and ion temperature on the Bohm criterion of the plasma sheath are numerically analyzed. The fluid equations are solved numerically in the plasma–wall transition region using a modified Bohm criterion as the boundary condition. The plasma sheath properties such as charged particle density, floating sheath potential and thickness are thoroughly investigated under different kinds of ion source terms, contributions of collisions, and magnetic fields. The results show that the effect of the ion source term on the properties of atmospheric-pressure collisional plasma sheath is significant. As the ionization frequency increases, the Mach number of the Bohm criterion decreases and the range of possible values narrows. When the ion source is considered, the space charge density increases, the sheath potential drops more rapidly, and the sheath thickness becomes narrower. In addition, ion–neutral collision, magnetic field angle and ion temperature also significantly affect the sheath potential profile and sheath thickness.

Characteristic studies on positive and negative streamers of double-sided pulsed surface dielectric barrier discharge

The mechanisms of streamer generation and propagation in double-sided pulsed surface dielectric barrier discharge (SDBD) on both sides have been analyzed and investigated by experiment and numerical simulation. The fully exposed asymmetric SDBD has two discharge processes located on the high voltage electrode (HVE) side and the ground electrode (GE) side. Discharge images of the HVE side and GE side are taken by a digital camera under continuous pulse and ICCD (Intensified Charge Coupled Device) is utilized to diagnose the generation and propagation of streamers in single pulse discharge. In order to understand the physical mechanisms of streamer evolution more deeply, we establish a 2D simulation model and analyze it from the aspects of electron density, ion density, reduced electric field and electron impact ionization source term. The results show that the primary and secondary discharges on the HVE side and the GE side of the double-sided SDBD are composed of positive streamer and negative streamer, respectively. On the HVE side, the accumulation of positive charges on the dielectric surface causes the direction of the electric field to reverse, which is the principal factor for the polarity reversal of the streamer. On the GE side, both the negative charges accumulated on the dielectric surface and the falling voltage are the key factors for the streamer polarity switch.

Plasma-based microwave power limitation in a printed transmission line: a self-consistent model compared with experimental data

Plasma-based microwave power limitation in a suspended microstrip transmission line integrating a micro hollow cathode discharge (MHCD) in its centre is experimentally and numerically studied. Transient and steady state microwave power measurements exhibit a limitation threshold of 28 dBm and time responses of 25 microseconds. Intensified charge-coupled device imaging shows that microwave breakdown occurs at the top of the MHCD. The plasma then extends towards the microwave source within the suspended microstrip transmission line. Besides, a self-consistent model is proposed to simulate the non-linear interaction between microwave and plasma. It gives numerical results in agreement with the measurements, and show that the plasma expansion during the transient response is related to a shift between the ionization source term and the electron density maximum. The propagation speed, under the tested conditions, depends mainly on the stepwise ionization from the excited states.

A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses

A 1D1V hybrid Vlasov-fluid model was developed for this study to elucidate discharge current oscillations of Hall thrusters (HTs). The Vlasov equation for ions velocity distribution function with ionization source term is solved using a constrained interpolation profile conservative semi-Lagrangian method. The fourth-order weighted essentially non-oscillatory (4th WENO) limiter is applied to the first derivative value to minimize numerical oscillation in the discharge oscillation analyses. The fourth-order accuracy is verified through a 1D scalar test case. Nonoscillatory and high-resolution features of the Vlasov model are confirmed by simulating the test cases of the Vlasov–Poisson system and by comparing the results with a particle-in-cell (PIC) method. A 1D1V HT simulation is performed through the hybrid Vlasov model. The ionization oscillation is analyzed. The oscillation amplitude and plasma density are compared with those obtained from a hybrid PIC method. The comparison indicates that the hybrid Vlasov-fluid model yields noiseless results and that the steady-state waveform is calculable in a short time period.

Electronegative magnetized plasma sheath properties in the presence of non-Maxwellian electrons with a homogeneous ion source

The three-fluid model was employed to study electronegative magnetized plasma sheath properties in the presence of non-Maxwellian electrons. The Bohm condition for the electronegative magnetized plasma was extended in the presence of a homogeneous ionization source term and an ion-neutral collision force. The effect of the following physical parameters: the degree of non-Maxwellian electrons, ion-neutral collisions, obliqueness of the magnetic field and source frequency on the plasma sheath parameters are numerically analyzed and presented. It was found that the magnitude of the potential increased in all cases and hence the velocity of the ions increased towards the wall. The plasma sheath parameters were not significantly varied about 2λ De from the presheath—sheath interface, but after that, the sheath parameters abruptly changed towards the wall. The effect of ion-neutral collisions and the obliqueness of the magnetic field on the potential distribution, net charge density and drift velocity of ions are discussed. Furthermore, a comparison of plasma sheath characteristics with and without the ion source term is systematically presented.

