Numerical simulation of atmospheric pulsemodulated radio-frequency glow discharge ignition characteristics assisted by a pulsed discharge

Chengxian PAN(潘呈献),Zhengming SHI(施政铭),Qianhan HAN(韩乾翰),Ying GUO (郭颖),2,3 and Jianjun SHI (石建军),2

1 College of Science, Donghua University, Shanghai 201620, People's Republic of China

2 Member of Magnetic Confinement Fusion Research Center, Ministry of Education of People's Republic of China, Shanghai 201620, People's Republic of China

3 Shanghai Center for High Performance Fibers and Composites, Center for Civil Aviation Composites of Donghua University, Shanghai 201620, People's Republic of China

Abstract A one-dimensional self-consistent fluid numerical model was developed to study the ignition characteristics of a pulse-modulated (PM) radio-frequency (RF) glow discharge in atmospheric helium assisted by a sub-microsecond voltage excited pulsed discharge.The temporal evolution of discharge current density and electron density during PM RF discharge burst was investigated to demonstrate the discharge ignition characteristics with or without the pulsed discharge.Under the assistance of pulsed discharge, the electron density in RF discharge burst reaches the magnitude of 1.87 × 1017 m−3 within 10 RF cycles, accompanied by the formation of sheath structure.It proposes that the pulsed discharge plays an important role in the ignition of PM RF discharge burst. Furthermore, the dynamics of PM RF glow discharge are demonstrated by the spatiotemporal evolution of the electron density with and without pulsed discharge. The spatial profiles of electron density,electron energy and electric field at specific time instants are given to explain the assistive role of the pulsed discharge on PM RF discharge ignition.

Keywords: atmospheric glow discharge, numerical simulation, discharge ignition, pulse modulation(Some figures may appear in colour only in the online journal)

1. Introduction

Atmospheric pressure glow discharges (APGDs) can operate even in open air,enabling plasma to be conveniently applied in various industries, such as waste-water treatment, film deposition, surface treatment of materials and synthesis of functional materials [1-4]. Atmospheric radio-frequency (RF) glow discharge has attracted much attention in the field of plasma application due to its low discharge voltage and high plasma density [5-8]. On the other hand, due to the high gas temperature and discharge consumption power,the discharge operation mode changes from a uniform stable discharge α mode to an unstable columnar discharge γ mode with increasing discharge intensity[9-13].It was proposed that the pulse-modulated(PM)RF discharge can reduce the discharge power consumption and improve the instantaneous discharge intensity with stable operation over a wide range of currents and voltages at atmospheric pressure[6-8].In PM RF discharges,the RF discharge ignition mechanisms were found to be assisted by residual electrons left in the discharge gap [6, 14]. The time interval between two consecutive RF discharge bursts is difficult to optimize because the requirements of discharge power consumption and discharge ignition are opposite.As the plasma produced by a pulsed discharge excited by sub-microsecond voltage pulses is relatively homogeneous and stable, and the instantaneous plasma density is higher than that of a dielectric barrier discharge excited sinusoidally [15], the experimental study suggested that by introducing a pulsed discharge between two consecutive RF discharge bursts,the breakdown voltage of RF discharge reduced with shortened RF discharge ignition time. Unfortunately, the interaction mechanism between the pulsed discharge and RF discharge burst is not well understood due to the limitation of experimental diagnostics.In this paper,a one-dimensional self-consistent fluid numerical model was developed with introducing a pulsed discharge between two consecutive RF discharge bursts.The effect of residual electrons generated in the pulsed discharge on PM RF discharges was studied. Furthermore, the time-averaged spatial profiles of electron density, electron energy and electric field are provided to study the discharge dynamics.

2. Model description

In the one-dimensional self-consistent fluid numerical model,atmospheric helium discharge is generated between two parallel plates, with the fixed discharge gap of 2.0 mm. Each electrode is covered by a dielectric barrier layer with a thickness of 1.0 mm and a relative permittivity of 10.0. Six plasma species are considered in the numerical model, which are electrons (e), helium atoms (He), helium ions (He+),helium molecule ions (), metastable helium atoms (He*),and metastable helium molecules (). For elementary reactions between plasma species and their rate coefficients,refer to Song et al [16].

The governing equations based on the mass conservation equation and the electron energy conservation equation are described as follows [13]:

Here,the subscripts i,j,e,ε and neut represent particle i,particle j, electron, electron energy and neutral helium atom, respectively.n is the number density of particles and Γ is the flux.Ki,jis the reaction coefficient between particle i and j,and KL,jis the electron energy loss reaction coefficient between an electron and particle j,accordingly.ε,E,e,k and D are the average electron energy, electric field, elementary charge, Boltzmann constant and diffusion coefficient, respectively. N is the number density of helium atoms. m and T represent the mass and the temperature of particles. Kmtis the momentum transfer coefficient of the reaction between an electron and helium atom. The initial gas temperature is fixed at 300 K.

3. Results and discussion

The typical voltage and current density waveforms of an atmospheric helium pulse-assisted PM RF glow discharge are shown in figures 1(a) and (b), respectively, in which, the repetition frequency of pulsed discharge and the modulation pulse frequency of RF power are both 20 kHz. The pulse voltage amplitude is 1500 V, and the full width at half maximum of voltage pulse is 500 ns,with the rising and falling times of both 100 ns.As shown in figure 1(a),the pulse voltage turns on at 100 ns and turns off at 700 ns,and there are two discharge current peaks that occur at the rising and falling phase of voltage pulse. The positive current peak at the rising phase is 434 A m−2, and the negative current peak at the falling phase is 316 A m−2, as shown in figure 1(b),which suggests that the discharge intensity at the falling phase is lower than that of the rising phase.After the pulsed discharge is turned off for 3 μs, the PM RF voltage is applied with the amplitude of 300 V and the frequency of 13.56 MHz.

In a PM RF discharge burst, the current density magnitude increases gradually with time delay,which is recognized as the ignition phase of RF discharge. Using the voltage waveform of PM RF discharge burst as a reference, the PM RF discharge burst is modulated to 30 RF cycles. The effect of pulsed discharge on the ignition phase of a PM RF discharge burst was studied, as shown in figure 2.

In figure 2, the PM RF current density amplitude increases gradually with time,which indicates that the PM RF discharge is in the ignition phase before reaching the stable state.When the PM RF discharge burst lasts 10 RF cycles(at 4.42 μs), the amplitude of current density with assistance of the pulsed discharge is significantly higher than that of without the pulsed discharge. This enhancement of PM RF discharge current demonstrates the assistance by the pulsed discharge on discharge ignition. It can be clearly seen in figure 2 that the amplitude of current density rapidly increases initially and the growth rate gradually decreases with time.The RF discharge current density amplitudes at the time instants of 4.0 μs and 4.7 μs are compared with and without the assistance of pulsed discharge. At 4.0 μs, the current density amplitude at point A is 205.6 A m−2, which is much higher than that at point B of 114.8 A m−2. Without the assistance of the pulse discharge, the current density amplitude reaches 196 A m−2at the instant of 4.7 μs(point C). In addition,when the PM RF discharge lasts for 30 RF cycles,it takes 1.68 μs for the amplitude of the current density to reach a stable magnitude with the pulsed discharge, while that is 2.08 μs without the pulsed discharge. It is shown that the assistance of pulsed discharge enhances the ignition of PM RF discharge, especially during the ignition phase of a PM RF discharge.

The spatial-temporal distribution of electron density within the time duration from 3.2 to 6.4 μs with and without the pulsed discharge is given in figures 3(a) and (b), respectively, which correspond to the ignition phase of PM RF discharge burst. In figure 3(b), without the pulsed discharge,the PM RF discharge ignites in the middle of the discharge gap with the spatial profile of bell shape. It can be seen in figure 3(a) that with the pulsed discharge, the PM RF discharge starts to glow above one of electrodes, forming a nonuniform spatial profile of electron density in discharge gap. The magnitude of electron density in discharge gap is significantly greater than that without the pulsed discharge(in figure 3(b)). It suggests that the abundant residual electrons from the pulsed discharge keep in the discharge gap as soon as the PM RF voltage is applied, which enhance the ignition of PM RF discharge [8, 17]. At the end of PM RF discharge burst with 30 RF cycles, the electrons are distributed evenly in the discharge gap with the formation of a symmetrical sheath structure.