Study on ion energy distribution in low-frequency oscillation time scale of Hall thrusters

This paper reports on the dynamic characteristics of the distribution of ion energy during Hall thruster discharge in the low-frequency oscillation time scale through experimental studies, and a statistical analysis of the time-varying peak and width of ion energy and the ratio of high-energy ions during the low-frequency oscillation. The results show that the ion energy distribution exhibits a periodic change during the low-frequency oscillation. Moreover, the variation in the ion energy peak is opposite to that of the discharge current, and the variations in width of the ion energy distribution and the ratio of high-energy ions are consistent with that of the discharge current. The variation characteristics of the ion density and discharge potential were simulated by one-dimensional hybrid-direct kinetic simulations; the simulation results and analysis indicate that the periodic change in the distribution of ion energy during the low-frequency oscillation depends on the relationship between the ionization source term and discharge potential distribution during ionization in the discharge channel.

Study of the impact of photoionization on negative and positive needle-plane corona discharge in atmospheric air

A 2D axisymmetric model of the atmospheric pressure needle-plane corona discharge incorporating the photoionization phenomenon is presented in this paper. The photoionization model was developed using a three-term exponential approximation based on a model suggested by Bourdon et al. The coefficients of the photoionization model were tuned by reproducing the results of a positive corona discharge and comparing them with the experimental data published previously in the literature. In fact, this photoionization model is an essential module for studying a self-sustained positive corona discharge. Incorporating the photoionization phenomenon in the numerical model for the negative corona discharge causes an average of 5% increase in both the frequency and the DC current of the discharge. The relative importance of the photoionization in both positive and negative coronas was put in a quantitative frame by introducing the ratio of the integral of the impact ionization source term (IIS) divided by the Integral of the photoionization source term (IPS). With the help of this ratio and the spatial distribution of the two source terms, the minor role played by the photoionization source term for the negative discharge is justified. In the case of the positive discharge, the vital importance of the photoionization for sustaining the discharge is explained. Moreover, for the negative corona discharge, comparison of the ratio of the secondary emitted electrons (SEE) from the cathode surface divided by the IPS, at different instants of the formation of a Trichel pulse was found to be beneficial for the purpose of evaluating the relative importance of the photoionization. It is concluded that, although SEE on the rising edge of the Trichel pulse is smaller than the IPS since the injected electrons from the cathode surface are generated in the area with the strongest electric field, they have a greater contribution to the discharge current.

The validity of the one-dimensional fluid model of electrical breakdown in synthetic air at low pressure

In this letter the validity of the fluid model used to simulate the electrical breakdown in air at low pressure is discussed. The new method for the determination of the ionization source term for the mixed gases is proposed. Paschen's curve obtained by the fluid model is compared to the available experimental data. The electron and ions density profiles calculated by the fluid model are presented. Based on Ohm's law, the current and voltage waveforms are calculated and compared to the ones measured by the oscilloscope in the synthetic-air filled tube with stainless-steel electrodes. It is shown that the one-dimensional fluid model can be used for modeling the electrical breakdown at pd values higher than Paschen's minimum and to determine stationary values of electron and ions densities.

Fluid model of dc glow discharge with nonlocal ionization source term

We developed and tested a simple hybrid model for a glow discharge, which incorporates nonlocal ionization by fast electrons into the fluid framework. Calculations have been performed for an argon gas. Comparison with the experimental data as well as with the hybrid (particle) and fluid modelling results demonstated good applicability of the proposed model.

On the accuracy and limitations of fluid models of the cathode region of dc glow discharges

This paper compares the performance and limitations of different models of the cathode region of cold-cathode low-pressure dc glow discharges: (i) we review known modelling approaches, (ii) develop our own simulation codes based on these approaches, (iii) perform calculations using these codes for reference sets of discharge conditions, which allows a critical comparison of the models and (iv) for a further check of the simulation results we carry out Langmuir probe measurements of electron densities in abnormal Ar glow discharges. The theoretical approaches include fluid models both neglecting and including the electron energy balance equation, as well as hybrid models, which combine the fluid treatment of slow plasma species with the kinetic simulation of fast electrons. We also test the effect of the choice of the ionization source term in fluid models. We find that the electron densities calculated from the fluid models are far (several orders of magnitude) below the experimental values even if the electron energy equation is considered in the calculations. This weakness of fluid models clearly points out the importance of an accurate calculation of the ionization source term, which can only be accomplished by a kinetic approach under the conditions of highly nonlocal electron transport in the cathode region of glow discharges. In hybrid models Monte Carlo simulation is used for this purpose, and indeed, this approach gives electron densities comparable to our experimental data.