The enhancement of PM RF discharge by the pulsed discharge can also be demonstrated by the magnitude of electron density,as shown in figure 4.The electron density in discharge gap is taken as the maximum magnitude at each time instant. When the sub-microsecond pulse voltage is applied,the electron density increases sharply from the initial magnitude of 1 × 1016m−3to 7.16 × 1017m−3,which drops when the pulse voltage is turned off. At the time instant before applying the PM RF voltage, the electron density is 1.37 × 1017m−3, which is higher than that of 1 × 1016m−3without the pulsed discharge. These residual electrons produced by the pulsed discharge enhance the initial electron density of the PM RF discharge during the ignition phase,which can act as the seed electrons to produce the ionization in the discharge gap and are responsible for the gas breakdown. The assistance of pulsed discharge on the PM RF APGD is demonstrated by the enhanced electron density in ignition phase and also the reduced ignition time of RF discharge. At the end of the PM RF discharge burst with 30 RF cycles, it is found that the electron densities in the PM RF discharge with or without the pulsed discharge are in the same magnitude. It suggests that the pulsed discharge assists the ignition of PM RF discharge to reach the stable operation of discharge, corresponding to figure 2.

To further explore the assistance on the characteristics of RF discharge in a PM RF discharge burst,the spatial profiles of the averaged electron density, electron energy and electric field during one RF cycle at different time instants are shown in figure 5.

Figure 5(a)shows the electron density at time instants of A, B and C, in which, point B and point C are the electron densities of PM RF discharges without the pulsed discharge at 4.0 μs and 4.7 μs, respectively. The electron density is in the middle of discharge gap than that above both electrodes.At 4.7 μs (point C), the electron density concentrates in the discharge bulk with the magnitude of 1.2 × 1017m−3,which is about four times higher than that at 4.0 μs of 0.3 × 1017m−3. The RF discharge also forms the double sheath structure in the discharge gap, which is the typical spatial profile of atmospheric PM RF glow discharge[18,19].On the other hand,with the assistance of the pulsed discharge, the electron density at 4.0 μs reaches 1.6 × 1017m−3, which is even higher than that at 4.7 μs without the pulsed discharge,as shown in figure 5(a).The spatial profile of electron density shows that the electron density above the right electrode is higher than that above the left electrode,which is induced by the distribution of residual electron from the pulsed discharge. It suggests that the magnitude of electron density and sheath structure in PM RF discharge are affected by the residual electrons generated by the pulsed discharge.

It can be seen in figure 5(b) that without the pulsed discharge, the average electron energy in the discharge gap is around 3.5 eV at the time instant of 4.0 μs.When the PM RF discharge develops to 4.7 μs, the average electron energy in the plasma bulk decreases and the electron energy above both electrodes increases to around 4.5 eV, which indicates that the sheath structure is formed above the both electrodes.With the pulsed discharge,the sheath structure is formed at 4.0 μs with the average electron energy of 4.5 eV.The asymmetry of the sheath structure above the electrode with different sheath thickness is consistent with the findings in figure 5(a) of electron density, which is also caused by the distribution of residual electrons from the pulsed discharge.

In figure 5(c), it is shown that as the PM RF discharge develops,the magnitude of electric field in the plasma bulk is close to zero and the electric field in the sheath region increases linearly from the boundary of sheath to electrode surface.The electrons in the sheath region can be accelerated and gain energy, as shown the spatial profiles of electron energy in figure 5(b). Given that the formation of sheath is due to the accumulation of net space charge above the electrodes, which is attributed to oscillation of the electrons with the RF electric field. Without the assistance of pulsed discharge, at the time instant of 4.0 μs (point B), the sheath region is not clearly formed.As the time evolves to 4.7 μs at C,the sheath region is formed above both electrodes with the maximum electric field magnitude of 2.2 kV cm−1. With the assistance of pulsed discharge, at the time instant of 4.0 μs(point A), the sheath region is already formed above both electrodes with the maximum electric field magnitude of 2.7 kV cm−1. The spatial profile of the electric field is asymmetric, which is also caused by the asymmetric distribution of electron density in the discharge gap.

4. Conclusions

In this paper, the assistance of a sub-microsecond pulsed discharge on the PM RF discharge ignition was studied by a one-dimensional self-consistent fluid numerical model.It was found that the residual electrons generated by the pulsed discharge can assist the ignition of PM RF discharge in terms of elevated electron density and current density and also reduced PM RF ignition time. The assistance of the pulsed discharge on the discharge dynamics and mechanics of PM RF discharge are demonstrated by the spatio-temporal evolution of an asymmetric sheath structure in the discharge gap.It is shown that the assistance role of the pulsed discharge is important especially during the ignition phase of PM RF discharge ignition.

Acknowledgments

This work was funded by National Natural Science Foundation of China (Nos. 11875104 and 11475043) and open fund of Shanghai center for high performance fibers and composites (No. X12811901/012) for providing financial support.