An Existence Result for a Stationary Vlasov–Poisson Model with Source Term

In the low energy part of an ion accelerator, the ion beam reaches the first accelerating device through a drift tube where a residual neutral gas is present. A process of ionization takes place and secondary electrons and ions are created. We analyze the coupling between these secondary particles, the beam density and the electrical potential. In a previous article,2 we proved that a stationary Vlasov–Poisson problem with ionization source terms, which, at first sight, seems the natural model for this system, does not admit solutions. To overcome this difficulty, we propose here a heuristic model which consists of modifying the electron source term. In this new frame, we prove that the problem can be solved and we give numerical examples.

Multichannel visible spectroscopy diagnostic for particle transport studies in the H-1 heliac

A multichannel spectroscopy diagnostic has been developed to study cross-field particle transport in the radiation-dominated low-temperature plasmas (Te<100 eV) in the H-1 heliac. The optical setup covers the full plasma minor radius in the poloidal plane collecting light from ten parallel chords arranged tangentially to the flux surfaces. The light collected from the plasma is coupled into optical fibers and through interference filters into photomultipliers. Two such ten-fiber arrays are aligned parallel to one another to allow the simultaneous monitoring of two different spectral lines. The net radial electron particle flux is determined from the continuity equation by integrating over the ionization source term in the steady-state partially ionized plasma. The diagnostic measures the neutral line intensities and their ratios (in case of helium using the line ratio technique) and also measures excited neutral and ion spectral lines (in case of the argon plasma transport studies). A comparative analysis of the radial particle transport in the low- and high-confinement regimes is presented.

Effect of anisotropy in the elastic scattering cross sections on the ionization source terms in glow discharges in argon

The main purpose of this work is to evaluate, using a Monte Carlo simulation, the extent to which anisotropy in the elastic electron-neutral scattering cross sections influences the spatial distribution of the electron-impact ionization profile in glow discharges in argon. We also briefly discuss the effect of anisotropic elastic scattering on the slowing down of an electron beam and on the transmission factor, the fraction of electrons emitted from the cathode that are not scattered back to the cathode. Monte Carlo simulations were performed using different functional forms for the anisotropy. We show that, for a given momentum transfer cross section and the assumption of isotropic scattering, the ionization profiles over a range of conditions in argon glow discharges in parallel plane electrode geometries are not significantly affected by the inclusion of higher order anisotropies in the elastic cross sections. The anisotropy in the elastic scattering cross section influences only slightly the electron transmission factor for low, uniform electric fields.

Two-dimensional, hybrid model of low-pressure glow discharges.

A self-consistent, two-dimensional hybrid fluid-particle model is presented and used to describe the electrical behavior of dc low-pressure discharges in the current range ${10}^{\mathrm{\ensuremath{-}}7}$--${10}^{\mathrm{\ensuremath{-}}2}$ A in argon for products of the gas pressure and the gap spacing (pd) from 1 to 3.3 cm torr. The two-dimensional distributions of the potential, charged particle densities and ionization source term at steady state are shown to illustrate the discharge behavior during the transition from the normal to the abnormal regimes. For the larger values of pd, a positive column region as well as the cathode regions are clearly apparent. The model used here consists of Poisson's equation for the electric field coupled to the continuity equations for the electrons and ions with the important feature that the ionization source term appearing in the continuity equations is nonlocal and determined from a Monte Carlo simulation. This description yields a unified physical picture of discharge behavior in the cathode fall, negative glow, and positive column regions over a wide range of discharge currents.

Analytical formulation of ionization source term for discharge models in argon, helium, nitrogen, and silane

Simple analytical representations of the ionization source terms in argon, helium, nitrogen, and silane dc glow discharges for steady-state and quasisteady-state conditions are presented. These analytical forms express well the highly nonequilibrium nature of the ionization in the cathode fall and negative glow regions which cannot be described by a Townsend ionization coefficient depending on the local value of the reduced electric field. These source terms can be easily incorporated into fluid models of gas discharges.

Pseudospark discharges via computer simulation

A hybrid fluid-particle (Monte Carlo) model to describe the initiation of pseudospark discharges has been developed. In this model, time-dependent fluid equations for the electrons and positive ions are solved self-consistently with Poisson's equation for the electric field in a two-dimensional, cylindrically symmetrical geometry. The Monte Carlo simulation is used to determine the ionization source term in the fluid equations. This model has been used to study the evolution of a discharge in helium at 0.5 torr, with an applied voltage of 2 kV and in a typical pseudospark geometry. From the numerical results, the authors have identified a sequence of physical events that lead to the rapid rise in current associated with the onset of the pseudospark discharge mode. They find that there is a maximum in the electron multiplication at the time which corresponds to the onset of the hollow cathode effect, and although the multiplication later decreases, it is always greater than needed for a steady-state discharge. >